Semiparametric Mixture Cure Model Analysis with Competing Risks Data: Application to Vascular Access Thrombosis Data

The article is motivated by a nephrology study in Taiwan, which enrolled hemodialysis patients who suffered from vascular access thrombosis. After treatment, some patients were cured of thrombosis, while some may experience recurrence of either type (acute or nonacute) of vascular access thrombosis. Our major interest is to estimate the cumulative incidence probability of time to the first recurrence of acute thrombosis after therapy. Since the occurrence of one type of vascular access thrombosis precludes occurrence of the other type, patients are subject to competing risks. To account for the presence of competing risks and cured patients, we develop a mixture model approach to the regression analysis of competing‐risks data with a cure fraction. We make inference about the effects of factors on both the cure rate and cumulative incidence function (CIF) for a failure of interest, which are separately specified in the logistic regression model and semiparametric regression model with time‐varying and time‐invariant effects. Based on two‐stage method, we develop novel estimation equations using the inverse probability censoring weight techniques. The asymptotic properties of the estimators are rigorously studied and the plug‐in variance estimators can be obtained for constructing interval estimators. We also propose a lack‐of‐fit test for assessing the adequacy of the proposed model and several tests for time‐varying effects. The simulation studies and vascular access thrombosis data analysis are conducted to illustrate the proposed method.