Efficient approximation of P-value of the maximum of correlated tests, with applications to genome-wide association studies.

Genome-wide association study (GWAS), typically involving 100,000 to 500,000 single-nucleotide polymorphisms (SNPs), is a powerful approach to identify disease susceptibility loci. In a GWAS, single-marker analysis, which tests one SNP at a time, is usually used as the first stage to screen SNPs across the genome in order to identify a small fraction of promising SNPs with relatively low p-values for further and more focused studies. For single-marker analysis, the trend test derived for an additive genetic model is often used. This may not be robust when the additive assumption is not appropriate for the true underlying disease model. A robust test, MAX, based on the maximum of three trend test statistics derived for recessive, additive, and dominant models, has been proposed recently for GWAS. But its p-value has to be evaluated through a resampling-based procedure, which is computationally challenging for the analysis of GWAS. Obtaining the p-value for MAX with adjustment for the covariates can be even more time-consuming. In this article, we provide a simple approximation for the p-value of the MAX test with or without adjusting for the covariates. The new method avoids resampling steps and thus makes the MAX test readily applicable to GWAS. We use simulation studies as well as real datasets on 17 confirmed disease-associated SNPs to assess the accuracy of the proposed method. We also apply the method to the GWAS of coronary artery disease.