Monitoring a general class of two-sample survival statistics with applications

This paper considers a general class of statistics for testing the equality of two survival distributions in clinical trials with sequential monitorin g. The tests can be expressed as Lebesgue-Stieltjes integrals of a weight f unction with respect to the difference between two survival distributions. Prominent members of this class include the two-sample difference in Kaplan -Meier estimates, the test of medians (Brookmeyer & Crowley, 1982), a trunc ated version of Efron's (1967) test and the Pepe-Fleming statistic (Pepe & Fleming, 1989, 1991). Statistics in this class are shown to converge to a G aussian process, indexed by information time, under both null and local alt ernatives even if different statistics are used at different information ti mes. Properly standardised, statistics in a subclass converge to Gaussian p rocesses with independent increments so that the usual group sequential tec hniques for monitoring a clinical trial can be applied. The design of a tri al comparing two treatments with respect to mother-to-newborn transmission of HIV is used to illustrate practical aspects of monitoring.