A comparison of sample size and power in case-only association studies of gene-environment interaction

Abstract

Assuming continuous, normally distributed environmental and categorical genotype variables, the authors compare 6 case-only designs for tests of association in gene-environment interaction. Novel tests modeling the environmental variable as either the response or the predictor and allowing a genetic variable with multiallelic variants are included. The authors show that tests imposing the same genotypic pattern of inheritance perform similarly regardless of whether genotype is the response variable or the predictor variable. The novel tests using the genetic variable as the response variable are advantageous because they are robust to non-normally distributed environmental exposures. Dominance deviance-deviation from additivity in the main or interaction effects-is key to test performance: When it is zero or modest, tests searching for a trend with increasing risk alleles are optimal; when it is large, tests for genotypic effects are optimal. However, the authors show that dominance deviance is attenuated when it is observed at a proxy locus, which is common in genome-wide association studies, so large dominance deviance is likely to be rare. The authors conclude that the trend test is the appropriate tool for large-scale association scans where the true gene-environment interaction model is unknown. The common practice of assuming a dominant pattern of inheritance can cause serious losses of power in the presence of any recessive, or modest dominant, effects.

Figure 1.

Statistical power to detect gene-environment interaction for 1,000 case participants as a function of the dominance deviance δ for tests EG_T (solid lines), EG_D (dashed lines), EG_G (dotted lines), and G_TE (dashed-dotted lines) at a disease susceptibility locus G for various values of the high-risk allele frequency p_A and interaction effect size b_EG: A) p_A = 0.1, b_EG = log(1.1); B) p_A = 0.1, b_EG = log(1.2); C) p_A = 0.1, b_EG = log(1.3); D) p_A = 0.25, b_EG = log(1.1); E) p_A = 0.25, b_EG = log(1.2); F) p_A = 0.25, b_EG = log(1.3). Dominance deviance is defined as the deviation from additivity in the main or interaction effects: Here we assume that the dominance deviance in the main effect and the interaction effect are the same. Results are shown for the situation where there is no main environmental effect, b_E = 0, and the main genetic effect is b_G = log(1.3); variation in the sizes of main environmental or genetic effects resulted in only minor variations in power and not did not alter conclusions regarding the relative efficacies of the tests considered. The environmental exposure variable was normally distributed and standardized.

Figure 2.

Statistical power to detect gene-environment interaction for 1,000 case participants as a function of the dominance deviance δ for tests EG_T (solid lines), EG_D (dashed lines), EG_G (dotted lines), and G_TE (dashed-dotted lines) at a noncausal locus H with minor allele frequency p_B = 0.2 for various values of the minor allele frequency p_A and interaction effect size b_EG at the disease susceptibility locus G: A) p_A = 0.1, b_EG = log(1.1); B) p_A = 0.1, b_EG = log(1.2); C) p_A = 0.1, b_EG = log(1.3); D) p_A = 0.25, b_EG = log(1.1); E) p_A = 0.25, b_EG = log(1.2); F) p_A = 0.25, b_EG = log(1.3). The alleles at H are in maximum linkage disequilibrium (r²) with the alleles at G: when p_A = 0.1, r² = 0.44; when p_A = 0.25, r² = 0.75; and when p_A = 0.4, r² = 0.37. Dominance deviance is defined as the deviation from additivity in the main or interaction effects: Here we assume that the dominance deviance in the main effect and the interaction effect are the same. Results are shown for the situation where there is no main environmental effect, b_E = 0, and the main genetic effect is b_G = log(1.3); variation in the sizes of main environmental or genetic effects resulted in only minor variations in power and not did not alter conclusions regarding the relative efficacies of the tests considered. The environmental exposure variable was normally distributed and standardized.