Interuniversity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium.
Department of Mathematics and Informatics, Faculty of Sciences, Eduardo Mondlane University, Maputo, Mozambique.
Stat Methods Med Res. 2019 Oct-Nov;28(10-11):3086-3099. doi: 10.1177/0962280218796252. Epub 2018 Sep 3.
Bivariate binary response data appear in many applications. Interest goes most often to a parameterization of the joint probabilities in terms of the marginal success probabilities in combination with a measure for association, most often being the odds ratio. Using, for example, the bivariate Dale model, these parameters can be modelled as function of covariates. But the odds ratio and other measures for association are not always measuring the (joint) characteristic of interest. Agreement, concordance, and synchrony are in general facets of the joint distribution distinct from association, and the odds ratio as in the bivariate Dale model can be replaced by such an alternative measure. Here, we focus on the so-called conditional synchrony measure. But, as indicated by several authors, such a switch of parameter might lead to a parameterization that does not always lead to a permissible joint bivariate distribution. In this contribution, we propose a new parameterization in which the marginal success probabilities are replaced by other conditional probabilities as well. The new parameters, one homogeneity parameter and two synchrony/discordance parameters, guarantee that the joint distribution is always permissible. Moreover, having a very natural interpretation, they are of interest on their own. The applicability and interpretation of the new parameterization is shown for three interesting settings: quantifying HIV serodiscordance among couples in Mozambique, concordance in the infection status of two related viruses, and the diagnostic performance of an index test in the field of major depression disorders.
双二元二项响应数据在许多应用中都有出现。人们通常对参数化联合概率感兴趣，这些概率可以用边缘成功概率与关联度量（通常是优势比）组合来表示。例如，使用双二元 Dale 模型，可以将这些参数建模为协变量的函数。但是，优势比和其他关联度量并不总是测量（联合）感兴趣的特征。一致性、一致性和同步性通常是联合分布的不同方面，而二元 Dale 模型中的优势比可以用这种替代度量来代替。在这里，我们关注所谓的条件同步性度量。但是，正如几位作者所指出的，这种参数的切换可能会导致参数化，而这种参数化并不总是导致可允许的联合双变量分布。在本研究中，我们提出了一种新的参数化方法，其中边缘成功概率被其他条件概率所取代。新的参数，一个同质性参数和两个同步性/不和谐性参数，确保了联合分布始终是可允许的。此外，由于具有非常自然的解释，它们本身就很有意义。该新参数化的适用性和解释性通过三个有趣的场景得到了展示：在莫桑比克量化夫妻之间的 HIV 血清不一致性、两种相关病毒感染状态的一致性以及主要抑郁障碍领域中一项指标检测的诊断性能。
