Aida Haro, Hayashi Kenichi, Takeuchi Ayano, Sugiyama Daisuke, Okamura Tomonori
Graduate School of Science and Technology, Keio University, Yokohama 223-0061, Japan.
Department of Mathematics, Keio University, Yokohama 223-0061, Japan.
Healthcare (Basel). 2022 Jul 25;10(8):1383. doi: 10.3390/healthcare10081383.
Survival analysis is a set of methods for statistical inference concerning the time until the occurrence of an event. One of the main objectives of survival analysis is to evaluate the effects of different covariates on event time. Although the proportional hazards model is widely used in survival analysis, it assumes that the ratio of the hazard functions is constant over time. This assumption is likely to be violated in practice, leading to erroneous inferences and inappropriate conclusions. The accelerated failure time model is an alternative to the proportional hazards model that does not require such a strong assumption. Moreover, it is sometimes plausible to consider the existence of cured patients or long-term survivors. The survival regression models in such contexts are referred to as cure models. In this study, we consider the accelerated failure time cure model with frailty for uncured patients. Frailty is a latent random variable representing patients' characteristics that cannot be described by observed covariates. This enables us to flexibly account for individual heterogeneities. Our proposed model assumes a shifted gamma distribution for frailty to represent uncured patients' heterogeneities. We construct an estimation algorithm for the proposed model, and evaluate its performance via numerical simulations. Furthermore, as an application of the proposed model, we use a real dataset, Specific Health Checkups, concerning the onset of hypertension. Results from a model comparison suggest that the proposed model is superior to existing alternatives.
生存分析是一组用于对事件发生前的时间进行统计推断的方法。生存分析的主要目标之一是评估不同协变量对事件时间的影响。尽管比例风险模型在生存分析中被广泛使用，但它假设风险函数的比率随时间恒定。在实际应用中，这一假设很可能被违背，从而导致错误的推断和不恰当的结论。加速失效时间模型是比例风险模型的一种替代方法，它不需要如此强的假设。此外，考虑存在治愈患者或长期幸存者有时是合理的。在这种情况下的生存回归模型被称为治愈模型。在本研究中，我们考虑针对未治愈患者的具有脆弱性的加速失效时间治愈模型。脆弱性是一个潜在随机变量，代表无法通过观察到的协变量描述的患者特征。这使我们能够灵活地考虑个体异质性。我们提出的模型假设脆弱性服从移位伽马分布以表示未治愈患者的异质性。我们为提出的模型构建了一种估计算法，并通过数值模拟评估其性能。此外，作为所提出模型的一个应用，我们使用了一个关于高血压发病的真实数据集“特定健康检查”。模型比较的结果表明，所提出的模型优于现有的替代模型。
