Test Selection with Application to Detecting Disease Association with Multiple SNPs

We consider the motivating problem of testing for association between a phenotype and multiple single nucleotide polymorphisms (SNPs) within a candidate gene or region. Various statistical approaches have been proposed, including those based on either (combining univariate) single-locus analyses or (multivariate) multilocus analyses. However, it is known in theory that there is no single uniformly most powerful test to detect association with multiple SNPs. On the other hand, several tests have been shown to be among frequent winners across a range of practical situations, but the identity of the most powerful one changes with the situation in an unknown way. Here we propose a novel test selection procedure to select from five such tests: a so-called UminP test that combines multiple univariate/single-locus score tests by taking the minimum of their p values as its test statistic, a multivariate score test and its two modifications, and a so-called sum test. We also illustrate its application to selecting genotype codings for the sum test since the performance of the sum test depends on its genotype coding in an unknown way. Our major contributions include the methodology of estimating the power of a given test with a given dataset and the idea of using the estimated power as the criterion for test selection. We also propose a fast simulation-based method to calculate p values for the test selection procedure and for any method of combining p values. Our numerical results indicated that the proposed test selection procedure always yielded power close to the most powerful test among the candidate tests at any given situation, and in particular, our proposed test selection performed either better than or as well as the popular combining method of taking the minimum p value of the candidate tests.