Versatile tests for comparing survival curves based on weighted logrank statistics

The logrank test is perhaps the most commonly used nonparametric method for comparing two survival curves and yields maximum power under proportional hazards (PH) alternatives. While PH is a reasonable assumption, it need not, of course, hold. Several authors have therefore developed versatile tests using combinations of weighted logrank statistics that are more sensitive to non-PH hazards. For example, Fleming and Harrington (1991) considered the family of G(rho) statistics, while JW Lee (1996) and S-H Lee (2007) proposed tests based on the more extended G(rho, gamma) family. In this talk we consider Zm=max(|Z1|,|Z2|,|Z3|), where Z1, Z2, and Z3 are z-statistics obtained from G(0,0), G(1,0), and G(0,1) tests, respectively. G(0,0) corresponds to the logrank test while G(1,0) and G(0,1) are more sensitive to early and late difference alternatives. Simulation results indicate that the method based on Zm maintains the type I error rate, provides increased power relative to the logrank test under early and late difference alternatives, and entails only a small to moderate power loss compared to the more optimally chosen test. The syntax for a Stata command to implement the method, verswlr, is described, and the user can specify other choices for rho and gamma.