Evaluating the Accuracy of Small P-Values In Genetic Association Studies Using Edgeworth Expansions

The asymptotic distributions of many classical test statistics are normal. The resulting approximations are often accurate for commonly used significance levels, 0.05 or 0.01. In genome-wide association studies, however, the significance level can be as low as 1×10⁻⁷, and the accuracy of the p-values can be challenging. We study the accuracies of these small p-values are using two-term Edgeworth expansions for three commonly used test statistics in GWAS. These tests have nuisance parameters not defined under the null hypothesis but estimable. We derive results for this general form of testing statistics using Edgeworth expansions, and find that the commonly used score test, maximin efficiency robust test and the chi-squared test are second order accurate in the presence of the nuisance parameter, justifying the use of the p-values obtained from these tests in the genome-wide association studies.