Nonparametric analysis of covariance for hypothesis testing with logrank and Wilcoxon scores and survival-rate estimation in a randomized clinical trial.

Many clinical trials have time-to-event variables as principal response criteria. When adjustment for covariates is of some importance, the relative role of methods for such analysis may be of some concern. For the Wilcoxon and logrank tests, there is an issue of how covariance adjustment can be nonparametric in the sense of not involving any further assumptions beyond those of the logrank and Wilcoxon test. Also of particular interest in a clinical trial is the estimation of the difference between survival probabilities for the treatment groups at several points in time. As with the Wilcoxon and logrank tests, there is no well known nonparametric way to incorporate covariate adjustment into such estimation of treatment effects for survival rates. We propose a method that enables covariate adjustment for hypothesis testing with logrank or Wilcoxon scores. Related extensions for applying covariate adjustment to estimation of treatment effects are provided for differences in survival-rate counterparts to Kaplan-Meier survival rates. The results represent differences in population average survival rates with adjustment for random imbalance of covariates between treatment groups. The methods are illustrated with a clinical trial example.