Nonparametric covariate adjustment in estimating hazard ratios

In randomized clinical trials with time-to-event outcomes, the hazard ratio is commonly used to quantify the treatment effect relative to a control. The Cox regression model is commonly used to adjust for relevant covariates to obtain more accurate estimates of the hazard ratio between treatment groups. However, it is well known that the treatment hazard ratio based on a covariate-adjusted Cox regression model is conditional on the specific covariates and differs from the unconditional hazard ratio that is an average across the population. Therefore, covariate-adjusted Cox models cannot be used when the unconditional inference is desired. In addition, the covariate-adjusted Cox model requires the relatively strong assumption of proportional hazards for each covariate. To overcome these challenges, a nonparametric randomization-based analysis of covariance method was proposed to estimate the covariate-adjusted hazard ratios for multivariate time-to-event outcomes. However, empirical evaluations of the performance (power and type I error rate) of the method have not been studied. Although the method is derived for multivariate situations, for most registration trials, the primary endpoint is a univariate outcome. Therefore, this approach is applied to univariate outcomes, and performance is evaluated through a simulation study in this paper. Stratified analysis is also investigated. As an illustration of the method, we also apply the covariate-adjusted and unadjusted analyses to an oncology trial.