Rondeau V, Filleul L, Joly P
INSERM EMI 0338 (Biostatistic), Université Victor Segalen Bordeaux2, 146 Rue Léo Saignat, Bordeaux Cedex, France.
Stat Med. 2006 Dec 15;25(23):4036-52. doi: 10.1002/sim.2510.
The frailty model is a random effect survival model, which allows for unobserved heterogeneity or for statistical dependence between observed survival data. The nested frailty model accounts for the hierarchical clustering of the data by including two nested random effects. Nested frailty models are particularly appropriate when data are clustered at several hierarchical levels naturally or by design. In such cases it is important to estimate the parameters of interest as accurately as possible by taking into account the hierarchical structure of the data. We present a maximum penalized likelihood estimation (MPnLE) to estimate non-parametrically a continuous hazard function in a nested gamma-frailty model with right-censored and left-truncated data. The estimators for the regression coefficients and the variance components of the random effects are obtained simultaneously. The simulation study demonstrates that this semi-parametric approach yields satisfactory results in this complex setting. In order to illustrate the MPnLE method and the nested frailty model, we present two applications. One is for modelling the effect of particulate air pollution on mortality in different areas with two levels of geographical regrouping. The other application is based on recurrent infection times of patients from different hospitals. We illustrate that using a shared frailty model instead of a nested frailty model with two levels of regrouping leads to inaccurate estimates, with an overestimation of the variance of the random effects. We show that even when the frailty effects are fairly small in magnitude, they are important since they alter the results in a systematic pattern.
脆弱模型是一种随机效应生存模型，它允许存在未观察到的异质性或观察到的生存数据之间的统计依赖性。嵌套脆弱模型通过纳入两个嵌套随机效应来考虑数据的层次聚类。当数据自然地或通过设计在几个层次水平上聚类时，嵌套脆弱模型特别适用。在这种情况下，考虑数据的层次结构尽可能准确地估计感兴趣的参数非常重要。我们提出一种最大惩罚似然估计（MPnLE）方法，用于在具有右删失和左截断数据的嵌套伽马脆弱模型中对连续风险函数进行非参数估计。同时获得回归系数和随机效应方差分量的估计值。模拟研究表明，这种半参数方法在这种复杂情况下能产生令人满意的结果。为了说明MPnLE方法和嵌套脆弱模型，我们给出两个应用实例。一个是对不同地区细颗粒物空气污染对死亡率的影响进行建模，该地区有两级地理分组。另一个应用实例基于不同医院患者的反复感染时间。我们说明，使用共享脆弱模型而非具有两级分组的嵌套脆弱模型会导致估计不准确，随机效应方差会被高估。我们表明，即使脆弱效应的量级相当小，它们也很重要，因为它们会以系统的方式改变结果。
