The role of environmental heterogeneity in meta-analysis of gene-environment interactions with quantitative traits

Abstract

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 (), 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.

Keywords: adaptively weighted estimator; covariate heterogeneity; gene-environment interaction; individual patient data; meta-analysis; meta-regression; power calculation.

Figure 1

Non-linear GEI model: the (red) sigmoid curve shows the true relationship between Y -G association and E, namely, β_G(E) = 2 exp(E − 50)/{1 + exp(E − 50)} +2; the boxplots show the covariate heterogeneity of E across studies where the dots show the corresponding covariate means of E.

Figure 2

Non-linear GEI model: the height of the bars represent the power to detect GEI across individual studies; the (green) curve shows the value of the true non-linear GEI parameter; the top panel shows the sample sizes n_k and the within study standard deviations σ_Ek of E, the four studies with relatively greater σ_Ek are highlighted (in red).

Figure 3

Comparison of the proposed meta-analytical methods (in terms of power) under different scenarios of susceptibility models and covariate heterogeneity through a simulation study, where data are simulated without any assumption on gene-environment independence or homogeneity in allele frequencies across studies.

Figure 4

Comparison of the proposed meta-analytical methods (in terms of power) under different scenarios of susceptibility models and covariate heterogeneity through a simulation study (representing the situation of lack of common set of covariates across studies), where data are simulated without any assumption on gene-environment independence or homogeneity in allele frequencies.

Figure 5

Power curves under misspecified susceptibility models (dominant/additive), where the gen erating co-dominant model has δ^AA = −δ^Aa, where data are simulated without any assumption on gene-environment independence or homogeneity in allele frequencies.

Figure 6

Forest plots showing the estimated gene-environment interactions (under additive model of rs1121980) across the 8 European cohorts, as well as the combined estimates through meta-analysis. [IPD: individual patient data; UIVW: univariate inverse-variance weighted estimator; MIVW: multi variate inverse-variance weighted estimator; AWE: adaptively weighted estimator combining UIVW and Meta-regression.]