A two-stage sequential design and analysis for comparing binomial rates with possibly random dropouts

Many clinical trials involve two-stage sequential designs with one interim analysis (Elashoff and Reedy, 1984, Biometrics 41, 791-795.) In this paper we present a situation where events are counted only at two fixed calendar time points and some patients may dropout during the time intervals. In the two-stage case, naive application of Tsiatis’s (1984, JASA 77, 855-861) logrank and Wilcoxon tests, which are for continuous survival time, is shown to lead to conservative type-I error rates and lower power. The two-stage sequential boundaries can also be calculated directly, rather than by simulation as was done by DeMets and Gail (1985, Biometrics 41, 1039-1044) with the assumption of some survival models, and are shown to be more flexible than the Pocock (1977, Biometrika 64, 191-199) and O’Brien-Fleming (1983, Biometrics 35, 549-556) boundaries since the former do not require an assumption on the correlation of the test statistics for the two stages. Repeated confidence intervals are also discussed. The design and approach are motivated by clinical trials studying treatment effects on vertebral fracture rates in elderly osteoporotic women. An example (Tilyard, et al. New England Journal of Medicine, 1992) is given to illustrate the method.