Bridges Lab Protocols - User contributions [en]

Mendelian Randomization

2026-07-31T21:02:03Z

Davebrid1: /* 5. Decision Matrix: Which Results to Report */ Updated decision tree

= Mendelian Randomization Standard Operating Procedure (SOP) =
[[ Category: Genetics ]]

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
y <- dat$beta.exposure; s <- dat$se.exposure
k <- length(y); w <- 1/s^2
mu <- sum(y * w) / sum(w) # inverse-variance weighted mean
Q <- sum(w * (y - mu)^2) # Cochran's Q for the exposure effects
max(0, (Q - (k - 1)) / Q)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

==== 3.5 Visual Diagnostics: Scatter and Funnel Plots ====

We generate a '''scatter plot''' and a '''funnel plot''' for '''every''' exposure–outcome
association before adjudicating the model in [[#5. Decision Matrix: Which Results to Report|Section 5]].
They reveal outlier and pleiotropic instruments that the summary statistics (Cochran's ''Q'',
the MR-Egger intercept) can under-flag, and they frequently drive the model choice on inspection
even when the numeric trigger is borderline. Record the model used '''and the reason''' for each
association.

'''Scatter plot.''' Each point is an instrument: SNP→exposure effect on ''x'', SNP→outcome effect
on ''y''; the overlaid lines are the method estimates (IVW, MR-Egger, weighted median).
* Points should scatter around a single line through the origin.
* A high-leverage point sitting off the IVW line (e.g. the ''APOE'' region for lipid exposures) is a candidate outlier / pleiotropic SNP.
* If the MR-Egger or weighted-median slope diverges from IVW, suspect pleiotropy.

<syntaxhighlight lang="r">
res <- mr(dat, method_list = c("mr_ivw_mre", "mr_egger_regression", "mr_weighted_median"))
mr_scatter_plot(res, dat)[[1]]
</syntaxhighlight>

'''Funnel plot.''' Per-SNP Wald ratio on ''x'' against instrument precision (1/SE) on ''y''.
* A '''symmetric''' inverted funnel around the pooled estimate ⇒ balanced pleiotropy; IVW valid.
* '''Asymmetry''' ⇒ directional pleiotropy ⇒ MR-Egger or weighted mode.
* A point far from the body of the funnel is the same outlier the scatter shows and a candidate for removal (MR-PRESSO).

<syntaxhighlight lang="r">
ss <- mr_singlesnp(dat)
mr_funnel_plot(ss)[[1]]
</syntaxhighlight>

How the plots map onto the model choice is given in the [[#5. Decision Matrix: Which Results to Report|Decision Matrix (Section 5)]]; the plots can trigger a model (e.g. MR-PRESSO) on visual grounds even when the numeric rule is ambiguous.

'''Worked example — LDL-C → Alzheimer's disease.''' The naive IVW estimate was a large positive
effect (β ≈ +0.58 per SD LDL-C; OR ≈ 1.8), biologically implausible. The scatter showed a
high-leverage ''APOE''-region cluster well off the IVW slope, and the funnel showed the matching
outlier and asymmetry. We selected '''MR-PRESSO''' on that visual basis; it removed the ''APOE''
outliers and the estimate attenuated to ≈ +0.03 (null). The naive positive was ''APOE''
horizontal pleiotropy (''APOE'' acts on AD through amyloid, not through LDL), not an LDL causal
effect. Cochran's ''Q'' is significant here too, but the plots identify the specific offending
locus and are what triggered the decision.

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in Section 3 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival axis, prognosis = outcome).
Because IVW is linear the correction is exact:
corrected(X→Y) = (X→Y) − b_SH × (X→S)

'''Requirements — an underpowered fit is worse than none:'''
* Use '''full genome-wide summary statistics''', LD-clumped (r²<0.01, 1 Mb, ancestry-matched panel). Clumped tophits from an API are '''not sufficient''' (a 10-SNP fit is unidentified).
* Target '''≳1,000 independent SNPs'''; report the fitted n and the slope CI.
* Report fits '''with and without major pleiotropic loci''' (e.g. APOE for AD/lifespan) and without the locus under test if the analysis is locus-specific.
* b_SH is a property of the (survival axis → outcome) pair, '''not''' of the exposure — fit once per outcome and reuse across exposures. Refit if the outcome dataset changes.

'''Coherence check (the falsifiable quantity).''' Report predicted induced effect vs observed
effect. If predicted ≈ observed, the selection pathway alone reproduces the signal.

=== 4.5 Reporting requirements ===
Always report '''uncorrected and corrected estimates side by side'''. The corrected value is a
'''sensitivity bound, never the primary estimate'''.

'''Stated limitation (include in all manuscripts using this section):''' the correction removes
the component collinear with the survival axis and '''cannot distinguish collider-induced
association from a genuine effect acting along that same axis'''. Because most exposures affect
mortality, mechanical application will attenuate real effects. Correction '''diagnoses''';
only '''design''' resolves — incident cohorts, age-stratified analyses, or younger-onset outcomes.

'''Worked example.''' Smoking → Alzheimer's. Passed stringent instrument criteria, mean F>10,
Egger intercept p=0.108, adjudicated Scenario 2 → MR-PRESSO b=−0.112, p=0.0015 (a reportable
positive). Both collider arms were present (instruments→lung cancer p=10⁻⁵¹; AD liability→shorter
lifespan p=0.003). A genome-wide index-event correction (2,346 SNPs, b_SH=−0.944) reduced the
pooled estimate from −0.129 to +0.005 (p=0.91), and the collider structure predicted 89–117% of
the observed effect across three instrument sets. The standard toolkit — including a
proxy-ascertainment sensitivity analysis that was '''falsely reassuring''' — did not detect this.

== 5. Decision Matrix: Which Results to Report ==

Every scenario below is adjudicated '''together with the scatter and funnel plots''' ([[#3.5 Visual Diagnostics: Scatter and Funnel Plots|§3.5]]): visual identification of outlier SNPs or funnel asymmetry can select MR-PRESSO or an Egger/mode model even when the numeric trigger (Cochran's ''Q'', the Egger intercept) is borderline. Record the model used and the visual rationale per association.

{| class="wikitable"
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal''' || F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05. || "IVW (Fixed Effects). All assumptions are met."
|-
| '''2. Balanced Pleiotropy''' || F > 10. Cochran's Q p < 0.05 '''or''' one/few outlier SNPs visible in the scatter/funnel (§3.5). Egger Intercept p > 0.05. || "MR-PRESSO (Outlier Corrected) or IVW (Random Effects). Support with Weighted Median."
|-
| '''3. Weak Instruments''' || Mean F < 10 OR Relaxed criteria (p < 5e-6) used. || "MR-RAPS. Baseline IVW is vulnerable to weak instrument bias."
|-
| '''4. Directional Pleiotropy''' || Egger Intercept p < 0.05 '''or''' clear funnel asymmetry (§3.5). || "Weighted Mode (if I2GX < 0.90) OR MR-Egger Slope (if I2GX >= 0.90). IVW is discarded."
|-
| '''5. Correlated Pleiotropy''' || CAUSE model comparison p > 0.05 (Sharing Model wins). || "Null Result (Discard Causality). The traits are correlated due to shared genetics, not a direct causal pathway."
|-
| '''6. Inconclusive''' || MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other. || "Unresolved / Inconclusive. State that genetic evidence is too pleiotropic to reliably disentangle."
|-
| '''7. Selection/collider bias''' || Both arms present AND predicted bias same sign as observed AND predicted ≈ observed magnitude. || "Report as selection-bias-consistent, not causal. Give uncorrected + corrected estimates."
|}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Mendelian Randomization

2026-07-31T21:01:11Z

Davebrid1: /* 3. Analytical Models to Test */ Added section about making funnel and scatter plots

= Mendelian Randomization Standard Operating Procedure (SOP) =
[[ Category: Genetics ]]

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
y <- dat$beta.exposure; s <- dat$se.exposure
k <- length(y); w <- 1/s^2
mu <- sum(y * w) / sum(w) # inverse-variance weighted mean
Q <- sum(w * (y - mu)^2) # Cochran's Q for the exposure effects
max(0, (Q - (k - 1)) / Q)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

==== 3.5 Visual Diagnostics: Scatter and Funnel Plots ====

We generate a '''scatter plot''' and a '''funnel plot''' for '''every''' exposure–outcome
association before adjudicating the model in [[#5. Decision Matrix: Which Results to Report|Section 5]].
They reveal outlier and pleiotropic instruments that the summary statistics (Cochran's ''Q'',
the MR-Egger intercept) can under-flag, and they frequently drive the model choice on inspection
even when the numeric trigger is borderline. Record the model used '''and the reason''' for each
association.

'''Scatter plot.''' Each point is an instrument: SNP→exposure effect on ''x'', SNP→outcome effect
on ''y''; the overlaid lines are the method estimates (IVW, MR-Egger, weighted median).
* Points should scatter around a single line through the origin.
* A high-leverage point sitting off the IVW line (e.g. the ''APOE'' region for lipid exposures) is a candidate outlier / pleiotropic SNP.
* If the MR-Egger or weighted-median slope diverges from IVW, suspect pleiotropy.

