Power prior distributions for regression models
Power prior distributions for regression models
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DOI：
10.1214/ss/1009212673
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发表时间：
2000-02
影响因子：
5.7
通讯作者：
J. Ibrahim;Ming-Hui Chen
中科院分区：
文献类型：
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作者：
J. Ibrahim;Ming-Hui Chen
我们针对任意回归模型提出了一类通用的先验分布。我们讨论参数和半参数模型。回归系数的先验规范集中于可确定的量，因为该推导基于历史数据Do的可用性和量化Do中的不确定性的标量ao。然后使用Do和ao以半自动方式指定回归系数的先验。Do的最自然的规格出现时，从类似的以前的研究的原始数据是可用的。历史数据的可用性在临床试验、致癌性研究和环境研究中非常常见，其中可从类似的既往研究中获得大量数据库。虽然我们在这里提出的方法是相当普遍的，我们将只关注使用历史数据从类似的以前的研究来构建先验分布。先验分布基于将历史数据的似然函数提高到ao次幂的想法，其中0 < ao < 1。我们称这种先验分布为幂先验分布。我们研究了四种常用的回归模型的功率先验。这些模型包括广义线性模型、广义线性混合模型、半参数比例风险模型和生存数据的治愈率模型。对于这几类模型，我们讨论了幂先验的构造、先验启发问题、适当性条件、模型选择以及其他一些性质。对于每一类模型，我们提出了真实的数据集，以证明所提出的方法。
We propose a general class of prior distributions for arbitrary regression models. We discuss parametric and semiparametric models. The prior specification for the regression coefficients focuses on observ- able quantities in that the elicitation is based on the availability of his- torical data Do and a scalar quantity ao quantifying the uncertainty in Do. Then Do and ao are used to specify a prior for the regression coeffi- cients in a semiautomatic fashion. The most natural specification of Do arises when the raw data from a similar previous study are available. The availability of historical data is quite common in clinical trials, car- cinogenicity studies, and environmental studies, where large data bases are available from similar previous studies. Although the methodology we present here is quite general, we will focus only on using historical data from similar previous studies to construct the prior distributions. The prior distributions are based on the idea of raising the likelihood function of the historical data to the power ao, where 0 < ao < 1. We call such prior distributions power prior distributions. We examine the power prior for four commonly used classes of regression models. These include generalized linear models, generalized linear mixed models, semipara- metric proportional hazards models, and cure rate models for survival data. For these classes of models, we discuss the construction of the power prior, prior elicitation issues, propriety conditions, model selec- tion, and several other properties. For each class of models, we present real data sets to demonstrate the proposed methodology.