Keywords
Multiple Testing; Alpha Exhaustive; Hypothesis Test
Abstract
A multiple testing procedure can be a single-step data-independent procedure, such as Bonferroni’s method, or a data-dependent stepwise procedure such as Hochberg’s step-up method and Hommel’s method. It can be an α-exhaustive, where the maximum type-I error rate under all configurations of null hypotheses equals α, or α-conservative, where the type-I error rate falls below the nominal level. We develop a simple one-step a-exhaustive procedure that can improve power 2%-5% over Hochberg’s and Hommel’s methods in common situations when the test statistics are mutually independent. The method can also be generalized to correlated test statistics. In our method we construct the stopping rules using the product of marginal p-values and control the upper bounds of the kth order terms so that α is exhausted for any configuration of k null hypotheses. Such upper bounds are determined progressively from k = 1 towards k = K, the number of null hypotheses in the problem. The method can be used in different multiple testing problems, including adaptive clinical trial designs.
Citation
Chang M, Deng X, Balser J and Bliss R. Progressive Alpha-Exhaustive Multiple Testing Procedure with Independent Test Statistics. SM J Biometrics Biostat. 2016; 1(1): 1003.