<syntaxhighlight lang="r">
res <- mr(dat, method_list = c("mr_ivw_mre", "mr_egger_regression", "mr_weighted_median"))
mr_scatter_plot(res, dat)[[1]]
</syntaxhighlight>

'''Funnel plot.''' Per-SNP Wald ratio on ''x'' against instrument precision (1/SE) on ''y''.
* A '''symmetric''' inverted funnel around the pooled estimate ⇒ balanced pleiotropy; IVW valid.
* '''Asymmetry''' ⇒ directional pleiotropy ⇒ MR-Egger or weighted mode.
* A point far from the body of the funnel is the same outlier the scatter shows and a candidate for removal (MR-PRESSO).

<syntaxhighlight lang="r">
ss <- mr_singlesnp(dat)
mr_funnel_plot(ss)[[1]]
</syntaxhighlight>

How the plots map onto the model choice is given in the [[#5. Decision Matrix: Which Results to Report|Decision Matrix (Section 5)]]; the plots can trigger a model (e.g. MR-PRESSO) on visual grounds even when the numeric rule is ambiguous.

'''Worked example — LDL-C → Alzheimer's disease.''' The naive IVW estimate was a large positive
effect (β ≈ +0.58 per SD LDL-C; OR ≈ 1.8), biologically implausible. The scatter showed a
high-leverage ''APOE''-region cluster well off the IVW slope, and the funnel showed the matching
outlier and asymmetry. We selected '''MR-PRESSO''' on that visual basis; it removed the ''APOE''
outliers and the estimate attenuated to ≈ +0.03 (null). The naive positive was ''APOE''
horizontal pleiotropy (''APOE'' acts on AD through amyloid, not through LDL), not an LDL causal
effect. Cochran's ''Q'' is significant here too, but the plots identify the specific offending
locus and are what triggered the decision.

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in Section 3 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival axis, prognosis = outcome).
Because IVW is linear the correction is exact:
corrected(X→Y) = (X→Y) − b_SH × (X→S)

'''Requirements — an underpowered fit is worse than none:'''
* Use '''full genome-wide summary statistics''', LD-clumped (r²<0.01, 1 Mb, ancestry-matched panel). Clumped tophits from an API are '''not sufficient''' (a 10-SNP fit is unidentified).
* Target '''≳1,000 independent SNPs'''; report the fitted n and the slope CI.
* Report fits '''with and without major pleiotropic loci''' (e.g. APOE for AD/lifespan) and without the locus under test if the analysis is locus-specific.
* b_SH is a property of the (survival axis → outcome) pair, '''not''' of the exposure — fit once per outcome and reuse across exposures. Refit if the outcome dataset changes.

'''Coherence check (the falsifiable quantity).''' Report predicted induced effect vs observed
effect. If predicted ≈ observed, the selection pathway alone reproduces the signal.

=== 4.5 Reporting requirements ===
Always report '''uncorrected and corrected estimates side by side'''. The corrected value is a
'''sensitivity bound, never the primary estimate'''.

'''Stated limitation (include in all manuscripts using this section):''' the correction removes
the component collinear with the survival axis and '''cannot distinguish collider-induced
association from a genuine effect acting along that same axis'''. Because most exposures affect
mortality, mechanical application will attenuate real effects. Correction '''diagnoses''';
only '''design''' resolves — incident cohorts, age-stratified analyses, or younger-onset outcomes.

'''Worked example.''' Smoking → Alzheimer's. Passed stringent instrument criteria, mean F>10,
Egger intercept p=0.108, adjudicated Scenario 2 → MR-PRESSO b=−0.112, p=0.0015 (a reportable
positive). Both collider arms were present (instruments→lung cancer p=10⁻⁵¹; AD liability→shorter
lifespan p=0.003). A genome-wide index-event correction (2,346 SNPs, b_SH=−0.944) reduced the
pooled estimate from −0.129 to +0.005 (p=0.91), and the collider structure predicted 89–117% of
the observed effect across three instrument sets. The standard toolkit — including a
proxy-ascertainment sensitivity analysis that was '''falsely reassuring''' — did not detect this.

== 5. Decision Matrix: Which Results to Report ==
Use the following adjudication criteria to synthesize the results from the models above.

{| class="wikitable"
|-
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal'''
| F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05.
| '''IVW (Fixed Effects)'''. All assumptions are met.
|-
| '''2. Balanced Pleiotropy'''
| F > 10. Cochran's Q p < 0.05. Egger Intercept p > 0.05.
| '''MR-PRESSO (Outlier Corrected)''' or '''IVW (Random Effects)'''. Support with Weighted Median.
|-
| '''3. Weak Instruments'''
| Mean F < 10 OR Relaxed criteria (p < 5e-6) used.
| '''MR-RAPS'''. Baseline IVW is vulnerable to weak instrument bias.
|-
| '''4. Directional Pleiotropy'''
| Egger Intercept p < 0.05.
| '''Weighted Mode''' (if I2GX < 0.90) OR '''MR-Egger Slope''' (if I2GX >= 0.90). IVW is discarded.
|-
| '''5. Correlated Pleiotropy'''
| CAUSE model comparison p > 0.05 (Sharing Model wins).
| '''Null Result (Discard Causality)'''. The traits are correlated due to shared genetics, not a direct causal pathway. Any significant IVW results are false positives.
|-
| '''6. Inconclusive'''
| MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other.
| '''Unresolved / Inconclusive'''. State that genetic evidence is too pleiotropic to reliably disentangle.
|-
| '''7. Selection/collider bias''' || Both arms present AND predicted bias same sign as observed
AND predicted ≈ observed magnitude
| - Report as '''selection-bias-consistent, not causal'''.
Give uncorrected + corrected estimates. Escalate to a design-based test before any causal claim.
|}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Talk:Mendelian Randomization

2026-07-18T18:20:07Z

Davebrid1: Fixed formatting

== MR SOP — outstanding items (selection/collider bias work, 2026-07-18) ==

Context: §4 "Selection and Collider Bias" was added to the [https://bridgeslab.sph.umich.edu/protocols/index.php/Mendelian_Randomization MR SOP] after the smoking→AD project found its headline result was most plausibly a survival-collider artefact.

=== Sections still missing ===
All three are cheap, and all three bit us on smoking→AD.

# '''Steiger directionality / reverse causation''' — absent entirely. One line (<code>TwoSampleMR::directionality_test()</code>). Important for the disease→AD portfolio, where reverse causation is plausible.
# '''Sample overlap''' — absent. Two-sample MR assumes independent samples; UK Biobank is in nearly every GWAS we use (it was in ''both'' our exposure and outcome). Tool: MRlap (needs full genome-wide sumstats + LD scores).
# '''Dataset provenance verification''' — absent. We caught '''two mislabelled OpenGWAS accessions''': <code>ieu-a-1001</code> labelled "parental lifespan" is actually Okbay EA; <code>ieu-b-5067</code> labelled "Wightman" is Woolf 2022 with 954 cases. Rule: verify N, case/control split and cohort composition via <code>gwasinfo()</code> before use; never trust the label.

=== MR-PRESSO / MR-Egger imbalance (raised, not yet drafted) ===
Observation: we report MR-PRESSO outlier-corrected far more often than MR-Egger. This is '''structural''', not accidental — Egger intercept tests are underpowered so Scenario 4 rarely fires, while Cochran's Q is almost always significant so Scenario 2 fires constantly.

Why it matters — our own Layer 0: IVW b=−0.065 '''p=0.296''' → MR-PRESSO b=−0.112 '''p=0.0015'''. Outlier removal ''manufactured'' the significant result later shown to be collider-driven. It removed only 2/22 SNPs (9%), so the existing ">30% removed" tripwire never fired.

Proposed amendments (Scenario 2 currently has '''no''' conclusion-change tripwire):
* Add a '''conclusion-change tripwire''' to Scenario 2: if outlier removal moves the estimate outside the original IVW 95% CI or flips significance → report corrected + uncorrected, with the corrected value as sensitivity only. Key on ''effect on the conclusion'', not SNP count.
* Stop treating '''Egger intercept p>0.05''' as evidence of no directional pleiotropy — it is an underpowered null, the same error pattern we rejected in §4.2. Report the intercept estimate with CI.
* Elevate '''Weighted Median''' to co-primary (better power ''and'' robustness than MR-Egger; currently only "support" in Scenario 2).
* Report the '''full estimator panel with a concordance flag''' — our estimates spanned −0.065 to −0.208 with p from 0.0015 to 0.647; single-winner adjudication hides that spread.

Talk:Mendelian Randomization

2026-07-18T18:18:52Z

Davebrid1: Added notes on what to add to MR SOP

## A. MR SOP — outstanding items

### Sections still missing (all cheap, all bit us on smoking→AD)
1. **Steiger directionality / reverse causation** — absent entirely. One line
(`TwoSampleMR::directionality_test()`). Important for the disease→AD portfolio, where
reverse causation is plausible.
2. **Sample overlap** — absent. Two-sample MR assumes independent samples; UK Biobank is in
nearly every GWAS we use (it was in *both* our exposure and outcome). Tool: MRlap
(needs full genome-wide sumstats + LD scores).
3. **Dataset provenance verification** — absent. We caught **two mislabelled OpenGWAS
accessions**: `ieu-a-1001` labelled "parental lifespan" is actually Okbay EA;
`ieu-b-5067` labelled "Wightman" is Woolf 2022 with 954 cases. Rule: verify N,
case/control split and cohort composition via `gwasinfo()` before use; never trust the label.

### MR-PRESSO / MR-Egger imbalance (raised, not yet drafted)
Observation: we report MR-PRESSO outlier-corrected far more than MR-Egger. This is
**structural**, not accidental — Egger intercept tests are underpowered so Scenario 4 rarely
fires, while Cochran's Q is almost always significant so Scenario 2 fires constantly.

Why it matters — our own Layer 0: IVW b=−0.065 **p=0.296** → MR-PRESSO b=−0.112 **p=0.0015**.
Outlier removal *manufactured* the significant result later shown to be collider-driven. It
removed only 2/22 SNPs (9%), so the existing ">30% removed" tripwire never fired.

Proposed amendments (Scenario 2 currently has **no** conclusion-change tripwire):
- Add a **conclusion-change tripwire** to Scenario 2: if outlier removal moves the estimate
outside the original IVW 95% CI or flips significance → report corrected + uncorrected,
corrected as sensitivity only. (Key on *effect on conclusion*, not SNP count.)
- Stop treating **Egger intercept p>0.05** as evidence of no directional pleiotropy — it's an
underpowered null, the same error pattern we rejected in §4.2. Report intercept + CI.
- Elevate **weighted median** to co-primary (better power *and* robustness than Egger; currently
only "support" in Scenario 2).
- Report the **full estimator panel with a concordance flag** — our estimates spanned
−0.065 to −0.208 with p from 0.0015 to 0.647; single-winner adjudication hides that.

Mendelian Randomization

2026-07-18T18:11:39Z

Davebrid1: /* 3.4 Calculating I-squared GX for MR-Egger */ Fixed error in I2 calculation

= Mendelian Randomization Standard Operating Procedure (SOP) =
[[ Category: Genetics ]]

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
y <- dat$beta.exposure; s <- dat$se.exposure
k <- length(y); w <- 1/s^2
mu <- sum(y * w) / sum(w) # inverse-variance weighted mean
Q <- sum(w * (y - mu)^2) # Cochran's Q for the exposure effects
max(0, (Q - (k - 1)) / Q)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in Section 3 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival axis, prognosis = outcome).
Because IVW is linear the correction is exact:
corrected(X→Y) = (X→Y) − b_SH × (X→S)

'''Requirements — an underpowered fit is worse than none:'''
* Use '''full genome-wide summary statistics''', LD-clumped (r²<0.01, 1 Mb, ancestry-matched panel). Clumped tophits from an API are '''not sufficient''' (a 10-SNP fit is unidentified).
* Target '''≳1,000 independent SNPs'''; report the fitted n and the slope CI.
* Report fits '''with and without major pleiotropic loci''' (e.g. APOE for AD/lifespan) and without the locus under test if the analysis is locus-specific.
* b_SH is a property of the (survival axis → outcome) pair, '''not''' of the exposure — fit once per outcome and reuse across exposures. Refit if the outcome dataset changes.

'''Coherence check (the falsifiable quantity).''' Report predicted induced effect vs observed
effect. If predicted ≈ observed, the selection pathway alone reproduces the signal.

=== 4.5 Reporting requirements ===
Always report '''uncorrected and corrected estimates side by side'''. The corrected value is a
'''sensitivity bound, never the primary estimate'''.

'''Stated limitation (include in all manuscripts using this section):''' the correction removes
the component collinear with the survival axis and '''cannot distinguish collider-induced
association from a genuine effect acting along that same axis'''. Because most exposures affect
mortality, mechanical application will attenuate real effects. Correction '''diagnoses''';
only '''design''' resolves — incident cohorts, age-stratified analyses, or younger-onset outcomes.

'''Worked example.''' Smoking → Alzheimer's. Passed stringent instrument criteria, mean F>10,
Egger intercept p=0.108, adjudicated Scenario 2 → MR-PRESSO b=−0.112, p=0.0015 (a reportable
positive). Both collider arms were present (instruments→lung cancer p=10⁻⁵¹; AD liability→shorter
lifespan p=0.003). A genome-wide index-event correction (2,346 SNPs, b_SH=−0.944) reduced the
pooled estimate from −0.129 to +0.005 (p=0.91), and the collider structure predicted 89–117% of
the observed effect across three instrument sets. The standard toolkit — including a
proxy-ascertainment sensitivity analysis that was '''falsely reassuring''' — did not detect this.

== 5. Decision Matrix: Which Results to Report ==
Use the following adjudication criteria to synthesize the results from the models above.

{| class="wikitable"
|-
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal'''
| F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05.
| '''IVW (Fixed Effects)'''. All assumptions are met.
|-
| '''2. Balanced Pleiotropy'''
| F > 10. Cochran's Q p < 0.05. Egger Intercept p > 0.05.
| '''MR-PRESSO (Outlier Corrected)''' or '''IVW (Random Effects)'''. Support with Weighted Median.
|-
| '''3. Weak Instruments'''
| Mean F < 10 OR Relaxed criteria (p < 5e-6) used.
| '''MR-RAPS'''. Baseline IVW is vulnerable to weak instrument bias.
|-
| '''4. Directional Pleiotropy'''
| Egger Intercept p < 0.05.
| '''Weighted Mode''' (if I2GX < 0.90) OR '''MR-Egger Slope''' (if I2GX >= 0.90). IVW is discarded.
|-
| '''5. Correlated Pleiotropy'''
| CAUSE model comparison p > 0.05 (Sharing Model wins).
| '''Null Result (Discard Causality)'''. The traits are correlated due to shared genetics, not a direct causal pathway. Any significant IVW results are false positives.
|-
| '''6. Inconclusive'''
| MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other.
| '''Unresolved / Inconclusive'''. State that genetic evidence is too pleiotropic to reliably disentangle.
|-
| '''7. Selection/collider bias''' || Both arms present AND predicted bias same sign as observed
AND predicted ≈ observed magnitude
| - Report as '''selection-bias-consistent, not causal'''.
Give uncorrected + corrected estimates. Escalate to a design-based test before any causal claim.
|}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Mendelian Randomization

2026-07-18T18:11:03Z

Davebrid1: /* 4.3 Step 2 — Direction check (free; resolves most cases) */ minor error in section link

= Mendelian Randomization Standard Operating Procedure (SOP) =
[[ Category: Genetics ]]

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
beta_x <- dat$beta.exposure
se_x <- dat$se.exposure

# Variance of the exposure estimates
var_beta_x <- var(beta_x)

# Mean of the squared standard errors
mean_se_x2 <- mean(se_x^2)

# Calculate I^2_GX
I2gx <- 1 - (mean_se_x2 / var_beta_x)

# Constrain between 0 and 1
I2gx <- max(0, I2gx)

return(I2gx)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in Section 3 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival axis, prognosis = outcome).
Because IVW is linear the correction is exact:
corrected(X→Y) = (X→Y) − b_SH × (X→S)

'''Requirements — an underpowered fit is worse than none:'''
* Use '''full genome-wide summary statistics''', LD-clumped (r²<0.01, 1 Mb, ancestry-matched panel). Clumped tophits from an API are '''not sufficient''' (a 10-SNP fit is unidentified).
* Target '''≳1,000 independent SNPs'''; report the fitted n and the slope CI.
* Report fits '''with and without major pleiotropic loci''' (e.g. APOE for AD/lifespan) and without the locus under test if the analysis is locus-specific.
* b_SH is a property of the (survival axis → outcome) pair, '''not''' of the exposure — fit once per outcome and reuse across exposures. Refit if the outcome dataset changes.

'''Coherence check (the falsifiable quantity).''' Report predicted induced effect vs observed
effect. If predicted ≈ observed, the selection pathway alone reproduces the signal.

=== 4.5 Reporting requirements ===
Always report '''uncorrected and corrected estimates side by side'''. The corrected value is a
'''sensitivity bound, never the primary estimate'''.

'''Stated limitation (include in all manuscripts using this section):''' the correction removes
the component collinear with the survival axis and '''cannot distinguish collider-induced
association from a genuine effect acting along that same axis'''. Because most exposures affect
mortality, mechanical application will attenuate real effects. Correction '''diagnoses''';
only '''design''' resolves — incident cohorts, age-stratified analyses, or younger-onset outcomes.

'''Worked example.''' Smoking → Alzheimer's. Passed stringent instrument criteria, mean F>10,
Egger intercept p=0.108, adjudicated Scenario 2 → MR-PRESSO b=−0.112, p=0.0015 (a reportable
positive). Both collider arms were present (instruments→lung cancer p=10⁻⁵¹; AD liability→shorter
lifespan p=0.003). A genome-wide index-event correction (2,346 SNPs, b_SH=−0.944) reduced the
pooled estimate from −0.129 to +0.005 (p=0.91), and the collider structure predicted 89–117% of
the observed effect across three instrument sets. The standard toolkit — including a
proxy-ascertainment sensitivity analysis that was '''falsely reassuring''' — did not detect this.

