Assessing the joint effect of population stratification and sample selection in studies of gene-gene (environment) interactions

The biases to the estimation of main and interaction effect are quantified and then their bounds derived. The estimated bounds can be used to compute conservative p-values for the association test. If the conservative p-value is smaller than the significance level, we can safely claim that the association test is significant regardless of the presence of PS or not, or if there is any selection bias. We also identify conditions for the null bias. The bias depends on the allele frequencies, exposure rates, gene-environment odds ratios and disease risks across subpopulations and the sampling of the cases and controls.Our results show that the bias cannot be ignored even the case and control data were matched in ethnicity. A real example is given to illustrate application of the conservative p-value. These results are useful to the genetic association studies of main and interaction effects.In the search of causative agents of human disease, both environmental and genetic risk factors have been identified. Overwhelming evidence indicates that there are reasons to believe that relative common polymorphisms in a wide spectrum of genes may modify the effect of environmental agents [1,2]. Several studies also have demonstrated the presence of gene-gene interaction in complex human diseases [3-7]. Gene-gene interaction, or epistasis, is also considered as a basic genetic concept which has been widely used by biologists for a long time [8].Many association designs have been proposed for studying gene-environment or gene-gene interactions. Recently, Wang and Zhao [9] found that in the study of gene-gene interactions, the unmatched case-control association design is more powerful than both the matched case-control design and case-parents design. They also found that when a logistic regression model is fitted for assessing gene-environment interactions based on case-parents sample, the approach may be susceptible to the PS bias [10]. However, case-control design is also well kno