Truncated product method for combining P-values

We present a new procedure for combining P-values from a set of L hypothesis tests. Our procedure is to take the product of only those P-values less than some specified cut-off value and to evaluate the probability of such a product, or a smaller value, under the overall hypothesis that all L hypotheses are true. We give an explicit formulation for this P-value, and find by simulation that it can provide high power for detecting departures from the overall hypothesis. We extend the procedure to situations when tests are not independent. We present both real and simulated examples where the method is especially useful. These include exploratory analyses when L is large, such as genome-wide scans for marker-trait associations and meta-analytic applications that combine information from published studies, with potential for dealing with the "publication bias" phenomenon. Once the overall hypothesis is rejected, an adjustment procedure with strong family-wise error protection is available for smaller subsets of hypotheses, down to the individual tests.