Departments of Health Services and Pharmacy, University of Washington, Seattle, WA (AB)
The National Bureau of Economic Research, Cambridge MA (AB)
Med Decis Making. 2012 Jan-Feb;32(1):56-69. doi: 10.1177/0272989X11416988. Epub 2011 Oct 18.
To develop regression models for outcomes with truncated supports, such as health-related quality of life (HRQoL) data, and account for features typical of such data such as a skewed distribution, spikes at 1 or 0, and heteroskedasticity.
Regression estimators based on features of the Beta distribution. First, both a single equation and a 2-part model are presented, along with estimation algorithms based on maximum-likelihood, quasi-likelihood, and Bayesian Markov-chain Monte Carlo methods. A novel Bayesian quasi-likelihood estimator is proposed. Second, a simulation exercise is presented to assess the performance of the proposed estimators against ordinary least squares (OLS) regression for a variety of HRQoL distributions that are encountered in practice. Finally, the performance of the proposed estimators is assessed by using them to quantify the treatment effect on QALYs in the EVALUATE hysterectomy trial. Overall model fit is studied using several goodness-of-fit tests such as Pearson's correlation test, link and reset tests, and a modified Hosmer-Lemeshow test.
The simulation results indicate that the proposed methods are more robust in estimating covariate effects than OLS, especially when the effects are large or the HRQoL distribution has a large spike at 1. Quasi-likelihood techniques are more robust than maximum likelihood estimators. When applied to the EVALUATE trial, all but the maximum likelihood estimators produce unbiased estimates of the treatment effect.
One and 2-part Beta regression models provide flexible approaches to regress the outcomes with truncated supports, such as HRQoL, on covariates, after accounting for many idiosyncratic features of the outcomes distribution. This work will provide applied researchers with a practical set of tools to model outcomes in cost-effectiveness analysis.
开发用于截断支持结果的回归模型，例如健康相关生活质量（HRQoL）数据，并考虑到此类数据的典型特征，例如偏态分布、在 1 或 0 处的尖峰以及异方差性。
基于 Beta 分布特征的回归估计量。首先，提出了单方程和两部分模型，以及基于最大似然、拟似然和贝叶斯马尔可夫链蒙特卡罗方法的估计算法。提出了一种新颖的贝叶斯拟似然估计器。其次，进行了模拟练习，以评估针对各种在实践中遇到的 HRQoL 分布的拟议估计器相对于普通最小二乘法（OLS）回归的性能。最后，通过使用它们来量化 EVALUATE 子宫切除术试验中 QALYs 的治疗效果来评估拟议估计器的性能。使用几种拟合优度检验（如 Pearson 相关检验、链接和重置检验以及修改后的 Hosmer-Lemeshow 检验）来研究总体模型拟合情况。
模拟结果表明，与 OLS 相比，拟议方法在估计协变量效果方面更稳健，特别是当效果较大或 HRQoL 分布在 1 处有较大尖峰时。拟似然技术比最大似然估计器更稳健。当应用于 EVALUATE 试验时，除最大似然估计器外，所有估计器都产生了治疗效果的无偏估计。
单部分和两部分 Beta 回归模型为在考虑到结果分布的许多特有特征后，将具有截断支持的结果（例如 HRQoL）回归到协变量提供了灵活的方法。这项工作将为应用研究人员提供一套实用的工具，用于在成本效益分析中建模结果。
