Abstract:

In clinical trials comparing therapeutic interventions, a subject may experience distinct types of events. We consider the problem of estimating the transition functions for a semi-competing risks model under illness-death model framework. We propose to estimate the intensity functions by maximizing a B-spline based sieve likelihood. The method yields smooth estimates without parametric assumptions. This approach also permits direct computation of the variance of parameters using the inverse of the Hessian matrix. Under some mild conditions, the estimators are shown to be strongly consistent; the convergence rate of the estimator for transition function is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real data set is used to illustrate our approach.