Survival Analysis USing Auxiliary Variables Via Nonparametric Multiple Imputation

We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variables to recover information for censored observations. To conduct the imputation, we use two working proportional hazards models to define an imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, two nonparametric multiple imputation models are considered: a risk set imputation, and a Kaplan-Meier imputation. For both methods a future event or censoring time is imputed for each censoring observation. In a situation with a categorical auxiliary variable, we show that with a large number of imputes the estimates from the Kaplan-Meier imputation method correspond to the weighted Kaplan-Meier estimator. We also show that the Kaplan-Meier imputation-based method is robust to misspecification of either one of the two working models. In a simulation study with time independent and time dependent auxiliary variables, we show that the use of multiple imputation methods can improve the efficiency of estimators and reduce bias due to dependent censoring. The Kaplan-Meier imputation method is shown to outperform the risk-set imputation approach. We apply the approach to AIDS clinical trial data comparing ZDV and placebo, in which CD4 count in the time-dependent auxiliary variable.