== 5. Decision Matrix: Which Results to Report ==
Use the following adjudication criteria to synthesize the results from the models above.

{| class="wikitable"
|-
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal'''
| F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05.
| '''IVW (Fixed Effects)'''. All assumptions are met.
|-
| '''2. Balanced Pleiotropy'''
| F > 10. Cochran's Q p < 0.05. Egger Intercept p > 0.05.
| '''MR-PRESSO (Outlier Corrected)''' or '''IVW (Random Effects)'''. Support with Weighted Median.
|-
| '''3. Weak Instruments'''
| Mean F < 10 OR Relaxed criteria (p < 5e-6) used.
| '''MR-RAPS'''. Baseline IVW is vulnerable to weak instrument bias.
|-
| '''4. Directional Pleiotropy'''
| Egger Intercept p < 0.05.
| '''Weighted Mode''' (if I2GX < 0.90) OR '''MR-Egger Slope''' (if I2GX >= 0.90). IVW is discarded.
|-
| '''5. Correlated Pleiotropy'''
| CAUSE model comparison p > 0.05 (Sharing Model wins).
| '''Null Result (Discard Causality)'''. The traits are correlated due to shared genetics, not a direct causal pathway. Any significant IVW results are false positives.
|-
| '''6. Inconclusive'''
| MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other.
| '''Unresolved / Inconclusive'''. State that genetic evidence is too pleiotropic to reliably disentangle.
|-
| '''7. Selection/collider bias''' || Both arms present AND predicted bias same sign as observed
AND predicted ≈ observed magnitude
| - Report as '''selection-bias-consistent, not causal'''.
Give uncorrected + corrected estimates. Escalate to a design-based test before any causal claim.
|}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Mendelian Randomization

2026-07-18T18:10:28Z

Davebrid1: Added category tags

= Mendelian Randomization Standard Operating Procedure (SOP) =
[[ Category: Genetics ]]

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
beta_x <- dat$beta.exposure
se_x <- dat$se.exposure

# Variance of the exposure estimates
var_beta_x <- var(beta_x)

# Mean of the squared standard errors
mean_se_x2 <- mean(se_x^2)

# Calculate I^2_GX
I2gx <- 1 - (mean_se_x2 / var_beta_x)

# Constrain between 0 and 1
I2gx <- max(0, I2gx)

return(I2gx)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in Section 3 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.5.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival axis, prognosis = outcome).
Because IVW is linear the correction is exact:
corrected(X→Y) = (X→Y) − b_SH × (X→S)

'''Requirements — an underpowered fit is worse than none:'''
* Use '''full genome-wide summary statistics''', LD-clumped (r²<0.01, 1 Mb, ancestry-matched panel). Clumped tophits from an API are '''not sufficient''' (a 10-SNP fit is unidentified).
* Target '''≳1,000 independent SNPs'''; report the fitted n and the slope CI.
* Report fits '''with and without major pleiotropic loci''' (e.g. APOE for AD/lifespan) and without the locus under test if the analysis is locus-specific.
* b_SH is a property of the (survival axis → outcome) pair, '''not''' of the exposure — fit once per outcome and reuse across exposures. Refit if the outcome dataset changes.

'''Coherence check (the falsifiable quantity).''' Report predicted induced effect vs observed
effect. If predicted ≈ observed, the selection pathway alone reproduces the signal.

=== 4.5 Reporting requirements ===
Always report '''uncorrected and corrected estimates side by side'''. The corrected value is a
'''sensitivity bound, never the primary estimate'''.

'''Stated limitation (include in all manuscripts using this section):''' the correction removes
the component collinear with the survival axis and '''cannot distinguish collider-induced
association from a genuine effect acting along that same axis'''. Because most exposures affect
mortality, mechanical application will attenuate real effects. Correction '''diagnoses''';
only '''design''' resolves — incident cohorts, age-stratified analyses, or younger-onset outcomes.

'''Worked example.''' Smoking → Alzheimer's. Passed stringent instrument criteria, mean F>10,
Egger intercept p=0.108, adjudicated Scenario 2 → MR-PRESSO b=−0.112, p=0.0015 (a reportable
positive). Both collider arms were present (instruments→lung cancer p=10⁻⁵¹; AD liability→shorter
lifespan p=0.003). A genome-wide index-event correction (2,346 SNPs, b_SH=−0.944) reduced the
pooled estimate from −0.129 to +0.005 (p=0.91), and the collider structure predicted 89–117% of
the observed effect across three instrument sets. The standard toolkit — including a
proxy-ascertainment sensitivity analysis that was '''falsely reassuring''' — did not detect this.

== 5. Decision Matrix: Which Results to Report ==
Use the following adjudication criteria to synthesize the results from the models above.

{| class="wikitable"
|-
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal'''
| F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05.
| '''IVW (Fixed Effects)'''. All assumptions are met.
|-
| '''2. Balanced Pleiotropy'''
| F > 10. Cochran's Q p < 0.05. Egger Intercept p > 0.05.
| '''MR-PRESSO (Outlier Corrected)''' or '''IVW (Random Effects)'''. Support with Weighted Median.
|-
| '''3. Weak Instruments'''
| Mean F < 10 OR Relaxed criteria (p < 5e-6) used.
| '''MR-RAPS'''. Baseline IVW is vulnerable to weak instrument bias.
|-
| '''4. Directional Pleiotropy'''
| Egger Intercept p < 0.05.
| '''Weighted Mode''' (if I2GX < 0.90) OR '''MR-Egger Slope''' (if I2GX >= 0.90). IVW is discarded.
|-
| '''5. Correlated Pleiotropy'''
| CAUSE model comparison p > 0.05 (Sharing Model wins).
| '''Null Result (Discard Causality)'''. The traits are correlated due to shared genetics, not a direct causal pathway. Any significant IVW results are false positives.
|-
| '''6. Inconclusive'''
| MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other.
| '''Unresolved / Inconclusive'''. State that genetic evidence is too pleiotropic to reliably disentangle.
|-
| '''7. Selection/collider bias''' || Both arms present AND predicted bias same sign as observed
AND predicted ≈ observed magnitude
| - Report as '''selection-bias-consistent, not causal'''.
Give uncorrected + corrected estimates. Escalate to a design-based test before any causal claim.
|}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Mendelian Randomization

2026-07-18T18:09:55Z

Davebrid1: /* 5. Decision Matrix: Which Results to Report */ minor typo

= Mendelian Randomization Standard Operating Procedure (SOP) =

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
beta_x <- dat$beta.exposure
se_x <- dat$se.exposure

# Variance of the exposure estimates
var_beta_x <- var(beta_x)

# Mean of the squared standard errors
mean_se_x2 <- mean(se_x^2)

# Calculate I^2_GX
I2gx <- 1 - (mean_se_x2 / var_beta_x)

# Constrain between 0 and 1
I2gx <- max(0, I2gx)

return(I2gx)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in Section 3 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.5.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival axis, prognosis = outcome).
Because IVW is linear the correction is exact:
corrected(X→Y) = (X→Y) − b_SH × (X→S)

'''Requirements — an underpowered fit is worse than none:'''
* Use '''full genome-wide summary statistics''', LD-clumped (r²<0.01, 1 Mb, ancestry-matched panel). Clumped tophits from an API are '''not sufficient''' (a 10-SNP fit is unidentified).
* Target '''≳1,000 independent SNPs'''; report the fitted n and the slope CI.
* Report fits '''with and without major pleiotropic loci''' (e.g. APOE for AD/lifespan) and without the locus under test if the analysis is locus-specific.
* b_SH is a property of the (survival axis → outcome) pair, '''not''' of the exposure — fit once per outcome and reuse across exposures. Refit if the outcome dataset changes.

'''Coherence check (the falsifiable quantity).''' Report predicted induced effect vs observed
effect. If predicted ≈ observed, the selection pathway alone reproduces the signal.

=== 4.5 Reporting requirements ===
Always report '''uncorrected and corrected estimates side by side'''. The corrected value is a
'''sensitivity bound, never the primary estimate'''.

'''Stated limitation (include in all manuscripts using this section):''' the correction removes
the component collinear with the survival axis and '''cannot distinguish collider-induced
association from a genuine effect acting along that same axis'''. Because most exposures affect
mortality, mechanical application will attenuate real effects. Correction '''diagnoses''';
only '''design''' resolves — incident cohorts, age-stratified analyses, or younger-onset outcomes.

'''Worked example.''' Smoking → Alzheimer's. Passed stringent instrument criteria, mean F>10,
Egger intercept p=0.108, adjudicated Scenario 2 → MR-PRESSO b=−0.112, p=0.0015 (a reportable
positive). Both collider arms were present (instruments→lung cancer p=10⁻⁵¹; AD liability→shorter
lifespan p=0.003). A genome-wide index-event correction (2,346 SNPs, b_SH=−0.944) reduced the
pooled estimate from −0.129 to +0.005 (p=0.91), and the collider structure predicted 89–117% of
the observed effect across three instrument sets. The standard toolkit — including a
proxy-ascertainment sensitivity analysis that was '''falsely reassuring''' — did not detect this.

