Sequential tests controlling generalized familywise error rates

Sequential methods are developed for conducting a large number of simultaneous tests while controlling the Type I and Type II generalized familywise error rates. Namely, for the chosen values of alpha, beta, k, and m, we derive simultaneous tests of d individual hypotheses, based on sequentially collected data, that keep the probability of at least k Type I errors not exceeding level alpha and the probability of at least m Type II errors not greater than beta. This generalization of the classical notions of familywise error rates allows substantial reduction of the expected sample size of the multiple testing procedure. (C) 2014 Elsevier B.V. All rights reserved.