Doubly robust inference procedure for relative survival ratio in population‐based cancer registry data

Cancer registry system has been playing important roles in research and policy making in cancer control. In general, information on cause of death is not available in cancer registry data. To make inference on survival of cancer patients in the absence of cause of death information, the relative survival ratio is widely used in the population‐based cancer research utilizing external life tables for the general population. Another difficulty arising in analyzing cancer registry data is informative censoring. In this article, we propose a doubly robust inference procedure for the relative survival ratio under a certain type of informative censoring, called the covariate‐dependent censoring. The proposed estimator is doubly robust in the sense that it is consistent if at least one of the regression models for the time‐to‐death and for the censoring time is correctly specified. Furthermore, we introduced a doubly robust test assessing underlying conditional independence assumption between the time‐to‐death and the censoring time. This test is model based, but is doubly robust in the sense that at least one of the models for the time to event and for the censoring time is correctly specified, it maintains its nominal significance level. This notable feature entails us to make inference on cancer registry data relying on assumptions, which are much weaker than the existing methods and are verifiable empirically. We examine the theoretical and empirical properties of our proposed methods by asymptotic theory and simulation studies. We illustrate the proposed method with cancer registry data in Osaka, Japan.