Estimation of covariate effects on net survivals in the relative survival progressive illness-death model

Recently, there has been a lot of development in relative survival field. In the absence of data on the cause of death, the research has tended to focus on the estimation of survival probability of a cancer (as a disease of interest). In many cancers, one nonfatal event that decreases the survival probability can occur. There are a few methods that assess the role of prognostic factors for multiple types of clinical events while dealing with uncertainty about the cause of death. However, these methods require proportional hazard or Markov assumptions. In practice, one or both of these assumptions might be violated. Violation of the proportional hazard assumption can lead to estimates that are biased, and difficult to interpret and violation of Markov assumption results in inconsistent estimators. In this work, we propose a semi-parametric approach to estimate the possibly time-varying regression coefficients in the likely non-Markov relative survival progressive illness-death model. The performance of the proposed estimator is investigated through simulations. We illustrate our approach using data from a study on rectal cancer resected for cure conducted in two French population-based digestive cancer registries.