== 5. Decision Matrix: Which Results to Report ==
Use the following adjudication criteria to synthesize the results from the models above.

{| class="wikitable"
|-
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal'''
| F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05.
| '''IVW (Fixed Effects)'''. All assumptions are met.
|-
| '''2. Balanced Pleiotropy'''
| F > 10. Cochran's Q p < 0.05. Egger Intercept p > 0.05.
| '''MR-PRESSO (Outlier Corrected)''' or '''IVW (Random Effects)'''. Support with Weighted Median.
|-
| '''3. Weak Instruments'''
| Mean F < 10 OR Relaxed criteria (p < 5e-6) used.
| '''MR-RAPS'''. Baseline IVW is vulnerable to weak instrument bias.
|-
| '''4. Directional Pleiotropy'''
| Egger Intercept p < 0.05.
| '''Weighted Mode''' (if I2GX < 0.90) OR '''MR-Egger Slope''' (if I2GX >= 0.90). IVW is discarded.
|-
| '''5. Correlated Pleiotropy'''
| CAUSE model comparison p > 0.05 (Sharing Model wins).
| '''Null Result (Discard Causality)'''. The traits are correlated due to shared genetics, not a direct causal pathway. Any significant IVW results are false positives.
|-
| '''6. Inconclusive'''
| MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other.
| '''Unresolved / Inconclusive'''. State that genetic evidence is too pleiotropic to reliably disentangle.
|-
| '''7. Selection/collider bias''' || Both arms present AND predicted bias same sign as observed
AND predicted ≈ observed magnitude
| - Report as '''selection-bias-consistent, not causal'''.
Give uncorrected + corrected estimates. Escalate to a design-based test before any causal claim.
|}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Mendelian Randomization

2026-07-18T18:08:03Z

Davebrid1: /* 5. Decision Matrix: Which Results to Report */ Added row to results to report table

= Mendelian Randomization Standard Operating Procedure (SOP) =

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
beta_x <- dat$beta.exposure
se_x <- dat$se.exposure

# Variance of the exposure estimates
var_beta_x <- var(beta_x)

# Mean of the squared standard errors
mean_se_x2 <- mean(se_x^2)

# Calculate I^2_GX
I2gx <- 1 - (mean_se_x2 / var_beta_x)

# Constrain between 0 and 1
I2gx <- max(0, I2gx)

return(I2gx)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in Section 3 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.5.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival axis, prognosis = outcome).
Because IVW is linear the correction is exact:
corrected(X→Y) = (X→Y) − b_SH × (X→S)

'''Requirements — an underpowered fit is worse than none:'''
* Use '''full genome-wide summary statistics''', LD-clumped (r²<0.01, 1 Mb, ancestry-matched panel). Clumped tophits from an API are '''not sufficient''' (a 10-SNP fit is unidentified).
* Target '''≳1,000 independent SNPs'''; report the fitted n and the slope CI.
* Report fits '''with and without major pleiotropic loci''' (e.g. APOE for AD/lifespan) and without the locus under test if the analysis is locus-specific.
* b_SH is a property of the (survival axis → outcome) pair, '''not''' of the exposure — fit once per outcome and reuse across exposures. Refit if the outcome dataset changes.

'''Coherence check (the falsifiable quantity).''' Report predicted induced effect vs observed
effect. If predicted ≈ observed, the selection pathway alone reproduces the signal.

=== 4.5 Reporting requirements ===
Always report '''uncorrected and corrected estimates side by side'''. The corrected value is a
'''sensitivity bound, never the primary estimate'''.

'''Stated limitation (include in all manuscripts using this section):''' the correction removes
the component collinear with the survival axis and '''cannot distinguish collider-induced
association from a genuine effect acting along that same axis'''. Because most exposures affect
mortality, mechanical application will attenuate real effects. Correction '''diagnoses''';
only '''design''' resolves — incident cohorts, age-stratified analyses, or younger-onset outcomes.

'''Worked example.''' Smoking → Alzheimer's. Passed stringent instrument criteria, mean F>10,
Egger intercept p=0.108, adjudicated Scenario 2 → MR-PRESSO b=−0.112, p=0.0015 (a reportable
positive). Both collider arms were present (instruments→lung cancer p=10⁻⁵¹; AD liability→shorter
lifespan p=0.003). A genome-wide index-event correction (2,346 SNPs, b_SH=−0.944) reduced the
pooled estimate from −0.129 to +0.005 (p=0.91), and the collider structure predicted 89–117% of
the observed effect across three instrument sets. The standard toolkit — including a
proxy-ascertainment sensitivity analysis that was '''falsely reassuring''' — did not detect this.

== 5. Decision Matrix: Which Results to Report ==
Use the following adjudication criteria to synthesize the results from the models above.

{| class="wikitable"
|-
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal'''
| F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05.
| '''IVW (Fixed Effects)'''. All assumptions are met.
|-
| '''2. Balanced Pleiotropy'''
| F > 10. Cochran's Q p < 0.05. Egger Intercept p > 0.05.
| '''MR-PRESSO (Outlier Corrected)''' or '''IVW (Random Effects)'''. Support with Weighted Median.
|-
| '''3. Weak Instruments'''
| Mean F < 10 OR Relaxed criteria (p < 5e-6) used.
| '''MR-RAPS'''. Baseline IVW is vulnerable to weak instrument bias.
|-
| '''4. Directional Pleiotropy'''
| Egger Intercept p < 0.05.
| '''Weighted Mode''' (if I2GX < 0.90) OR '''MR-Egger Slope''' (if I2GX >= 0.90). IVW is discarded.
|-
| '''5. Correlated Pleiotropy'''
| CAUSE model comparison p > 0.05 (Sharing Model wins).
| '''Null Result (Discard Causality)'''. The traits are correlated due to shared genetics, not a direct causal pathway. Any significant IVW results are false positives.
|-
| '''6. Inconclusive'''
| MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other.
| '''Unresolved / Inconclusive'''. State that genetic evidence is too pleiotropic to reliably disentangle.
|-
| '''7. Selection/collider bias''' || Both arms present AND predicted bias same sign as observed
AND predicted ≈ observed magnitude
| - Report as '''selection-bias-consistent, not causal'''.
Give uncorrected + corrected estimates. Escalate to a design-based test before any causal claim.
|}}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Mendelian Randomization

2026-07-18T18:06:23Z

Davebrid1: /* 4 Selection and Collider Bias (Survival / Ascertainment) */ Added remainder of collider bias adjustement

= Mendelian Randomization Standard Operating Procedure (SOP) =

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
beta_x <- dat$beta.exposure
se_x <- dat$se.exposure

# Variance of the exposure estimates
var_beta_x <- var(beta_x)

# Mean of the squared standard errors
mean_se_x2 <- mean(se_x^2)

# Calculate I^2_GX
I2gx <- 1 - (mean_se_x2 / var_beta_x)

# Constrain between 0 and 1
I2gx <- max(0, I2gx)

return(I2gx)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in Section 3 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.5.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival axis, prognosis = outcome).
Because IVW is linear the correction is exact:
corrected(X→Y) = (X→Y) − b_SH × (X→S)

'''Requirements — an underpowered fit is worse than none:'''
* Use '''full genome-wide summary statistics''', LD-clumped (r²<0.01, 1 Mb, ancestry-matched panel). Clumped tophits from an API are '''not sufficient''' (a 10-SNP fit is unidentified).
* Target '''≳1,000 independent SNPs'''; report the fitted n and the slope CI.
* Report fits '''with and without major pleiotropic loci''' (e.g. APOE for AD/lifespan) and without the locus under test if the analysis is locus-specific.
* b_SH is a property of the (survival axis → outcome) pair, '''not''' of the exposure — fit once per outcome and reuse across exposures. Refit if the outcome dataset changes.

'''Coherence check (the falsifiable quantity).''' Report predicted induced effect vs observed
effect. If predicted ≈ observed, the selection pathway alone reproduces the signal.

=== 4.5 Reporting requirements ===
Always report '''uncorrected and corrected estimates side by side'''. The corrected value is a
'''sensitivity bound, never the primary estimate'''.

'''Stated limitation (include in all manuscripts using this section):''' the correction removes
the component collinear with the survival axis and '''cannot distinguish collider-induced
association from a genuine effect acting along that same axis'''. Because most exposures affect
mortality, mechanical application will attenuate real effects. Correction '''diagnoses''';
only '''design''' resolves — incident cohorts, age-stratified analyses, or younger-onset outcomes.

'''Worked example.''' Smoking → Alzheimer's. Passed stringent instrument criteria, mean F>10,
Egger intercept p=0.108, adjudicated Scenario 2 → MR-PRESSO b=−0.112, p=0.0015 (a reportable
positive). Both collider arms were present (instruments→lung cancer p=10⁻⁵¹; AD liability→shorter
lifespan p=0.003). A genome-wide index-event correction (2,346 SNPs, b_SH=−0.944) reduced the
pooled estimate from −0.129 to +0.005 (p=0.91), and the collider structure predicted 89–117% of
the observed effect across three instrument sets. The standard toolkit — including a
proxy-ascertainment sensitivity analysis that was '''falsely reassuring''' — did not detect this.

