Kelly P J, Lim L L
Centre for Clinical Epidemiology and Biostatistics, The University of Newcastle, Level 3, David Maddison Building, Royal Newcastle Hospital, Newcastle, NSW, 2300, Australia.
Stat Med. 2000 Jan 15;19(1):13-33. doi: 10.1002/(sici)1097-0258(20000115)19:1<13::aid-sim279>3.0.co;2-5.
Many extensions of survival models based on the Cox proportional hazards approach have been proposed to handle clustered or multiple event data. Of particular note are five Cox-based models for recurrent event data: Andersen and Gill (AG); Wei, Lin and Weissfeld (WLW); Prentice, Williams and Peterson, total time (PWP-CP) and gap time (PWP-GT); and Lee, Wei and Amato (LWA). Some authors have compared these models by observing differences that arise from fitting the models to real and simulated data. However, no attempt has been made to systematically identify the components of the models that are appropriate for recurrent event data. We propose a systematic way of characterizing such Cox-based models using four key components: risk intervals; baseline hazard; risk set, and correlation adjustment. From the definitions of risk interval and risk set there are conceptually seven such Cox-based models that are permissible, five of which are those previously identified. The two new variant models are termed the 'total time - restricted' (TT-R) and 'gap time - unrestricted' (GT-UR) models. The aim of the paper is to determine which models are appropriate for recurrent event data using the key components. The models are fitted to simulated data sets and to a data set of childhood recurrent infectious diseases. The LWA model is not appropriate for recurrent event data because it allows a subject to be at risk several times for the same event. The WLW model overestimates treatment effect and is not recommended. We conclude that PWP-GT and TT-R are useful models for analysing recurrent event data, providing answers to slightly different research questions. Further, applying a robust variance to any of these models does not adequately account for within-subject correlation.
基于Cox比例风险方法的生存模型已有许多扩展，用于处理聚类或多事件数据。特别值得注意的是五种基于Cox的复发事件数据模型：安徒生和吉尔（AG）模型；魏、林和韦斯费尔德（WLW）模型；普伦蒂斯、威廉姆斯和彼得森的总时间（PWP-CP）模型和间隔时间（PWP-GT）模型；以及李、魏和阿马托（LWA）模型。一些作者通过观察将这些模型应用于真实和模拟数据时出现的差异来比较这些模型。然而，尚未有人尝试系统地识别适用于复发事件数据的模型组成部分。我们提出了一种系统的方法，使用四个关键组成部分来描述此类基于Cox的模型：风险区间；基线风险；风险集和相关性调整。从风险区间和风险集的定义来看，理论上有七种这样的基于Cox的模型是可行的，其中五种是之前已识别的。这两个新的变体模型被称为“总时间受限”（TT-R）模型和“间隔时间无限制”（GT-UR）模型。本文的目的是使用这些关键组成部分来确定哪些模型适用于复发事件数据。这些模型被应用于模拟数据集和一组儿童复发性传染病数据集。LWA模型不适用于复发事件数据，因为它允许一个受试者因同一事件多次处于风险中。WLW模型高估了治疗效果，不建议使用。我们得出结论，PWP-GT和TT-R是分析复发事件数据的有用模型，能为略有不同的研究问题提供答案。此外，对这些模型中的任何一个应用稳健方差都不能充分考虑受试者内部相关性。
