Genotype-Based Bayesian Analysis of Gene-Environment Interactions with Multiple Genetic Markers and Misclassification in Environmental Factors

Table 1

Biases and root mean squared errors (RMSEs) of risk parameters for the naive approach that ignores existence of misclassification and the proposed method in the case when pr(𝐷=1) is known and when it is estimated. The results are based on 500 samples of 1,500 cases and 1,500 controls. Genotype is simulated at the three marker loci with 𝑃_𝑀𝑖=0.25, 𝑖=1,2,3, with linkage disequilibrium corresponding to Δ_{𝑀𝑖𝑀𝑗}=0.03. The environmental covariate (𝑋) is binary and measured with error with misclassification probabilities being 0.20 for exposed and 0.25 for nonexposed subjects. The data is simulated and analyzed under the genotype effect model.

Parameter	True value	Naive analysis		Pseudo-MLE		MCMC
		Bias	RMSE	Bias	RMSE	Bias	RMSE
κ	0.484	0.481	0.231	−0.054	0.020	−0.032	0.013
β X	0.693	−0.351	0.132	0.014	0.039	0.008	0.021
β A1	0.406	0.257	0.073	−0.011	0.016	−0.003	0.009
β A2	0.789	0.194	0.046	−0.003	0.015	−0.002	0.006
β A3	0.693	0.283	0.089	−0.005	0.016	−0.003	0.008
β AX1	0.916	−0.425	0.193	0.039	0.046	0.017	0.025
β AX2	0.693	−0.317	0.113	0.038	0.041	0.023	0.021
β AX3	1.099	−0.515	0.282	0.039	0.058	0.019	0.032
β D1	0.262	0.299	0.133	0.026	0.152	0.009	0.368
β D2	0.095	0.258	0.105	0.005	0.099	0.003	0.039
β D3	0.693	0.231	0.092	0.018	0.128	0.008	0.087
β DX1	1.099	−0.495	0.326	0.018	0.301	0.006	0.093
β DX2	0.916	−0.413	0.235	0.006	0.208	0.005	0.121
β DX3	1.099	−0.486	0.313	0.023	0.286	0.017	0.138
𝑃𝑀𝑖	0.250	<0.001	<0.001	−0.001	<0.001	<0.001	<0.001
pr(𝑋=1)	0.500			0.003	0.001	<0.001	<0.001
pr(𝐷=1)	0.005			0.003	<0.001	<0.001	<0.001