A class of sequential tests for two-sample composite hypotheses

The authors propose a class of statistics based on Rao's score for the sequential testing of composite hypotheses comparing two treatments (populations). Asymptotic approximations of the statistics lead them to propose sequential tests. and to derive their monitoring boundaries. As special cases, they construct sequential versions of the two-sample t-test for normal populations and two-sample z-score tests for binomial populations. The proposed algorithms are simple and easy to compute, as no numerical integration is required. Furthermore, the user can analyze the data at any time regardless of how many inspections have been made. Monte Carlo simulations allow the authors to compare the power and the average stopping time (also known as average sample number) of the proposed tests to those of nonsequential and group sequential tests. A two-armed comparative clinical trial in patients with adult leukemia allows them to illustrate the efficiency of their methods in the case of binary responses.