Semiparametric maximum likelihood estimation for the Cox model with length-biased survival data

Right censored survival data collected on a prevalent cohort with constant incidence rate are termed as length-biased survival data. In this paper, we consider semiparametric estimation for the Cox proportional hazards model with length-biased survival data. Utilizing the special structure of length-biased sampling, we give the semiparametric maximum likelihood estimators for the regression parameter and cumulative hazard function. The estimators are shown to be consistent and asymptotically normal, and the limiting variance of the regression parameter estimator achieves the semiparametric efficiency bound. The asymptotic variance of the estimators can be estimated consistently. Simulation studies show the proposed semiparametric maximum likelihood estimator is more efficient than existing estimators in the literature. An analysis of the prevalent data from Canadian Study of Health and Aging (CSHA) illustrates the proposed method.