A comparison of robust Mendelian randomization methods using summary data

Abstract

The number of Mendelian randomization (MR) analyses including large numbers of genetic variants is rapidly increasing. This is due to the proliferation of genome-wide association studies, and the desire to obtain more precise estimates of causal effects. Since it is unlikely that all genetic variants will be valid instrumental variables, several robust methods have been proposed. We compare nine robust methods for MR based on summary data that can be implemented using standard statistical software. Methods were compared in three ways: by reviewing their theoretical properties, in an extensive simulation study, and in an empirical example. In the simulation study, the best method, judged by mean squared error was the contamination mixture method. This method had well-controlled Type 1 error rates with up to 50% invalid instruments across a range of scenarios. Other methods performed well according to different metrics. Outlier-robust methods had the narrowest confidence intervals in the empirical example. With isolated exceptions, all methods performed badly when over 50% of the variants were invalid instruments. Our recommendation for investigators is to perform a variety of robust methods that operate in different ways and rely on different assumptions for valid inferences to assess the reliability of MR analyses.

Keywords: Mendelian randomization; causal inference; pleiotropy; robust estimation; summary statistics.

Figure 1

Illustrative diagram showing the model assumed for genetic variant $G_j$, with effect ${\varphi }_j$ on the unobserved confounder $U$, effect ${\gamma }_j$ on exposure $X$, and direct effect ${\alpha }_j$ on outcome $Y$. The causal effect of the exposure on the outcome is $\theta$. Dotted lines represent possible ways the instrumental variable assumptions could be violated

Figure 2

Scatter plot of genetic associations with body mass index (standard deviation units) and coronary artery disease risk (log odds ratios) for 94 variants taken from the GIANT and CARDIoGRAMplusC4D consortia, respectively

Figure 3

Mean squared errors for the different methods in Scenario 2 (directional pleiotropy, InSIDE satisfied) with a null causal effect for 30 variants. Note the vertical axis is on a logarithmic scale

Figure 4

Mean squared errors for the different methods in Scenario 3 (directional pleiotropy, InSIDE violated) with a null causal effect for 30 variants. Note the vertical axis is on a logarithmic scale