Weighting estimation in the cause‐specific Cox regression with partially missing causes of failure

Complex diseases are often analyzed using disease subtypes classified by multiple biomarkers to study pathogenic heterogeneity. In such molecular pathological epidemiology research, we consider a weighted Cox proportional hazard model to evaluate the effect of exposures on various disease subtypes under competing‐risk settings in the presence of partially or completely missing biomarkers. The asymptotic properties of the inverse and augmented inverse probability‐weighted estimating equation methods are studied with a general pattern of missing data. Simulation studies have been conducted to demonstrate the double robustness of the estimators. For illustration, we applied this method to examine the association between pack‐years of smoking before the age of 30 and the incidence of colorectal cancer subtypes defined by a combination of four tumor molecular biomarkers (statuses of microsatellite instability, CpG island methylator phenotype, BRAF mutation, and KRAS mutation) in the Nurses' Health Study cohort.