Survival Analysis Using Auxiliary Variables Via Nonparametric Multiple Imputation

Chiu-Hsieh Hsu, University of Arizona
Jeremy Taylor, University of Michigan
Susan Murray, University of Michigan Biostatistics
Daniel Commenges, INSERM


We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variable to recover information for censored observations. To conduct the imputation, we use two working survival model to define the nearest neighbor 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 methods are considered: risk set imputation, and Kaplan-Meier estimator. For both methods a future event or censoring time is imputed for each censored observation. 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 method is robust to misspecification of either one of the two working models. In a simulation study with the time independent and time dependent auxiliary variables, we compare the multiple imputation approaches with an inverse probability of censoring weighted method. We show that all approaches can reduce bias due to dependent censoring and improve the efficiency. We apply the approaches to AIDS clinical trial data comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable.