Doubly robust estimator for net survival rate in analyses of cancer registry data

Cancer population studies based on cancer registry databases are widely conducted to address various research questions. In general, cancer registry databases do not collect information on cause of death. The net survival rate is defined as the survival rate if a subject would not die for any causes other than cancer. This counterfactual concept is widely used for the analyses of cancer registry data. Perme, Stare, and Estève (2012) proposed a nonparametric estimator of the net survival rate under the assumption that the censoring time is independent of the survival time and covariates. Kodre and Perme (2013) proposed an inverse weighting estimator for the net survival rate under the covariate-dependent censoring. An alternative approach to estimating the net survival rate under covariate-dependent censoring is to apply a regression model for the conditional net survival rate given covariates. In this article, we propose a new estimator for the net survival rate. The proposed estimator is shown to be doubly robust in the sense that it is consistent at least one of the regression models for survival time and for censoring time. We examine the theoretical and empirical properties of our proposed estimator by asymptotic theory and simulation studies. We also apply the proposed method to cancer registry data for gastric cancer patients in Osaka, Japan.