The Role of Environmental Heterogeneity in Meta‐Analysis of Gene–Environment Interactions With Quantitative Traits

With challenges in data harmonization and environmental heterogeneity across various data sources, meta‐analysis of gene–environment interaction studies can often involve subtle statistical issues. In this paper, we study the effect of environmental covariate heterogeneity (within and between cohorts) on two approaches for fixed‐effect meta‐analysis: the standard inverse‐variance weighted meta‐analysis and a meta‐regression approach. Akin to the results in Simmonds and Higgins ( 2007 ), we obtain analytic efficiency results for both methods under certain assumptions. The relative efficiency of the two methods depends on the ratio of within versus between cohort variability of the environmental covariate. We propose to use an adaptively weighted estimator (AWE), between meta‐analysis and meta‐regression, for the interaction parameter. The AWE retains full efficiency of the joint analysis using individual level data under certain natural assumptions. Lin and Zeng (2010a, b) showed that a multivariate inverse‐variance weighted estimator retains full efficiency as joint analysis using individual level data, if the estimates with full covariance matrices for all the common parameters are pooled across all studies. We show consistency of our work with Lin and Zeng (2010a, b). Without sacrificing much efficiency, the AWE uses only univariate summary statistics from each study, and bypasses issues with sharing individual level data or full covariance matrices across studies. We compare the performance of the methods both analytically and numerically. The methods are illustrated through meta‐analysis of interaction between Single Nucleotide Polymorphisms in FTO gene and body mass index on high‐density lipoprotein cholesterol data from a set of eight studies of type 2 diabetes.