== 5. Decision Matrix: Which Results to Report ==
Use the following adjudication criteria to synthesize the results from the models above.

{| class="wikitable"
|-
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal'''
| F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05.
| '''IVW (Fixed Effects)'''. All assumptions are met.
|-
| '''2. Balanced Pleiotropy'''
| F > 10. Cochran's Q p < 0.05. Egger Intercept p > 0.05.
| '''MR-PRESSO (Outlier Corrected)''' or '''IVW (Random Effects)'''. Support with Weighted Median.
|-
| '''3. Weak Instruments'''
| Mean F < 10 OR Relaxed criteria (p < 5e-6) used.
| '''MR-RAPS'''. Baseline IVW is vulnerable to weak instrument bias.
|-
| '''4. Directional Pleiotropy'''
| Egger Intercept p < 0.05.
| '''Weighted Mode''' (if I2GX < 0.90) OR '''MR-Egger Slope''' (if I2GX >= 0.90). IVW is discarded.
|-
| '''5. Correlated Pleiotropy'''
| CAUSE model comparison p > 0.05 (Sharing Model wins).
| '''Null Result (Discard Causality)'''. The traits are correlated due to shared genetics, not a direct causal pathway. Any significant IVW results are false positives.
|-
| '''6. Inconclusive'''
| MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other.
| '''Unresolved / Inconclusive'''. State that genetic evidence is too pleiotropic to reliably disentangle.
|}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Mendelian Randomization

2026-07-18T18:02:37Z

Davebrid1: Added section about survival bias and how to address it

= Mendelian Randomization Standard Operating Procedure (SOP) =

This SOP outlines the standardized pipeline for conducting two-sample Mendelian Randomization (MR) analyses, from instrument selection through to causal inference adjudication.

== Biological Plausibility & Gene-Environment Equivalence (G-EE) ==

As outlined in [https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1005013 ''Gene-environment equivalence: The fundamental principle of Mendelian randomization''] (Davey Smith, Hemani, & Ebrahim, 2026), Mendelian Randomization (MR) is a biological question evaluated with statistics, not a statistical pipeline applied blindly to biological data.

Before defining your genetic instruments, explicitly document the biological plausibility of your study by answering the following three criteria. If the Gene-Environment Equivalence (G-EE) is implausible, the statistical robustness checks in the subsequent sections cannot validate the study.

=== The Target Intervention ===
* '''Question:''' What specific real-world environmental or clinical intervention is this MR simulating?
* '''Action:''' Clearly define the hypothetical "Target Trial." If your exposure is a highly complex or broad behavioral trait (e.g., "television watching" or "loneliness") for which no cohesive, targeted clinical intervention exists, you must heavily scrutinize whether MR is the appropriate tool for your research question.

=== Mechanistic Overlap (The G-EE Assumption) ===
* '''Question:''' Do the proposed genetic variants alter biological pathways in the exact same way as the proposed real-world intervention?
* '''Action:''' Justify the biological function of your intended instruments. For example, if evaluating a pharmaceutical-mimicking target (like statins), your SNPs should specifically lower LDL cholesterol via the targeted pathway (e.g., HMG-CoA reductase inhibition), rather than through nonspecific, highly pleiotropic secondary pathways.

=== Timing and Canalization (Developmental Adaptation) ===
* '''Question:''' How does the lifelong nature of genetic exposure differ from a targeted late-life intervention for this specific trait?
* '''Action:''' Acknowledge the dimension of time. Genetic variants exert influence from conception, meaning human biology may adapt or compensate (canalize) during development. Explicitly state in your preregistration that the resulting causal estimates represent the effect of ''lifelong exposure liability''. Document a warning that these effect estimates cannot be directly translated into predicted outcomes for short-term or late-life clinical trials.

== 1. Genetic Instrument Selection ==
Instruments must be robustly associated with the exposure and independent of one another.

=== 1.1 Stringent Criteria (Primary Analysis) ===
For exposures with well-powered GWAS, apply the following strict inclusion criteria:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-8}</math> (Genome-wide significance)
* '''Linkage Disequilibrium (LD) Clumping:''' <math>r^2 < 0.001</math>
* '''Clumping Distance:''' > 10,000 kb
* '''Reference Panel:''' 1000 Genomes European (or population-matched to the GWAS)

=== 1.2 Loose Criteria (Relaxed Analysis) ===
If the stringent criteria yield fewer than 5 Single Nucleotide Polymorphisms (SNPs), the analysis lacks the degrees of freedom required for standard sensitivity tests. In this case, relax the threshold:
* '''P-value Threshold:''' <math>p < 5 \times 10^{-6}</math>
* '''Requirement:''' If this relaxed threshold is used, '''MR-RAPS''' becomes a mandatory primary reporting model due to the guaranteed introduction of weak instruments and measurement error.

== 2. Estimating Instrument Strength ==
Before conducting MR, validate the strength of the genetic instruments to rule out weak instrument bias.

=== 2.1 Variance Explained (R-squared) ===
Calculate the proportion of variance in the exposure explained by each SNP using the Minor Allele Frequency (MAF) and the effect size (<math>\beta</math>):

<math>R^2 = 2 \times MAF \times (1 - MAF) \times \beta^2</math>

''Note: Review the average MAF. If the average MAF is very low (< 0.05), the instruments rely on rare variants, which may have less stable effect estimates.''

=== 2.2 F-Statistics ===
Calculate the individual F-statistic for each SNP to measure instrument strength, where <math>N</math> is the sample size of the exposure GWAS:

<math>F = \frac{R^2 \times (N - 2)}{1 - R^2}</math>

* '''Individual F-statistic:''' Any single SNP with <math>F < 10</math> should be excluded from the standard IVW analysis.
* '''Total/Mean F-statistic:''' Calculate the average F-statistic across all retained SNPs. If the Mean <math>F < 10</math>, the overall instrument is weak, and MR-RAPS must be prioritized.

== 3. Analytical Models to Test ==
Run the following suite of models to assess causality, heterogeneity, and horizontal pleiotropy.

=== 3.1 The Baseline Model ===
* '''Inverse Variance Weighted (IVW):''' The primary meta-analysis of all SNPs.
** Check Cochran's Q statistic. If <math>p > 0.05</math>, report the '''IVW Fixed Effects (FE)''' model.
** If Cochran's Q <math>p < 0.05</math>, switch to the '''IVW Multiplicative Random Effects (RE)''' model to account for heterogeneity.

=== 3.2 Standard Sensitivity Models (The Big Three) ===
* '''MR-Egger:''' Used to detect directional pleiotropy via the intercept.
* '''Weighted Median:''' Provides a valid estimate if up to 50% of the instrument weight comes from invalid (pleiotropic) SNPs.
* '''Weighted Mode:''' Provides a valid estimate if the largest single cluster of SNPs is valid (ZEro InSIDE assumption).

=== 3.3 Advanced Robustness Models ===
* '''MR-PRESSO:''' Run if Cochran's Q is significant. It detects and removes specific outlier SNPs driving horizontal pleiotropy and provides an outlier-corrected estimate.
* '''MR-RAPS:''' Run if Mean F < 10 or if loose inclusion criteria were used. It handles measurement error from weak instruments.
* '''CAUSE:''' Run as the ultimate robustness check to differentiate true causality from correlated pleiotropy (shared genetic architecture).

=== 3.4 Calculating I-squared GX for MR-Egger ===
To determine if the MR-Egger slope is reliable, you must test the No Measurement Error (NOME) assumption by calculating <math>I^2_{GX}</math>. If <math>I^2_{GX} < 0.90</math>, the MR-Egger slope suffers from dilution bias and should not be trusted.

<syntaxhighlight lang="R">
# R Script for calculating I^2_GX using a harmonised TwoSampleMR dataframe ('dat')

calculate_i2gx <- function(dat) {
beta_x <- dat$beta.exposure
se_x <- dat$se.exposure

# Variance of the exposure estimates
var_beta_x <- var(beta_x)

# Mean of the squared standard errors
mean_se_x2 <- mean(se_x^2)

# Calculate I^2_GX
I2gx <- 1 - (mean_se_x2 / var_beta_x)

# Constrain between 0 and 1
I2gx <- max(0, I2gx)

return(I2gx)
}

i2gx_value <- calculate_i2gx(dat)
print(paste("I^2_GX =", round(i2gx_value, 3)))
</syntaxhighlight>

== 4 Selection and Collider Bias (Survival / Ascertainment) ==

Every model in §4 targets '''pleiotropy''' or '''weak instruments'''. None detects
'''selection bias'''. A signal can pass Cochran's Q, the Egger intercept, MR-PRESSO and
the weighted median while being entirely generated by conditioning on sample membership.
This section is mandatory when any trigger below applies.

