Variable selection in logistic regression for detecting SNP-SNP interactions: the rheumatoid arthritis example.

Many complex disease traits are observed to be associated with single nucleotide polymorphism (SNP) interactions. In testing small-scale SNP-SNP interactions, variable selection procedures in logistic regressions are commonly used. The empirical evidence of variable selection for testing interactions in logistic regressions is limited. This simulation study was designed to compare nine variable selection procedures in logistic regressions for testing SNP-SNP interactions. Data on 10 SNPs were simulated for 400 and 1000 subjects (case/control ratio=1). The simulated model included one main effect and two 2-way interactions. The variable selection procedures included automatic selection (stepwise, forward and backward), common 2-step selection, AIC- and SC-based selection. The hierarchical rule effect, in which all main effects and lower order terms of the highest-order interaction term are included in the model regardless of their statistical significance, was also examined. We found that the stepwise variable selection without the hierarchical rule, which had reasonably high authentic (true positive) proportion and low noise (false positive) proportion, is a better method compared to other variable selection procedures. For testing interactions, the hierarchical rule effect was obvious. The procedure without the hierarchical rule requires fewer terms in testing interactions, so it can accommodate more SNPs than the procedure with the hierarchical rule. For testing interactions, the procedures without the hierarchical rule had higher authentic proportion and lower noise proportion compared with ones with the hierarchical rule. These variable selection procedures were also applied and compared in a rheumatoid arthritis study.