Bebu Ionut, Luta George, Mathew Thomas, Agan Brian K
The Biostatistics Center, Department of Epidemiology and Biostatistics, The George Washington University, 6110 Executive Blvd., Rockville, MD 20852, USA.
Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, 4000 Reservoir Road, Washington, DC 20057, USA.
Int J Environ Res Public Health. 2016 Jun 18;13(6):605. doi: 10.3390/ijerph13060605.
For binary outcome data from epidemiological studies, this article investigates the interval estimation of several measures of interest in the absence or presence of categorical covariates. When covariates are present, the logistic regression model as well as the log-binomial model are investigated. The measures considered include the common odds ratio (OR) from several studies, the number needed to treat (NNT), and the prevalence ratio. For each parameter, confidence intervals are constructed using the concepts of generalized pivotal quantities and fiducial quantities. Numerical results show that the confidence intervals so obtained exhibit satisfactory performance in terms of maintaining the coverage probabilities even when the sample sizes are not large. An appealing feature of the proposed solutions is that they are not based on maximization of the likelihood, and hence are free from convergence issues associated with the numerical calculation of the maximum likelihood estimators, especially in the context of the log-binomial model. The results are illustrated with a number of examples. The overall conclusion is that the proposed methodologies based on generalized pivotal quantities and fiducial quantities provide an accurate and unified approach for the interval estimation of the various epidemiological measures in the context of binary outcome data with or without covariates.
对于流行病学研究中的二元结局数据，本文研究了在有无分类协变量的情况下几种感兴趣的指标的区间估计。当存在协变量时，研究了逻辑回归模型以及对数二项模型。所考虑的指标包括来自多项研究的共同比值比（OR）、治疗所需人数（NNT）和患病率比。对于每个参数，使用广义枢轴量和 fiducial 量的概念构建置信区间。数值结果表明，即使样本量不大，如此获得的置信区间在保持覆盖概率方面也表现出令人满意的性能。所提出解决方案的一个吸引人的特点是它们不基于似然最大化，因此不存在与最大似然估计器数值计算相关的收敛问题，特别是在对数二项模型的背景下。通过多个例子对结果进行了说明。总体结论是，所提出的基于广义枢轴量和 fiducial 量的方法为有或无协变量的二元结局数据背景下各种流行病学指标的区间估计提供了一种准确且统一的方法。
