Robust covariate-adjusted logrank tests

In testing for significance of treatment effect within two-sample censored survival data with measured covariates, it is known (Tsiatis, Rosner & Tritchler, 1985) that adjusting the logrank test statistic using a proportional-hazards model for covariate effect can substantially increase efficiency. Extending the robust score statistics described by Lin & Wei (1989), we show how to estimate and optimise the relative efficiencies of such score statistics based on various possible working models, providing a flexible and statistically valid two-sample testing methodology which improves upon the purely nonparametric logrank without sacrificing model robustness. Numerical calculations indicate some nonproportional-hazard settings within which the power of the logrank is erratic while the tests described here have reliably good power.