Efficient designs of gene-environment interaction studies: implications of Hardy-Weinberg equilibrium and gene-environment independence

Abstract

It is important to investigate whether genetic susceptibility variants exercise the same effects in populations that are differentially exposed to environmental risk factors. Here, we assess the power of four two-stage case-control design strategies for assessing multiplicative gene-environment (G-E) interactions or for assessing genetic or environmental effects in the presence of G-E interactions. We considered a di-allelic single nucleotide polymorphism G and a binary environmental variable E under the constraints of G-E independence and Hardy-Weinberg equilibrium and used the Wald statistic for all tests. We concluded that (i) for testing G-E interactions or genetic effects in the presence of G-E interactions when data for E are fully available, it is preferable to ascertain data for G in a subsample of cases with similar numbers of exposed and unexposed and a random subsample of controls; and (ii) for testing G-E interactions or environmental effects in the presence of G-E interactions when data for G are fully available, it is preferable to ascertain data for E in a subsample of cases that has similar numbers for each genotype and a random subsample of controls. In addition, supplementing external control data to an existing case-control sample leads to improved power for assessing effects of G or E in the presence of G-E interactions.

Figure 1

Power of the three methods under the standard case-control design. Panels A and B display the power for testing β_I = 0 or β_g = β_I = 0 in the absence (panel A) or presence (panel B) of the genetic main effect (e^βg = 1.2). Other parameters included p_e = 0.3, p_a = 0.3, and e^βI = 1.5. Each of the 1,000 replicates included 500 cases and 500 controls. Panels C and D display the power for testing β_I = 0 or β_e = β_I = 0 in the absence (panel C) or presence (panel D) of the environmental main effect (e^βe = 1.5). Other parameters included p_e = 0.3, p_a = 0.3, and e^βg = 1.2. Each of the 1,000 replicates included 300 cases and 300 controls. The size of the test was set at 0.0001.

Figure 2

Power of GE-HWE under Design I when phase II subjects were selected randomly or by stratifying on E. Phase I included 1,000 cases and 1,000 controls, and the significance level was set at 0.0001. Panels A and B present the power when an equal number of cases and controls were selected into phase II. Panels C and D present the power when 300 cases were selected into phase II by stratifying on E and varying numbers of controls were selected either randomly or also by stratifying on E. Other parameters included p_e = 0.15, e^βg = 1.2, e^βe = 1.2, and e^βI = 1.5.

Figure 3

Power of GE-HWE under Design II when phase II subjects were selected randomly or by stratifying on G. Phase I included 1,000 cases and 1,000 controls, and the significance level was set at 0.0001. Panels A and B present the power when an equal number of cases and controls were selected into phase II. Panels C and D present the power when 300 cases were selected into phase II by stratifying on G and varying numbers of controls were selected either randomly or also by stratifying on G. Other parameters included e^βg = 1.2, e^βe = 1.2, e^βI = 1.5, and p_a = 0.2.

Figure 4

Power of GE-HWE for testing β_e = β_I = 0 under Supplemented Design I, where data for (G, E) for 300 cases and 300 controls was supplemented by data for E from varying numbers of controls. The significance level was set at 0.0001. The OR for the genetic main effect was e^βg = 1.2, and the MAF was p_a = 0.2.

Figure 5

Power of GE-HWE for testing β_g = β_I = 0 under Supplemented Design II where data for (G, E) for 500 cases and 500 controls was supplemented by data for G from varying numbers of controls. The significance level was set at 0.0001. The OR for the environmental main effect was e^βe = 1.5, and the MAF was p_e = 0.15.