Study design for a three-arm equivalence clinical trial with binomially distributed outcomes.

Equivalence in a clinical trial may be assessed through a three-arm trial (test drug, reference drug, and placebo). A three-arm equivalence trial consists of three hypothesis tests in practice, with two hypothesis tests demonstrating the superiority of the test and reference drugs against placebo, and the other one demonstrating the equivalence of the test and reference drugs. When designing a three-arm equivalence clinical trial, the practitioner should minimize the chances that a test drug will be found to be equivalent to the reference drug but non-superior to the placebo. One way to minimize these chances at the design stage, for a three-arm equivalence trial with a binary primary outcome, is to test the equivalence through hypotheses based upon the ratio of the differences of the proportions. In this article, we derived the test statistics and the power functions based on maximum likelihood estimate (MLE) and restricted MLE for the proposed hypotheses. The required sample size for achieving the desired power at the given significance level can be obtained by solving the power function. We illustrated the proposed design through an example and investigated the required sample sizes for various conditions.

A useful design utilizing the information fraction in a group sequential clinical trial with censored survival data.

Lan and DeMets (1983) proposed the alpha spending function for group sequential trials to permit the use of unspecified frequencies and timings of interim analyses in the trial design. Regarding a trial with censored time to endpoint, Lan and DeMets (1989) later defined information time at an interim analysis in a maximum duration trial. To compare two survival curves utilizing such a design, information times for group sequential logrank and Wilcoxon-type statistics have been developed by assuming that the survival time follows an exponential distribution or a Weibull distribution without considering the censoring distribution. To better address the practical concerns inherent in clinical trials with survival endpoints, we present a new approach to adequately design a group sequential trial using the Harrington-Fleming (1982) test based on our proposed information fractions by assuming the censoring distribution depends on the patient's accrual time according to various entry distributions and by extending the underlying survival distribution to the generalized gamma distribution. We also determine associated sample sizes, expected number of events and expected stopping time. Two phase III trials of non-small-cell lung cancer originally designed using fixed-sample tests are utilized to illustrate the potential advantages of using a group sequential design with the proposed approach. This enhanced method facilitates the design and analysis of group sequential clinical trials studying survival endpoints by increasing implemental flexibility.