On hazard-based penalized likelihood estimation of accelerated failure time model with partly interval censoring

In survival analysis, the semiparametric accelerated failure time model is an important alternative to the widely used Cox proportional hazard model. The existing methods for accelerated failure time models include least-squares, log rank-based estimating equations and approximations to the nonparametric error distribution. In this paper, we propose another fitting method for the accelerated failure time model, formulated from the hazard function of the exponential error term. Our method can handle partly interval-censored data which contains event time, as well as left, right and interval censoring time. We adopt the maximum penalized likelihood method to estimate all the parameters in the model, including the nonparametric component. The penalty function is used to regularize the nonparametric component of the accelerated failure time model. Asymptotic properties of the penalized likelihood estimate are developed. A simulation study is conducted to investigate the performance of the proposed method and an application of this method to an AIDS study is presented as an example.