A tutorial on frailty models

被引:147
|
作者
Balan, Theodor A. [1 ]
Putter, Hein [1 ]
机构
[1] Leiden Univ, Dept Biomed Data Sci, Med Ctr, POB 9600, NL-2300 RC Leiden, Netherlands
关键词
Correlated failure times; frailty models; random effects models; survival analysis; unobserved heterogeneity; RECURRENT EVENTS; SURVIVAL MODELS; MAXIMUM-LIKELIHOOD; PERIOPERATIVE CHEMOTHERAPY; HETEROGENEOUS POPULATIONS; EUROPEAN ORGANIZATION; REGRESSION-MODEL; BREAST-CANCER; COX MODEL; FAILURE;
D O I
10.1177/0962280220921889
中图分类号
R19 [保健组织与事业(卫生事业管理)];
学科分类号
摘要
The hazard function plays a central role in survival analysis. In a homogeneous population, the distribution of the time to event, described by the hazard, is the same for each individual. Heterogeneity in the distributions can be accounted for by including covariates in a model for the hazard, for instance a proportional hazards model. In this model, individuals with the same value of the covariates will have the same distribution. It is natural to think that not all covariates that are thought to influence the distribution of the survival outcome are included in the model. This implies that there is unobserved heterogeneity; individuals with the same value of the covariates may have different distributions. One way of accounting for this unobserved heterogeneity is to include random effects in the model. In the context of hazard models for time to event outcomes, such random effects are called frailties, and the resulting models are called frailty models. In this tutorial, we study frailty models for survival outcomes. We illustrate how frailties induce selection of healthier individuals among survivors, and show how shared frailties can be used to model positively dependent survival outcomes in clustered data. The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to hazards and survival functions observed in a population. Available software, mainly in R, will be discussed, and the use of frailty models is illustrated in two different applications, one on center effects and the other on recurrent events.
引用
收藏
页码:3424 / 3454
页数:31
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