Semiparametric accelerated failure time models with time-varying covariates under partly interval censoring

In survival analysis, accelerated failure time (AFT) models are often used as an alternative to the Cox model. A benefit of the AFT model is that it provides a direct link between covariates and event times, and therefore offers meaningful interpretations of the regression coefficients directly on the event times. This paper is motivated by a randomised clinical trial dataset on advanced melanoma patients, in which the event times are interval-censored and one of the covariates in the model is time-varying. To allow direct assessment of the effects of covariates on the event time, we aim to fit an AFT model. However, there are no readily available computational packages for AFT models with time-varying covariates and interval censoring. In this paper, we propose a maximum penalised likelihood approach for fitting such models. The effectiveness of our method is demonstrated through extensive simulations. Also, an application to the above mentioned melanoma dataset is used to demonstrate practical utility of our method.