Valid inference for two sample summary data Mendelian randomization

Music City Center 

Mendelian randomization (MR) studies commonly utilize summary statistics from genome-wide association studies (GWASs). However, a rigorous theoretical foundation for this practice remains underdeveloped. Assuming that the instrumental single nucleotide polymorphisms (SNPs) are in linkage equilibrium, we derive exact analytical expressions for both the two-stage least squares (TSLS) estimator and the two-sample TSLS (TSTSLS) estimator, along with their corresponding variances, directly in terms of GWAS summary statistics. These derivations yield several important insights. Notably, the widely used inverse variance weighted (IVW) estimator is shown to be nonequivalent to either the TSLS or TSTSLS estimators. Furthermore, the standard error of the IVW estimator is inconsistent when the causal effect is non-zero. Given the proliferation of IVW-based methods in MR research, our findings underscore the need to critically reassess these approaches to ensure valid causal inference. We validate our theoretical results through extensive simulation studies and apply them to a broad spectrum of complex traits using publicly available GWAS summary data. The simulations reveal two novel findings: (1) causal effect estimates derived from GWAS summary statistics using the IVW, TSLS, or TSTSLS estimators exhibit finite sample bias, as evidenced by the coverage rates of the 95\% Wald confidence intervals; and (2) this bias has a negligible impact on the standard error of these estimators.

Mendelian randomization


summary statistics


two-stage least-squares regression


inverse variance weighting


generalized method of moment 

Section on Statistics in Genomics and Genetics