Semiparametric sieve estimation for survival data with two-layer censoring

SummaryDisease registry data provide important information on the progression of disease conditions. However, reports of death or drop-out of patients enrolled in the registry are always subject to a noticeable delay. Reporting delays, together with the administrative censoring that arises from a freeze date in data collection, lead to two layers of right censoring in the data. The first layer results from random drop-out and acts on the survival time. The second layer is the administrative censoring, which acts on the sum of the reporting delay and the minimum of the survival time and random drop-out time. The heterogeneities among patients further complicate data analysis. This paper proposes a novel semiparametric sieve method based on phase-type distributions, in which covariates can be readily accommodated by the accelerated failure time model. A well-orchestrated EM algorithm is developed to compute the sieve maximum likelihood estimator. We establish the consistency and rate of convergence of the proposed sieve estimators, as well as the asymptotic normality and semiparametric efficiency of the estimators for the regression parameters. Comprehensive simulations and a real example of lung cancer registry data are used to demonstrate the proposed method. The results reveal substantial biases if reporting delays are overlooked.