Robustness of sample size re-estimation procedure in clinical trials (arbitrary populations)

In clinical trials, one of the main questions that is being asked is how many additional observations, if any, are needed beyond those originally planned. In a two-treatment double-blind clinical experiment, one is interested in testing the null hypothesis of equality of the means against one-sided alternative when the common variance sigma2 is unknown. We wish to determine the required total sample size when the error probabilities alpha and beta are specified at a predetermined alternative. Shih provided a two-stage procedure which is an extension of Stein's one-sample procedure, assuming normal response. He estimates sigma2 by the method of maximum likelihood via the EM algorithm and carries out a simulation study in order to evaluate the effective level of significance and the power. The author proposed a closed-form estimator for sigma2 and showed analytically that the difference between the effective and nominal levels of significance is negligible and that the power exceeds 1-beta when the initial sample size is large. Here we consider responses from arbitrary distributions in which the mean and the variance are not functionally related and show that when the initial sample size is large, the conclusions drawn previously by the author still hold. The effective coverage probability of a fixed-width interval is also evaluated. Proofs of certain assertions are deferred to the Appendix.