Estimation of the additive hazards model with case [formula omitted] interval-censored failure time data in the presence of informative censoring

Abstract

The additive hazards model is one of the most commonly used model in regression analysis of failure time data and many estimation procedures have been developed for its inference under various situations (Kalbfleisch and Prentice (2002); Lin and Ying (1994); Sun (2006)). In this paper, we consider a situation, case K interval-censored data with informative interval censoring, that often occurs in practice such as medical follow-up studies but has not been discussed much in the literature due to the difficulties involved. For the problem, a joint model is proposed to describe the correlation between the failure time of interest and the underlying censoring or observation process and a sieve maximum likelihood approach is developed. In particular, an EM algorithm is presented for the implementation of the proposed estimation procedure and the asymptotic properties of the resulting estimators are established. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that it works well for practical situations. Also the method is applied to an AIDS study that motivated this study.