A Nonparametric Multiple Imputation Approach for Survival Data Subject to Informative Censoring

Abstract

Most existing survival analysis methods work under the assumption that censoring times are independent of failure times. When censoring is informative of failure times, those methods will produce biased survival estimates. We have developed a nonparametric multiple imputation approach that uses the estimated correlation between failure and censoring times to impute missing failure times for every censored observation. A sensitivity analysis shows the efficacy of the imputation approach by comparing survival estimates of the imputed data sets to estimates from data where all failure times are known. Dependence between the failure and censoring data is then induced using a shared frailty model. Parametric assumptions of failure and censoring times are applied allowing for the dependence parameter to be estimated using the EM algorithm. The dependence parameter is used to create an imputing risk set for each censored observation. A Kaplan-Meier survival curve is then fit to the imputing risk set to impute a failure time from this set for the censored observation. Traditional Kaplan-Meier estimation is performed on the imputed data sets to estimate survival. The method is then extended using a Cox proportional hazards model to include auxiliary variables in the dependence parameter estimation. Simulations along with results using the ACTG-175 clinic trial HIV data set are presented for each approach.