Ordinal cumulative probability models (CPMs) -- also known as cumulative link models -- such as the proportional odds regression model are typically used for discrete ordered outcomes, but can accommodate both continuous and mixed discrete/continuous outcomes since these are also ordered. Recent papers describe ordinal CPMs in this setting using non-parametric maximum likelihood estimation. We formulate a Bayesian CPM for continuous or mixed outcome data. Bayesian CPMs inherit many of the benefits of frequentist CPMs and have advantages with regard to interpretation, flexibility, and exact inference (within simulation error) for parameters and functions of parameters. We explore characteristics of the Bayesian CPM through simulations and a case study using HIV biomarker data. In addition, we provide the package 'bayesCPM' which implements Bayesian CPM models using the R interface to the Stan probabilistic programing language. The Bayesian CPM for continuous outcomes can be implemented with only minor modifications to the prior specification and, despite some limitations, has generally good statistical performance with moderate or large sample sizes.
翻译:例常累积概率模型 -- -- 也称为累积链接模型 -- -- 例如比例差值回归模型通常用于离散定结果,但可以同时包含连续和混合的离散/连续结果,因为这些结果也是定购的结果。最近的文件使用非参数最大可能性估计值来描述在这一背景下的交点的CPM。我们为连续或混合结果数据制定了一种Bayesian CPM模型。Bayesian CPM模型继承了常住式CPM的许多好处,在解释、灵活性和精确推断(模拟误差)参数和参数功能方面具有优势。我们通过模拟和利用艾滋病毒生物标记数据进行案例研究来探索Bayesian CPM模型的特性。此外,我们提供包包“BayesCPM”用于使用R界面与斯坦概率性编程语言的Bayesian CPM模型。Bayesian CPM模型的连续结果可以在对先前的规格进行微小的修改后实施,尽管存在一些限制,但通常具有中或大样本大小的良好统计性能。