The Versatility of Function-indexed Weighted Log-rank Statistics (version 2c) Department of Biostatistics Technical Report 105

Two-sample weighted log-rank statistics are used in the presence of right censoring to test whether failure times from two populations have diierent survival distributions. Kosorok (1998a) showed that large families of these statistics form stochastic processes indexed by weight functions and that these function-indexed statistics can be used to construct versatile test procedures simultaneously sensitive to a wide array of both ordered hazards and stochastic ordering alternatives. The complexity of the asymptotic distribution of these statistics precludes obtaining p-values through analytical means. In this paper, we develop a Monte Carlo method for accurately obtaining these p-values, and we evaluate the moderate sample size properties of this method as well as compare the power of function-indexed statistics with previously developed weighted log-rank tests. These statistics are also examined in a data analysis of the-Blocker Heart Attack Trial (BHAT). The results of this paper demonstrate that the proposed function-indexed procedures can be more powerful for a variety of clinically relevant alternatives than previously described weighted log-rank tests. The authors would like to thank Richard J. Chappell and David L. DeMets for several insightful discussions as well as the editors and referees for several helpful suggestions and comments.