Use of Multivariable Mendelian Randomization to Address Biases Due to Competing Risk Before Recruitment

Abstract

Background: Mendelian randomization (MR) provides unconfounded estimates. MR is open to selection bias when the underlying sample is selected on surviving to recruitment on the genetically instrumented exposure and competing risk of the outcome. Few methods to address this bias exist. Methods: We show that this selection bias can sometimes be addressed by adjusting for common causes of survival and outcome. We use multivariable MR to obtain a corrected MR estimate for statins on stroke. Statins affect survival, and stroke typically occurs later in life than ischemic heart disease (IHD), making estimates for stroke open to bias from competing risk. Results: In univariable MR in the UK Biobank, genetically instrumented statins did not protect against stroke [odds ratio (OR) 1.33, 95% confidence interval (CI) 0.80-2.20] but did in multivariable MR (OR 0.81, 95% CI 0.68-0.98) adjusted for major causes of survival and stroke [blood pressure, body mass index (BMI), and smoking initiation] with a multivariable Q-statistic indicating absence of selection bias. However, the MR estimate for statins on stroke using MEGASTROKE remained positive and the Q statistic indicated pleiotropy. Conclusion: MR studies of harmful exposures on late-onset diseases with shared etiology need to be conceptualized within a mechanistic understanding so as to identify any potential bias due to survival to recruitment on both genetically instrumented exposure and competing risk of the outcome, which may then be investigated using multivariable MR or estimated analytically and results interpreted accordingly.

Keywords: Mendelian randomization; competing risk; instrumental variable analysis; selection bias; shared etiology.

FIGURE 1

Directed acyclic graphs with instrument (Z), outcome (Y), exposure (X), confounders (U₁), and survival (S), where a box indicates selection, for (A) a valid Mendelian randomization study and (B) a Mendelian randomization study with an invalid instrument through violation of the exclusion-restriction assumption via pleiotropy, (C) a Mendelian randomization study with an invalid instrument through violation of the exclusion-restriction assumption via survival on instrument and shared etiology with the outcome (U₂), (D) a Mendelian randomization study with an invalid instrument through violation of the exclusion restriction assumption via survival (S), competing risk of another disease (Y₂) and shared causes (U₂) with (Y₂) and the outcome (Y), and (E) a Mendelian randomization illustrating both conditions which have to be met to satisfy the exclusion restriction assumption.

FIGURE 2

Directed acyclic graphs showing how selection bias could occur because of selection on survival (S), indicated by a box, on the instrument (GV) and on competing risk of ischemic heart disease (IHD) which shares causes with the outcome of interest, i.e., stroke, with U₁ as confounders of exposure and outcome, when assessing (A) effects of an exposure on stroke or AF, (B) effects of lipid modifiers on stroke, and (C) effects of body mass index on stroke.

FIGURE A1

Observed odds ratio against the True odds ratio in the presence of different proportions of death before recruitment due to the exposure (P_E) and different proportions of death before recruitment due to competing risk of the outcome (P_CR) for true odds ratios large than 1 (left hand side) and smaller than 1 (right hand side, obtained by taking the inverse of the odds ratio).