Semiparametric sieve maximum likelihood estimation for accelerated hazards model with interval-censored data

Abstract

Interval censored data arise from many clinical studies when the failure event cannot be directly observed. Methods developed in the literature for semiparametric regression analysis of such data are mainly based on common survival models, such as the proportional hazards, proportional odds and accelerated failure time models. As an alternative, the accelerated hazards (AH) model is of great practical interest for modeling survival data in some situations for which those conventional models would be inappropriate. However, inference in the AH model is particularly challenging due to the fact that the stochastic order of the observations depends on the finite dimensional parameters in the model. In this paper, we propose a sieve maximum likelihood estimation procedure based on polynomial splines for the AH model with interval censored data and develop a two-step maximization algorithm for its implementation. We establish large sample properties of the resulting estimator and evaluate its finite sample performance through simulation studies. For illustration purpose, the proposed method is applied to analysis of diabetes conversion data collected from an intervention study of individuals at high risk of developing diabetes.