=== 4.1 Triggers (run this section if ANY apply) ===
* The outcome is '''late-onset or age-related''' (AD, dementia, PD, most cancers, CVD).
* The exposure is '''associated with mortality or study participation''' (smoking, BMI, BP, alcohol, diabetes, SES).
* The outcome GWAS uses '''proxy/GWAX, prevalent-case, or volunteer-cohort''' designs (UK Biobank by-proxy AD, FinnGen prevalent cases).

=== 4.2 Step 1 — Establish both collider arms ===
Conditioning on being sampled biases the X–Y association only if '''both''' arms exist:
* '''X→S''': exposure affects survival/participation. Test '''per analysis''' (MR of exposure → parental lifespan or all-cause mortality).
* '''Y→S''': outcome liability affects survival. Test '''once per outcome''' and reuse; use '''clinically ascertained''' instruments for the outcome, never a proxy GWAS (circular).

'''Decision rule.''' Report a three-way verdict using an equivalence test (TOST) against a
pre-registered bound δ, '''not''' p>0.05:
* '''equivalence-null''' — 95% CI ⊂ ±δ → that arm is absent; collider cannot operate; stop.
* '''real association''' — CI excludes 0 → arm present; go to 4.5.3.
* '''inconclusive''' — CI covers 0 but exceeds ±δ → '''report as unresolved''', never as "clean".

Set δ relative to the effect under test (default: δ = 15% of the observed X→Y estimate;
report a permissive δ = 40% as sensitivity). An underpowered null is not evidence of absence.

=== 4.3 Step 2 — Direction check (free; resolves most cases) ===
Compute the predicted induced effect:
predicted bias = b_SH × (X→S)
where b_SH is the selection slope (§4.5.4). Then:
* '''Bias OPPOSITE in sign to the observed effect''' → bias is conservative; the true effect is
if anything larger. Note it and proceed to normal adjudication.
* '''Bias SAME sign as the observed effect''' → the estimate may be partly or wholly induced.
Go to 4.5.4.

For a life-shortening exposure the induced bias is '''protective'''. Therefore
'''risk-increasing associations are relatively robust''' to this bias, while
'''protective or surprisingly-null findings are the danger zone'''.

=== 4.4 Step 3 — Index-event correction (sensitivity only) ===
Estimate the selection slope with SlopeHunter (incidence = survival

== 5. Decision Matrix: Which Results to Report ==
Use the following adjudication criteria to synthesize the results from the models above.

{| class="wikitable"
|-
! Scenario !! Data Presentation !! Adjudicated Result to Report
|-
| '''1. Clean Signal'''
| F > 10. Cochran's Q p > 0.05. Egger Intercept p > 0.05. CAUSE Causal Model p < 0.05.
| '''IVW (Fixed Effects)'''. All assumptions are met.
|-
| '''2. Balanced Pleiotropy'''
| F > 10. Cochran's Q p < 0.05. Egger Intercept p > 0.05.
| '''MR-PRESSO (Outlier Corrected)''' or '''IVW (Random Effects)'''. Support with Weighted Median.
|-
| '''3. Weak Instruments'''
| Mean F < 10 OR Relaxed criteria (p < 5e-6) used.
| '''MR-RAPS'''. Baseline IVW is vulnerable to weak instrument bias.
|-
| '''4. Directional Pleiotropy'''
| Egger Intercept p < 0.05.
| '''Weighted Mode''' (if I2GX < 0.90) OR '''MR-Egger Slope''' (if I2GX >= 0.90). IVW is discarded.
|-
| '''5. Correlated Pleiotropy'''
| CAUSE model comparison p > 0.05 (Sharing Model wins).
| '''Null Result (Discard Causality)'''. The traits are correlated due to shared genetics, not a direct causal pathway. Any significant IVW results are false positives.
|-
| '''6. Inconclusive'''
| MR-PRESSO removes >30% of SNPs causing power loss, OR Median and Mode significantly contradict each other.
| '''Unresolved / Inconclusive'''. State that genetic evidence is too pleiotropic to reliably disentangle.
|}

==Reproducible Reporting of Results==

In addition to loading code into shareable repository, for our lab Github, once the manuscript is written complete the [https://www.strobe-mr.org/ STROBE-MR checklist] to ensure robust and clear reporting of key aspects of study design. Include this as supplementary data to the submission even if not strictly required by the journal.

Mendelian Randomization

2026-04-14T01:21:00Z

Davebrid1: Added link to STROBE-MR

Mendelian Randomization

2026-04-14T01:16:24Z

Davebrid1: /* Mendelian Randomization Standard Operating Procedure (SOP) */ Added notes from the recent PLOS paper about biological plausibility

Mendelian Randomization

2026-04-14T00:24:03Z

Davebrid1: Generated intitial SOP for MR analyses

LDLR Genotyping

2026-04-01T12:40:56Z

Davebrid1: Removed table of contents

Modified from https://www.jax.org/Protocol?stockNumber=002207&protocolID=27075

__NOTOC__

* [[SOP - Ethidium Bromide]]
* [[SOP - Electrophoresis]]

== Reagents Needed ==

=== PCR Primers ===
* '''Ldlr Common Forward''': 5'-TAT GCA TCC CCA GTC TTT GG-3'
* '''Ldlr Wild-type Reverse''': 5'-CTA CCC AAC CAG CCC CTT AC-3'
* '''Ldlr Mutant Reverse''': 5'-ATA GAT TCG CCC TTG TGT CC-3'

=== Master Mix ===
* '''DreamTaq Green PCR Master Mix (2X)''' - Thermo Fisher Scientific, Cat# K1081

=== Additional Reagents ===
* Nuclease-free water
* Template DNA ([[Preparation of Tail Samples (for Genotyping)|tail lysate]] or purified genomic DNA)

== Primer Preparation ==

=== Stock Primer Preparation (100 µM) ===
# Resuspend each lyophilized primer in nuclease-free water to 100 µM concentration. Look on the tube from IDT, for example if there is 23.7 nmoles then you would resuspend in 237 µL of water
# Store at -20°C

=== Primer Master Mix (10 µM each primer) ===
For a 1 mL primer master mix:
* 100 µL of 100 µM Primer 19799
* 100 µL of 100 µM Primer 19800
* 100 µL of 100 µM Primer oIMR7770
* 700 µL nuclease-free water

'''Final concentrations in primer master mix:''' 10 µM each primer

Store at -20°C

== PCR Master Mix Preparation ==

=== Per Reaction (25 µL total volume) ===
* 12.5 µL DreamTaq Green PCR Master Mix (2X)
* 3.75 µL Primer Master Mix (10 µM each)
* 7.75 µL nuclease-free water
* 1 µL template DNA

'''Final primer concentrations in PCR:''' 1.5 µM each primer

=== For Multiple Reactions ===
Prepare master mix for (n+1) reactions, where n = number of samples:
* DreamTaq Green PCR Master Mix (2X): 12.5 µL × (n+1)
* Primer Master Mix: 3.75 µL × (n+1)
* Nuclease-free water: 7.75 µL × (n+1)

Aliquot 24 µL of master mix per tube, then add 1 µL template DNA to each

== PCR Cycling Program ==

This program takes 1:50 to run.

{| class="wikitable"
|+ '''Ldlr''' PCR Program
|-
! Step !! Temperature (°C) !! Time !! Cycles !! Notes
|-
| Initial Denaturation || 94 || 3 min || 1 ||
|-
| '''Touchdown Phase''' || || || ||
|-
| Denature || 94 || 30 sec || rowspan="3" | 10 || rowspan="3" | Decrease annealing temp by 0.5°C per cycle
|-
| Anneal || 65→60 || 30 sec
|-
| Extend || 68 || 45 sec
|-
| '''Standard Cycles''' || || || ||
|-
| Denature || 94 || 30 sec || rowspan="3" | 28 ||
|-
| Anneal || 60 || 30 sec ||
|-
| Extend || 72 || 45 sec ||
|-
| Final Extension || 72 || 5 min || 1 ||
|-
| Hold || 4 || ∞ || ||
|-
|}

== Expected Results ==

* '''Wild type:''' 351 bp
* '''Heterozygote:''' 179 bp AND 351 bp
* '''Mutant:''' 179 bp (GC-rich band)

'''Note:''' Run on 2% agarose gel. The mutant band (179 bp) is GC-rich and may appear fainter than expected.

