Efficient p-value evaluation for resampling-based tests

S UMMARY The resampling-based test, which often relies on permutation or bootstrap procedures, has been widely used for statistical hypothesis testing when the asymptotic distribution of the test statistic is unavailable or unreliable. It requires repeated calculations of the test statistic on a large number of simulated data sets for its significance level assessment, and thus it could become very computationally intensive. Here, we propose an efficient p-value evaluation procedure by adapting the stochastic approximation Markov chain Monte Carlo algorithm. The new procedure can be used easily for estimating the p-value for any resampling-based test. We show through numeric simulations that the proposed procedure can be 100– 500 000 times as efficient (in term of computing time) as the standard resampling-based procedure when evaluating a test statistic with a small p-value (e.g. less than 10 −6 ). With its computational burden reduced by this proposed procedure, the versatile resampling-based test would become computationally feasible for a much wider range of applications. We demonstrate the application of the new method by applying it to a large-scale genetic association study of prostate cancer.