The Versatility of Function-Indexed Weighted Log-Rank Statistics

Two-sample weighted log-rank statistics are used in the presence of right censoring to test whether failure times from two populations have different survival distributions. Kosorok has 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 article we develop a Monte Carlo method for accurately obtaining these p values, and we evaluate the moderate sample size properties of this method and 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 Beta-Blocker Heart Attack Trial (BHAT). The results of this article 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.