Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Health Economics and Health Care Management, Neuherberg, Germany.
Value Health. 2011 Jul-Aug;14(5):759-67. doi: 10.1016/j.jval.2010.12.009. Epub 2011 May 31.
Preference-weighted index scores of health-related quality of life are commonly skewed to the left and bounded at one. Beta regression is used in various disciplines to address the specific features of bounded outcome variables such as heteroscedasticity, but has rarely been used in the context of health-related quality of life measures. We aimed to examine if beta regression is appropriate for analyzing the relationship between subject characteristics and SF-6D index scores.
We used data from the population-based German KORA F4 study. Besides classical beta regression, we also fitted extended beta regression models by allowing a regression structure on the precision parameter. Regression coefficients and predictive accuracy of the models were compared to those from a linear regression model with model-based and robust standard errors.
The beta distribution fitted the empirical distribution of the SF-6D index better than the normal distribution. Extended beta regression performed best in terms of predictive accuracy but confidence intervals of the fit measures suggested that no model was superior to the others. Age had a significant negative effect on the precision parameter indicating higher variation of health utilities in older age groups. The observations reporting perfect health had a high influence on model results.
Beta regression, especially with precision covariates is a possible supplement to the methods currently used in the analysis of health utility data. In particular, it accounted for the boundedness and heteroscedasticity of the SF-6D index. A pitfall of the beta regression is that it does not work well in handling one-valued observations.
健康相关生活质量的偏好加权指数得分通常向左偏态分布且有界在一。贝塔回归在各个学科中用于解决有界结果变量的特定特征，如异方差，但在健康相关生活质量测量方面很少使用。我们旨在研究贝塔回归是否适合分析受试者特征与 SF-6D 指数得分之间的关系。
我们使用了基于人群的德国 KORA F4 研究的数据。除了经典的贝塔回归，我们还通过允许在精度参数上存在回归结构来拟合扩展的贝塔回归模型。模型的回归系数和预测准确性与基于模型和稳健标准误差的线性回归模型进行了比较。
贝塔分布比正态分布更能拟合 SF-6D 指数的经验分布。扩展的贝塔回归在预测准确性方面表现最佳，但拟合度量的置信区间表明没有一个模型优于其他模型。年龄对精度参数有显著的负效应，表明在老年组中健康效用的变化更大。报告完美健康的观察值对模型结果有很大的影响。
贝塔回归，特别是带有精度协变量的贝塔回归，可以作为目前用于分析健康效用数据的方法的补充。特别是，它考虑了 SF-6D 指数的有界性和异方差性。贝塔回归的一个缺陷是它在处理有界值观测值时效果不佳。
