Semiparametric varying-coefficient model with right-censored and length-biased data

The analysis of right-censored and length-biased data is commonly encountered in prevalent cohort studies. The special structure of length-biased data is different from the structure of traditional survival data and the methods for traditional survival data cannot be directly applied to length-biased data, because the assumption of independent censoring is often violated in the presence of biased sampling and the assumed model for the underlying population is no longer satisfied. In this paper, we propose a flexible semiparametric varying-coefficient model for analyzing the covariate effects on the population survival time under length-biased sampling. To estimate the parameters, we develop a three-stage estimation procedure, which can improve the efficiency of the estimators. In addition to the case where the censoring variable is independent of the covariates, we consider the case where the censoring variable depends on covariates. The asymptotic properties of the proposed estimators are derived under regularity conditions, and a resampling procedure is used to confirm the methods through simulations. Finally, we illustrate the methods using data concerning the Academy Awards.