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 monitoring. The tests can be expressed as Lebesgue-Stieltjes integrals of a weight function 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 truncated 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 Gaussian process, indexed by information time, under both null and local alternatives even if different statistics are used at different information times. Properly standardised, statistics in a subclass converge to Gaussian processes with independent increments so that the usual group sequential techniques for monitoring a clinical trial can be applied. The design of a trial comparing two treatments with respect to mother-to-newborn transmission of HIV is used to illustrate practical aspects of monitoring.