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 α, β, 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 α and the probability of at least m Type II errors not greater than β. This generalization of the classical notions of familywise error rates allows substantial reduction of the expected sample size of the multiple testing procedure.