Competing risks often arise where more than one event compete with each other for a subject. The cumulative incidence function is a proper summary quantity for analyzing competing risks data. In epidemiologic cohort studies, case-cohort study design has been widely used to evaluate the effects of covariates on failure times when the occurrence of the failure event is rare. In this dissertation, we introduce the semiparametric model for the cumulative incidence function by allowing some covariates to have missing values. Missing pattern follows the case-cohort study design in the form of two-phase sampling. The estimation procedure is based on the direct binomial regression method, which enables us to evaluate the effects of the covariates directly under the competing risks data. We develop an estimating equation for the semiparametric missing model by using the inverse probability weighted of complete case method. However, the IPW method loses the efficiency because it uses only complete data of subjects. To overcome this difficulty, we also propose an estimating equation for the semiparametric model by using augmented inverse probability of complete case method. The AIPW method is doubly robust and it can improve efficiency. The asymptotic properties of the proposed IPW and AIPW estimators are established. The finite-sample properties of those estimators are investigated by the simulation studies. The proposed estimating methods are applied to analyze data from the RV144 vaccine efficacy trial.