TY - JOUR

T1 - Severity of bias of a simple estimator of the causal odds ratio in Mendelian randomization studies

AU - Harbord, Roger M.

AU - Didelez, Vanessa

AU - Palmer, Tom M.

AU - Meng, Sha

AU - Sterne, Jonathan A. C.

AU - Sheehan, Nuala A.

N1 - Copyright © 2012 John Wiley & Sons, Ltd.

PY - 2013/3/30

Y1 - 2013/3/30

N2 - Mendelian randomization studies estimate causal effects using genetic variants as instruments. Instrumental variable methods are straightforward for linear models, but epidemiologists often use odds ratios to quantify effects. Also, odds ratios are often the quantities reported in meta-analyses. Many applications of Mendelian randomization dichotomize genotype and estimate the population causal log odds ratio for unit increase in exposure by dividing the genotype-disease log odds ratio by the difference in mean exposure between genotypes. This 'Wald-type' estimator is biased even in large samples, but whether the magnitude of bias is of practical importance is unclear. We study the large-sample bias of this estimator in a simple model with a continuous normally distributed exposure, a single unobserved confounder that is not an effect modifier, and interpretable parameters. We focus on parameter values that reflect scenarios in which we apply Mendelian randomization, including realistic values for the degree of confounding and strength of the causal effect. We evaluate this estimator and the causal odds ratio using numerical integration and obtain approximate analytic expressions to check results and gain insight. A small simulation study examines finite sample bias and mild violations of the normality assumption. For our simple data-generating model, we find that the Wald estimator is asymptotically biased with a bias of around 10% in fairly typical Mendelian randomization scenarios but which can be larger in more extreme situations. Recently developed methods such as structural mean models require fewer untestable assumptions and we recommend their use when the individual-level data they require are available. The Wald-type estimator may retain a role as an approximate method for meta-analysis based on summary data.

AB - Mendelian randomization studies estimate causal effects using genetic variants as instruments. Instrumental variable methods are straightforward for linear models, but epidemiologists often use odds ratios to quantify effects. Also, odds ratios are often the quantities reported in meta-analyses. Many applications of Mendelian randomization dichotomize genotype and estimate the population causal log odds ratio for unit increase in exposure by dividing the genotype-disease log odds ratio by the difference in mean exposure between genotypes. This 'Wald-type' estimator is biased even in large samples, but whether the magnitude of bias is of practical importance is unclear. We study the large-sample bias of this estimator in a simple model with a continuous normally distributed exposure, a single unobserved confounder that is not an effect modifier, and interpretable parameters. We focus on parameter values that reflect scenarios in which we apply Mendelian randomization, including realistic values for the degree of confounding and strength of the causal effect. We evaluate this estimator and the causal odds ratio using numerical integration and obtain approximate analytic expressions to check results and gain insight. A small simulation study examines finite sample bias and mild violations of the normality assumption. For our simple data-generating model, we find that the Wald estimator is asymptotically biased with a bias of around 10% in fairly typical Mendelian randomization scenarios but which can be larger in more extreme situations. Recently developed methods such as structural mean models require fewer untestable assumptions and we recommend their use when the individual-level data they require are available. The Wald-type estimator may retain a role as an approximate method for meta-analysis based on summary data.

KW - Bias (Epidemiology)

KW - Biostatistics

KW - Causality

KW - Humans

KW - Mendelian Randomization Analysis

KW - Meta-Analysis as Topic

KW - Models, Statistical

KW - Odds Ratio

U2 - 10.1002/sim.5659

DO - 10.1002/sim.5659

M3 - Journal article

C2 - 23080538

VL - 32

SP - 1246

EP - 1258

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 7

ER -