Department of Statistics, Kangwon National University, Chuncheon, Gangwon, Korea.
Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA.
Stat Med. 2022 Sep 10;41(20):3941-3957. doi: 10.1002/sim.9485. Epub 2022 Jun 7.
In the analysis for competing risks data, regression modeling of the cause-specific hazard functions has been usually conducted using the same time scale for all event types. However, when the true time scale is different for each event type, it would be appropriate to specify regression models for the cause-specific hazards on different time scales for different event types. Often, the proportional hazards model has been used for regression modeling of the cause-specific hazard functions. However, the proportionality assumption may not be appropriate in practice. In this article, we consider the additive risk model as an alternative to the proportional hazards model. We propose predictions of the cumulative incidence functions under the cause-specific additive risk models employing different time scales for different event types. We establish the consistency and asymptotic normality of the predicted cumulative incidence functions under the cause-specific additive risk models specified on different time scales using empirical processes and derive consistent variance estimators of the predicted cumulative incidence functions. Through simulation studies, we show that the proposed prediction methods perform well. We illustrate the methods using stage III breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute.
在竞争风险数据分析中，通常使用相同的时间尺度对所有事件类型进行特定原因的危险函数回归建模。然而，当每种事件类型的真实时间尺度不同时，为不同事件类型的特定原因危险函数指定不同时间尺度的回归模型是合适的。通常，比例风险模型已用于特定原因危险函数的回归建模。然而，在实践中，比例假设可能并不合适。在本文中，我们将加性风险模型视为比例风险模型的替代模型。我们考虑了针对不同事件类型使用不同时间尺度的特定原因加性风险模型的累积发生率函数的预测。我们使用经验过程建立了在不同时间尺度下指定的特定原因加性风险模型下预测的累积发生率函数的一致性和渐近正态性，并推导出预测的累积发生率函数的一致方差估计量。通过模拟研究，我们表明所提出的预测方法表现良好。我们使用从国家癌症研究所的监测、流行病学和最终结果（SEER）计划获得的 III 期乳腺癌数据说明了这些方法。
