An Approximate Likelihood Procedure for Competing Risks Data

Parametric estimation of cause-specific hazard functions in a competing risks model is considered. An approximate likelihood procedure for estimating parameters of cause-specific hazard functions based on competing risks data subject to right censoring is proposed. In an assumed parametric model that may have been misspecified, an estimator of a parameter is said to be consistent if it converges in probability to the pseudo-true value of the parameter as the sample size becomes large. Under censorship, the ordinary maximum likelihood method does not necessarily give consistent estimators. The proposed approximate likelihood procedure is consistent even if the parametric model is misspecified. An asymptotic distribution of the approximate maximum likelihood estimator is obtained, and the efficiency of the estimator is discussed. Datasets from a simulation experiment, an electrical appliance test, and a pneumatic tire test are used to illustrate the procedure.