Proportional hazards models with frailties and random effects
Proportional hazards models with frailties and random effects
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DOI：
10.1002/sim.1259
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发表时间：
2002-11-15
影响因子：
2
通讯作者：
Stare, J
中科院分区：
文献类型：
--
作者：
O'Quigley, J;Stare, J
我们讨论了生存中脆弱性和随机效应模型发展的一些基本概念。这些基本概念之一是脆弱模型的想法，在该模型中，每个受试者都有自己的失败倾向，即他们所谓的脆弱，以及我们希望通过回归来量化的任何影响。尽管个体脆弱性的概念在思考数据是如何产生的或在拟合模型的背景下解释参数估计时可能是有价值的，但我们认为这个概念的实用价值有限。无论何时检测到个体随机效应(弱点)，都可以通过基本模型变换来使其消失。因此，除非我们将某种模型形式视为无懈可击、无懈可击、刻骨铭心，而且如果我们要将“脆弱”一词理解为指个体的随机效应，那么脆弱模型就没有价值了。另一方面，随机效应模型可以用来发挥优势，在随机效应模型中，一组个体共享一些共同的效应。然而，即使在这种情况下，如果我们准备牺牲一些效率，我们也可以通过使用分层比例风险模型已经提供的相当大的能力来避免复杂的建模。分层模型和随机效应模型都可以看作是部分比例风险模型的特例，这一观点提供了进一步的见解。随机效应模型的附加结构被视为具有一些附加的分布约束的分层比例风险模型，对于五个或更多的群体规模，即使附加的假设完全正确，也只能提供适度的效率收益。另一方面，对于中等到大量的规模为2或3的非常小的群体，双胞胎的研究是一个众所周知的例子，随机效应模型的效率收益远远不能忽略不计。对于这样的应用，使用随机效应模型而不是分层模型的理由很充分。考虑到随机效应模型良好的稳健性，这一点尤其明显。尽管如此，基于分层模型的更简单的分析仍然有效，尽管对资源的利用效率较低。版权所有(C)2002 John Wiley Sons，Ltd.
We discuss some of the fundamental concepts underlying the development of frailty and random effects models in survival. One of these fundamental concepts was the idea of a frailty model where each subject has his or her own disposition to failure, their so-called frailty, additional to any effects we wish to quantify via regression. Although the concept of individual frailty can be of value when thinking about how data arise or when interpreting parameter estimates in the context of a fitted model, we argue that the concept is of limited practical value. Individual random effects (frailties), whenever detected, can be made to disappear by elementary model transformation. In consequence, unless we are to take some model form as unassailable, beyond challenge and carved in stone, and if we are to understand the term 'frailty' as referring to individual random effects, then frailty models have no value. Random effects models on the other hand, in which groups of individuals share some common effect, can be used to advantage. Even in this case however, if we are prepared to sacrifice some efficiency, we can avoid complex modelling by using the considerable power already provided by the stratified proportional hazards model. Stratified models and random effects models can both be seen to be particular cases of partially proportional hazards models, a view that gives further insight. The added structure of a random effects model, viewed as a stratified proportional hazards model with some added distributional constraints, will, for group sizes of five or more, provide no more than modest efficiency gains, even when the additional assumptions are exactly true. On the other hand, for moderate to large numbers of very small groups, of sizes two or three, the study of twins being a well known example, the efficiency gains of the random effects model can be far from negligible. For such applications, the case for using random effects models rather than the stratified model is strong. This is especially so in view of the good robustness properties of random effects models. Nonetheless, the simpler analysis, based upon the stratified model, remains valid, albeit making a less efficient use of resources. Copyright (C) 2002 John Wiley Sons, Ltd.