Fitzmaurice G M, Laird N M, Shneyer L
Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston MA 02115, USA.
Stat Med. 2001 Apr 15;20(7):1009-21. doi: 10.1002/sim.718.
This paper considers the mixture model methodology for handling non-ignorable drop-outs in longitudinal studies with continuous outcomes. Recently, Hogan and Laird have developed a mixture model for non-ignorable drop-outs which is a standard linear mixed effects model except that the parameters which characterize change over time depend also upon time of drop-out. That is, the mean response is linear in time, other covariates and drop-out time, and their interactions. One of the key attractions of the mixture modelling approach to drop-outs is that it is relatively easy to explore the sensitivity of results to model specification. However, the main drawback of mixture models is that the parameters that are ordinarily of interest are not immediately available, but require marginalization of the distribution of outcome over drop-out times. Furthermore, although a linear model is assumed for the conditional mean of the outcome vector given time of drop out, after marginalization, the unconditional mean of the outcome vector is not, in general, linear in the regression parameters. As a result, it is not possible to parsimoniously describe the effects of covariates on the marginal distribution of the outcome in terms of regression coefficients. The need to explicitly average over the distribution of the drop-out times and the absence of regression coefficients that describe the effects of covariates on the outcome are two unappealing features of the mixture modelling approach. In this paper we describe a particular parameterization of the general linear mixture model that circumvents both of these problems.
本文考虑了用于处理具有连续结果的纵向研究中不可忽略的失访问题的混合模型方法。最近，霍根和莱尔德开发了一种用于不可忽略失访的混合模型，它是一个标准的线性混合效应模型，只是表征随时间变化的参数也取决于失访时间。也就是说，平均响应在时间、其他协变量和失访时间及其交互作用方面是线性的。混合建模方法处理失访问题的一个关键吸引力在于，相对容易探究结果对模型设定的敏感性。然而，混合模型的主要缺点是通常感兴趣的参数不能直接得到，而是需要对结果分布在失访时间上进行边缘化。此外，尽管对于给定失访时间的结果向量的条件均值假设为线性模型，但在边缘化之后，结果向量的无条件均值一般在回归参数方面不是线性的。因此，不可能用回归系数简洁地描述协变量对结果边际分布的影响。需要在失访时间分布上明确求平均以及缺乏描述协变量对结果影响的回归系数是混合建模方法的两个不吸引人的特征。在本文中，我们描述了一般线性混合模型的一种特定参数化，它规避了这两个问题。
