Complex diseases can often be further analyzed using disease subtypes classified by multiple biomarkers to study pathogenic heterogeneity. In this article, we consider a weighted Cox proportional hazard model to evaluate the effect of exposures on various disease subtypes under the competing-risk settings in the presence of partially or completely missing biomarkers. We derive asymptotic properties of an augmented inverse probability weighted estimating equation method with a general pattern of missingness. Simulation studies are conducted to demonstrate doubly robustness of the estimators. For illustration, we apply this method to examine an association between smoke status and colorectal cancer subtypes defined by 3 molecular biomarkers in the Nurses' Health Study cohort.