Nonparametric comparison of two survival functions with dependent censoring via nonparametric multiple imputation

When the event time of interest depends on the censoring time, conventional two-sample test methods, such as the log-rank and Wilcoxon tests, can produce an invalid test result. We extend our previous work on estimation using auxiliary variables to adjust for dependent censoring via multiple imputation, to the comparison of two survival distributions. To conduct the imputation, we use two working models to define a set of similar observations called the imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, a nonparametric multiple imputation method, Kaplan-Meier imputation, is used to impute a future event or censoring time for each censored observation. After imputation, the conventional nonparametric two-sample tests can be easily implemented on the augmented data sets. Simulation studies show that the sizes of the log-rank and Wilcoxon tests constructed on the imputed data sets are comparable to the nominal level and the powers are much higher compared with the tests based on the unimputed data in the presence of dependent censoring if either one of the two working models is correctly specified. The method is illustrated using AIDS clinical trial data comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable.