School of Mathematical and Physical Sciences, Macquarie University, Sydney, Australia.
Stat Med. 2023 Dec 30;42(30):5577-5595. doi: 10.1002/sim.9926. Epub 2023 Oct 16.
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.
加速失效时间 (AFT) 模型为传统 Cox 比例风险模型提供了一种重要且有用的替代方法，特别是当 Cox 模型的比例风险假设不成立时。由于 AFT 模型本质上是一种对数线性模型，因此可以直接对失效时间上的协变量效应进行有意义的解释。然而，即使 AFT 模型仅具有时间固定的协变量，估计半参数 AFT 模型也会带来计算上的挑战，而当包含时变协变量时，情况会变得更加复杂。在本文中，我们提出了一种惩罚似然方法来估计具有右删失失效时间的半参数 AFT 模型，其中允许同时存在时间固定和时变协变量。我们采用高斯基函数来构建非参数基线风险的平滑逼近。这种模型拟合方法需要约束优化方法。我们进行了全面的模拟研究来验证所提出方法的性能。还提供了我们的方法在运动神经元疾病数据集上的应用。
