On semiparametric accelerated failure time models with time‐varying covariates: A maximum penalised likelihood estimation

Abstract

The accelerated failure time (AFT) model offers an important and useful alternative to the conventional Cox proportional hazards model, particularly when the proportional hazards assumption for a Cox model is violated. Since an AFT model is basically a log‐linear model, meaningful interpretations of covariate effects on failure times can be made directly. However, estimation of a semiparametric AFT model imposes computational challenges even when it only has time‐fixed covariates, and the situation becomes much more complicated when time‐varying covariates are included. In this paper, we propose a penalised likelihood approach to estimate the semiparametric AFT model with right‐censored failure time, where both time‐fixed and time‐varying covariates are permitted. We adopt the Gaussian basis functions to construct a smooth approximation to the nonparametric baseline hazard. This model fitting method requires a constrained optimisation approach. A comprehensive simulation study is conducted to demonstrate the performance of the proposed method. An application of our method to a motor neuron disease data set is provided.