A powerful truncated tail strength method for testing multiple null hypotheses in one dataset

In microarray analysis, medical imaging analysis and functional magnetic resonance imaging, we often need to test an overall null hypothesis involving a large number of single hypotheses (usually larger than 1000) in one dataset. A tail strength statistic (Taylor and Tibshirani, 2006) and Fisher's probability method are useful and can be applied to measure an overall significance for a large set of independent single hypothesis tests with the overall null hypothesis assuming that all single hypotheses are true. In this paper we propose a new method that improves the tail strength statistic by considering only the values whose corresponding p-values are less than some pre-specified cutoff. We call it truncated tail strength statistic. We illustrate our method using a simulation study and two genome-wide datasets by chromosome. Our method not only controls type one error rate quite well, but also has significantly higher power than the tail strength method and Fisher's method in most cases.