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.

翻译：加速失效时间模型常用于生存数据建模。该方法具有吸引力，因为它量化了事件发生时间与多种协变量之间的直接关系，并断言当存在这些协变量时，失效时间会通过乘性因子经历加速或减速。尽管现有文献提供了多种适用于时间固定协变量的加速失效时间模型拟合方法，但将这些方法推广至同时包含时间变化协变量和部分区间删失数据的情形仍具挑战性。本文提出一种最大惩罚似然方法以拟合半参数加速失效时间模型。该方法专为带有部分区间删失失效时间的生存数据设计，可同时处理时间固定和时间变化协变量。我们利用高斯基函数构建非参数基准风险的平滑近似，并通过约束优化方法拟合模型。为验证所提方法的有效性，我们开展了全面的模拟研究，并在晚期黑色素瘤患者的随机临床试验数据集上实现了该方法。