A maximum penalised likelihood approach for semiparametric accelerated failure time models with time-varying covariates and partly interval censoring

Accelerated failure time (AFT) models are frequently used for modelling survival data. This approach is attractive as it quantifies the direct relationship between the time until an event occurs and various covariates. It asserts that the failure times experience either acceleration or deceleration through a multiplicative factor when these covariates are present. While existing literature provides numerous methods for fitting AFT models with time-fixed covariates, adapting these approaches to scenarios involving both time-varying covariates and partly interval-censored data remains challenging. In this paper, we introduce a maximum penalised likelihood approach to fit a semiparametric AFT model. This method, designed for survival data with partly interval-censored failure times, accommodates both time-fixed and time-varying covariates. We utilise Gaussian basis functions to construct a smooth approximation of the nonparametric baseline hazard and fit the model via a constrained optimisation approach. To illustrate the effectiveness of our proposed method, we conduct a comprehensive simulation study. We also present an implementation of our approach on a randomised clinical trial dataset on advanced melanoma patients.