Sun BaoLuo, VanderWeele Tyler, Tchetgen Tchetgen Eric J
Am J Epidemiol. 2017 Nov 1;186(9):1097-1103. doi: 10.1093/aje/kwx161.
When a risk factor affects certain categories of a multinomial outcome but not others, outcome heterogeneity is said to be present. A standard epidemiologic approach for modeling risk factors of a categorical outcome typically entails fitting a polytomous logistic regression via maximum likelihood estimation. In this paper, we show that standard polytomous regression is ill equipped to detect outcome heterogeneity and will generally understate the degree to which such heterogeneity may be present. Specifically, nonsaturated polytomous regression will often a priori rule out the possibility of outcome heterogeneity from its parameter space. As a remedy, we propose to model each category of the outcome as a separate binary regression. For full efficiency, we propose to estimate the collection of regression parameters jointly using a constrained Bayesian approach that ensures that one remains within the multinomial model. The approach is straightforward to implement in standard software for Bayesian estimation.
当一个风险因素影响多项结果的某些类别而不影响其他类别时，就称存在结果异质性。对分类结果的风险因素进行建模的标准流行病学方法通常需要通过最大似然估计来拟合多分类逻辑回归。在本文中，我们表明标准的多分类回归没有能力检测结果异质性，并且通常会低估这种异质性可能存在的程度。具体而言，非饱和多分类回归通常会先验地从其参数空间中排除结果异质性的可能性。作为一种补救措施，我们建议将结果的每个类别建模为一个单独的二元回归。为了实现完全效率，我们建议使用一种约束贝叶斯方法联合估计回归参数的集合，该方法确保仍处于多项模型内。该方法在用于贝叶斯估计的标准软件中易于实现。
