Checking Genetic Homogeneity Between Two Samples Using Summary Statistics With Application to Mendelian Randomization

A common assumption in two-sample summary-data Mendelian randomization (MR) studies is that the effect of an instrumental single nucleotide polymorphism (SNP) on both the exposure and the outcome is consistent across the exposure and outcome samples. This assumption is more likely to hold when the minor allele frequency (MAF) of the instrumental SNP is similar in the two samples. However, in the common situation where MAF information is unavailable, there is currently no formal method to assess this condition, apart from heuristically matching the ethnic backgrounds of the exposure and outcome samples.

We propose a simple method to assess whether the genetic variance of a SNP, which is uniquely determined by its minor allele frequency (MAF) under Hardy-Weinberg equilibrium, is the same across two genome-wide association studies (GWASs). The method is motivated by the observation that, in linear-model GWASs, although the absolute magnitude of a SNP's variance cannot be recovered from summary statistics, its variance relative to that of other SNPs can be inferred. This observation continues to hold approximately when the underlying model is nonlinear.

We propose a V-V plot and a modified Bland-Altman plot to identify SNPs that have different genetic variances between two GWASs. Some published two-sample summary-data MR studies, unfortunately, seem to include SNPs that are not genetically homogeneous.

The proposed method provides a useful tool for enhancing the quality of a two-sample summary-data MR study. We advocate checking for equality of SNP MAFs between the exposure and the outcome GWASs before conducting a two-sample summary-data MR analysis, and our proposed method serves this purpose when the MAF information is missing in at least one of the two GWASs.