Nonparametric estimation in an illness‐death model with component‐wise censoring

In disease settings where study participants are at risk for death and a serious nonfatal event, composite endpoints defined as the time until the earliest of death or the nonfatal event are often used as the primary endpoint in clinical trials. In practice, if the nonfatal event can only be detected at clinic visits and the death time is known exactly, the resulting composite endpoint exhibits “component‐wise censoring.” The standard method used to estimate event‐free survival in this setting fails to account for component‐wise censoring. We apply a kernel smoothing method previously proposed for a marker process in a novel way to produce a nonparametric estimator for event‐free survival that accounts for component‐wise censoring. The key insight that allows us to apply this kernel method is thinking of nonfatal event status as an intermittently observed binary time‐dependent variable rather than thinking of time to the nonfatal event as interval‐censored. We also propose estimators for the probability in state and restricted mean time in state for reversible or irreversible illness‐death models, under component‐wise censoring, and derive their large‐sample properties. We perform a simulation study to compare our method to existing multistate survival methods and apply the methods on data from a large randomized trial studying a multifactor intervention for reducing morbidity and mortality among men at above average risk of coronary heart disease.