Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies

Competing risks refer to the situation where there are multiple causes of failure and the occurrence of one type of event prohibits the occurrence of the other types of event or alters the chance to observe them. In large cohort studies with long-term follow-up, there are often competing risks. When the failure events are rare, or the information on certain risk factors is difficult or costly to measure for the full cohort, a case-cohort study design can be a desirable approach. In this paper, we consider a semiparametric proportional subdistribution hazards model in the presence of competing risks in case-cohort studies. The subdistribution hazards function, unlike the cause-specific hazards function, gives the advantage of outlining the marginal probability of a particular type of event. We propose estimating equations based on inverse probability weighting techniques for the estimation of the model parameters. In the estimation methods, we considered a weighted availability indicator to properly account for the case-cohort sampling scheme. We also proposed a Breslow-type estimator for the cumulative baseline subdistribution hazard function. The resulting estimators are shown, using empirical processes and martingale properties, to be consistent and asymptotically normally distributed. The performance of the proposed methods in finite samples are examined through simulation studies by considering different levels of censoring and event of interest percentages. The simulation results from the different scenarios suggest that the parameter estimates are reasonably close to the true values of the respective parameters in the model. Finally, the proposed estimation methods are applied to a case-cohort sample from the Sister Study, in which we illustrated the proposed methods by studying the association between selected CpGs and invasive breast cancer in the presence of ductal carcinoma in situ as competing risk.