Composite partial likelihood estimation for length-biased and right-censored data with competing risks

This paper considers a competing risks model for survival data from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a composite partial likelihood estimating procedure for cause-specific failure probabilities using competing risks data. We establish the asymptotic properties of the proposed estimators, and present predictions of the cumulative incidence functions. Furthermore, we show how to construct simultaneous confidence bands for the cause-specific cumulative incidence functions for subjects with given risk factors. A simulation study demonstrates that the proposed estimators have good finite-sample performance. A real data example illustrates the method and the theory.