[[ Category:Genotyping ]]
[[ Category:Mouse Work ]]
[[ Category:PCR ]]

Preparing an Agarose Gel

2026-03-27T12:45:48Z

Davebrid1: Added SOP

[[ SOP - Ethidium Bromide ]]

==Materials==
*Agarose
*TAE Buffer (1X): Dilute from 100X stock
*Thermo Apparatus (Mold, Holder, Comb and Gel Rig)

==Prepare Gel==
#Place plastic mold securely in holder
#Put well comb in mold
#Weight out 2.0g agarose and add 100 mL of TAE (2% solution).
#Microwave 90s until dissolved
#Add 2 uL Ethidium Bromide or Gel Red. Swirl to mix and eliminate sediments
#Pour into mold, add the comb, and wait for it to solidify
#Place gel in cold room if in a hurry
#After loading, run gel at 100V

Preparing an Agarose Gel

2026-03-27T12:44:06Z

Davebrid1: /* Prepare Gel (BioRad Gel Rig) */ Updated instructions

==Materials==
*Agarose
*TAE Buffer (1X): Dilute from 100X stock
*Thermo Apparatus (Mold, Holder, Comb and Gel Rig)

==Prepare Gel==
#Place plastic mold securely in holder
#Put well comb in mold
#Weight out 2.0g agarose and add 100 mL of TAE (2% solution).
#Microwave 90s until dissolved
#Add 2 uL Ethidium Bromide or Gel Red. Swirl to mix and eliminate sediments
#Pour into mold, add the comb, and wait for it to solidify
#Place gel in cold room if in a hurry
#After loading, run gel at 100V

QPCR

2026-03-23T20:08:13Z

Davebrid1: Formatting for GCal link

__NOTOC__
==Real Time qPCR==
===Materials===
*cDNA: see [[First_Strand_cDNA_Synthesis_(AB_Kit)|First Strand cDNA Synthesis (AB Kit)]] for details
*SYBR Green PCR Master Mix Applied Biosystems (ThermoFisher Catalog # 4367659; [https://www.thermofisher.com/order/catalog/product/4367659 Vendor Link])
*384 well qPCR plate (ThermoFisher Catalog # 4309849) and covers (Catalog # 4360954)
*Primers (Dilute to 0.4 uM mixture of fwd and rev. From 100 uM stocks- the 100uM stock is prepared by adding 227 uL of distilled water to 22.7nmol of a gene as an example- this is 4uL Forward Primer, 4 uL Reverse Primer and 992 uL Water). This primer mix can be stored at -20 in a Working Primers box. Design primers according to [[Primer Design for qPCR]]

===Plate Preparation===
#Book 2h on qPCR machine by signing up on the [https://calendar.google.com/calendar/u/0?cid=Y19jN2RhYmJlMjJiNmQ1YTY0YjAzYzU1NzVmOGUxNmEyZmZjNjAwOTJjYWIyZmYwM2VjY2M1NjkyNzljYmQwY2QzQGdyb3VwLmNhbGVuZGFyLmdvb2dsZS5jb20 Google Calendar]
#Prepare cDNA and dilute in water in a 96 well plate. Typically a 20x dilution of cDNA leaves enough to be detected.
#Get optically clear 384 well plate and keep on paper towel. Do not touch bottom of plate.
#Sketch out the plate in your notes. Typically rows are different primers while columns are different cDNA's
#Calculate how many samples x how many replicates/per sample (start with 3 or 4 until you are consistent enough technically to decrease). This will be the number of wells need for each primer.
#Prepare a Primer/SYBR Green mixture for each primer. For each well you will need 5 uL SYBR green + 2.5 uL Primer working stock, so if you have calculated you need 10 wells per primer that is 50 uL SYBR Green + 25 uL Primers. Make up 20-25% more than you need.
#Using the repeater multichannel pipette put on 2 or 3 tips (depending on your plate arrangement) and set to aspirate however many samples you have and dispense 7.5 uL per well.
#Dispense 7.5 uL of Primer/SYBR mixture into each well, dispensing at the bottom of the well.
#Using the ClipTip multichannel add 2.5 uL of cDNA to each applicable well. You don't need to change tips between wells.
#Once the plate is completed, carefully put an optically clear cover on it using the plastic square to ensure the edges are sealed, being very careful not to leave fingerprints on the seal. Apply cover by starting in the middle of plate, working out towards edges, and finish by applying high pressure to edges, ensuring a proper seal.
#You can prepare the plate ~3h beforehand, keeping it at 4C until the machine is ready.
#Immediately before the run spin the plate briefly (2 mins at 4000 RPM) in the swinging bucket centrifuge.

===Run Protocol===
* Set up run using [[Set up qPCR Run on Thermo Cloud and QuantStudio|Thermo Cloud/QuantStudio]] or [[Set up qPCR Run on Roche LightCycler|Roche LightCycler]]
Briefly, log into thermo cloud
*Select "Design and Analysis New, qPCR" from the home screen
*Select "set up plate"
*Select "comparative CT-SYBR"
*Correct volume to read, "10.0uL" instead of "20.0uL"
*Select "Plate set up"
*Navigate to the drop down menu marked "passive reference" and select "none."
*Then import [https://docs.google.com/spreadsheets/d/e/2PACX-1vQpOEYWkqKe6tELqIerA7fcwe2LoEQy_8ANGuhOppmGXbD0sBGvKXHnR3z7aYnfEF7--r4FbOd6yCYM/pub?output=csv plate setup] with linked CSV (MUST be a csv file).
*Save to the cloud and upload on the machine when you insert the plate.

==Calculations==
see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC55695 for considerations on calculations

[[ Category: Molecular Biology ]]
[[ Category: RNA ]]
[[ Category: qPCR ]]
[[ Category: Transcription ]]
[[ Category: Expression ]]

QPCR

2026-03-23T20:05:39Z

Davebrid1: Updated calendar link

__NOTOC__
==Real Time qPCR==
===Materials===
*cDNA: see [[First_Strand_cDNA_Synthesis_(AB_Kit)|First Strand cDNA Synthesis (AB Kit)]] for details
*SYBR Green PCR Master Mix Applied Biosystems (ThermoFisher Catalog # 4367659; [https://www.thermofisher.com/order/catalog/product/4367659 Vendor Link])
*384 well qPCR plate (ThermoFisher Catalog # 4309849) and covers (Catalog # 4360954)
*Primers (Dilute to 0.4 uM mixture of fwd and rev. From 100 uM stocks- the 100uM stock is prepared by adding 227 uL of distilled water to 22.7nmol of a gene as an example- this is 4uL Forward Primer, 4 uL Reverse Primer and 992 uL Water). This primer mix can be stored at -20 in a Working Primers box. Design primers according to [[Primer Design for qPCR]]

===Plate Preparation===
#Book 2h on qPCR machine by signing up on the sheet in room 7013 and on the [https://calendar.google.com/calendar/u/0?cid=Y19jN2RhYmJlMjJiNmQ1YTY0YjAzYzU1NzVmOGUxNmEyZmZjNjAwOTJjYWIyZmYwM2VjY2M1NjkyNzljYmQwY2QzQGdyb3VwLmNhbGVuZGFyLmdvb2dsZS5jb20]
#Prepare cDNA and dilute in water in a 96 well plate. Typically a 20x dilution of cDNA leaves enough to be detected.
#Get optically clear 384 well plate and keep on paper towel. Do not touch bottom of plate.
#Sketch out the plate in your notes. Typically rows are different primers while columns are different cDNA's
#Calculate how many samples x how many replicates/per sample (start with 3 or 4 until you are consistent enough technically to decrease). This will be the number of wells need for each primer.
#Prepare a Primer/SYBR Green mixture for each primer. For each well you will need 5 uL SYBR green + 2.5 uL Primer working stock, so if you have calculated you need 10 wells per primer that is 50 uL SYBR Green + 25 uL Primers. Make up 20-25% more than you need.
#Using the repeater multichannel pipette put on 2 or 3 tips (depending on your plate arrangement) and set to aspirate however many samples you have and dispense 7.5 uL per well.
#Dispense 7.5 uL of Primer/SYBR mixture into each well, dispensing at the bottom of the well.
#Using the ClipTip multichannel add 2.5 uL of cDNA to each applicable well. You don't need to change tips between wells.
#Once the plate is completed, carefully put an optically clear cover on it using the plastic square to ensure the edges are sealed, being very careful not to leave fingerprints on the seal. Apply cover by starting in the middle of plate, working out towards edges, and finish by applying high pressure to edges, ensuring a proper seal.
#You can prepare the plate ~3h beforehand, keeping it at 4C until the machine is ready.
#Immediately before the run spin the plate briefly (2 mins at 4000 RPM) in the swinging bucket centrifuge.

===Run Protocol===
* Set up run using [[Set up qPCR Run on Thermo Cloud and QuantStudio|Thermo Cloud/QuantStudio]] or [[Set up qPCR Run on Roche LightCycler|Roche LightCycler]]
Briefly, log into thermo cloud
*Select "Design and Analysis New, qPCR" from the home screen
*Select "set up plate"
*Select "comparative CT-SYBR"
*Correct volume to read, "10.0uL" instead of "20.0uL"
*Select "Plate set up"
*Navigate to the drop down menu marked "passive reference" and select "none."
*Then import [https://docs.google.com/spreadsheets/d/e/2PACX-1vQpOEYWkqKe6tELqIerA7fcwe2LoEQy_8ANGuhOppmGXbD0sBGvKXHnR3z7aYnfEF7--r4FbOd6yCYM/pub?output=csv plate setup] with linked CSV (MUST be a csv file).
*Save to the cloud and upload on the machine when you insert the plate.

==Calculations==
see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC55695 for considerations on calculations

[[ Category: Molecular Biology ]]
[[ Category: RNA ]]
[[ Category: qPCR ]]
[[ Category: Transcription ]]
[[ Category: Expression ]]