Reporting Assumptions And Sensitivity Results

Why Reporting Is Part of the Analysis

A Mendelian-randomization (MR) estimate is interpretable only in relation to the variants, samples, assumptions, and outcome scale that produced it. A reader needs enough information to understand which instruments entered the analysis, whether their genetic associations are plausibly valid, and how conclusions change under alternative estimators or analysis choices. Reporting only a point estimate and p-value hides these dependencies.

A transparent report does not claim that diagnostics establish instrument validity. It distinguishes what was observed—for example, little heterogeneity—from what must be assumed—for example, that the instruments have no outcome pathway outside the exposure. It also separates the estimated association from the causal interpretation that follows only if the relevant assumptions are credible.

State the Instruments and Samples

Describe the exposure and outcome GWAS sources, ancestry, sample sizes, phenotype definitions, and effect scales. State whether the samples are independent, partly overlapping, or of unknown overlap, and how that was determined. If overlap is partial, report the available number or proportion of shared participants and explain the source of that information. When the amount is unknown, say so rather than implying independence.

For instrument selection, report the association threshold, linkage-disequilibrium (LD) clumping procedure and thresholds, and any additional filters. Give the number of variants at key stages: identified, retained after clumping, removed during harmonization, and included in the final analysis. State how alleles were aligned, how palindromic variants were handled, and whether variants were excluded because their alleles or associations could not be resolved. These details matter because different choices can change the instruments and the resulting estimate.

Relevance means that the variants are associated with the exposure. Report exposure associations and their uncertainty when available, and summarize instrument strength appropriately. For a single variant, a commonly used approximate strength statistic is \(F_j=(\hat{\beta}_{Xj}/SE(\hat{\beta}_{Xj}))^2\), where \(\hat{\beta}_{Xj}\) is its estimated exposure association and \(SE(\hat{\beta}_{Xj})\) is its standard error. This is a diagnostic of association strength, not a test of all MR assumptions. State whether variants are treated as independent; if LD remains, the analysis and uncertainty calculation must account for that dependence.

Make Assumptions and Estimator Choices Explicit

The standard instrumental-variable assumptions are: relevance, that the genetic instruments are associated with the exposure; independence, that the instruments are independent of factors that confound the exposure–outcome relationship; and exclusion restriction, that the instruments affect the outcome only through the exposure. MR estimates have a causal interpretation only to the extent that these conditions and the analysis model are credible.

In genetic studies, ancestry differences, population structure, selection into a study, assortative mating, and parental or family effects can challenge independence. Horizontal pleiotropy—an effect of a variant on the outcome through a pathway other than the exposure—can challenge exclusion restriction. These are substantive concerns, not issues that a single statistical test can settle. State design features or adjustments intended to address them, and describe what remains uncertain.

Also state what assumptions the chosen estimator adds. For example, conventional inverse-variance weighted (IVW) estimation is most straightforward to interpret when the variants are valid instruments and their associations are handled with an appropriate model. An MR-Egger analysis relies on its own assumptions, including the InSIDE condition, and can be imprecise. A weighted-median estimate requires at least half of the total weight to come from valid instruments. These approaches answer related but not identical questions; list the primary estimator and justify why it is suitable for the stated setting. If variants are correlated, report how the LD structure was incorporated.

Present an estimate with its scale and units, standard error or confidence interval, and a p-value if one is used. For a continuous outcome, for example, an estimate may be stated as outcome units per one-unit increase in the exposure, or per standard-deviation increase if that is how the exposure was scaled. For a binary outcome, state whether the estimate is on the log-odds scale or has been exponentiated to an odds ratio. Avoid describing an estimate as a causal effect without qualifying the assumptions required for that interpretation.

Report Diagnostics and Sensitivity Analyses as Evidence

Diagnostics and sensitivity analyses examine particular ways the primary analysis might be misleading. Report what was evaluated, the result, and what the result can and cannot establish. Heterogeneity, funnel-plot, influence, and directionality assessments can inform interpretation, but none verifies the core assumptions. A non-significant diagnostic result may reflect limited power rather than absence of bias.

Give sensitivity estimates alongside the primary estimate, with uncertainty and units on the same scale. Explain which assumption or failure mode each method addresses. For instance, compare a pleiotropy-robust estimator with the primary estimator when horizontal pleiotropy is a concern; summarize influence analyses when a small number of variants may dominate. If estimates differ, discuss the pattern and plausible reasons rather than choosing whichever estimate has the smallest p-value. If they agree, say that this is reassuring under the methods’ assumptions, not proof that all instruments are valid.

A short derivation clarifies why uncertainty belongs in the comparison. Under an approximately normal sampling distribution for an estimate \(\hat{\theta}\), with standard error \(SE\), a 95% confidence interval is \(\hat{\theta}\pm1.96SE\). The interval describes values compatible with the data under the model and repeated-sampling procedure; it is not a probability statement about a fixed parameter after the interval has been computed.

If \(\hat{\theta}\) is a continuous-outcome effect per standard-deviation increase in exposure, the interval has the same units. A sensitivity estimate with a wider interval may be less precise, so a difference in statistical significance alone does not establish a difference between estimates. Conversely, overlapping confidence intervals do not constitute a formal test that two estimators agree.

Limits and Common Reporting Failures

A useful report distinguishes the result from its interpretation. “The IVW estimate was 0.20 outcome units per standard-deviation increase in exposure (95% CI 0.102 to 0.298)” describes an estimate. “This proves that increasing exposure causes the outcome to rise” does not follow without credible instruments and an appropriate design. Even consistent sensitivity estimates cannot rule out pleiotropy shared across instruments, systematic selection bias, or other violations that the analyses do not detect.

State relevant limitations, such as weak or few instruments, imprecise robust estimates, uncertain overlap, unresolved variants, ancestry mismatch, possible residual LD, or limited generalizability. Identify which conclusions are supported by the data and which depend on assumptions. This is especially important when the outcome scale is transformed or the target population differs from the GWAS samples.

• Mistake: “The pleiotropy test was not significant, so there is no pleiotropy.” Correction: a non-significant test is not proof of no pleiotropy; state the result and note limited power or the test’s scope.
• Mistake: “The robust estimator gave a significant p-value, so it is the correct result.” Correction: choose and justify estimators by their assumptions, not by which p-value is smallest.
• Mistake: “The samples were independent” when overlap was not checked. Correction: report overlap as unknown if it is unknown, and discuss the resulting uncertainty.
• Mistake: reporting an estimate without an outcome scale or exposure increment. Correction: give the units and the contrast represented by the estimate.