A global odds ratio regression model for bivariate ordered categorical data from ophthalmologic studies.

In typical clinical trials or epidemiologic studies of a bilateral eye disease, the primary outcome data consist of pairs of ordered categorical responses that tend to be highly correlated. In such studies, interest often centres in associating the outcome data with a grouping variable such as the treatment indicator or the exposure status and other person- and eye-specific covariates. In this paper, we propose a latent variable regression model to analyse such bivariate ordered categorical data. We use as a joint distribution for bivariate latent random variables the cross ratio distribution proposed by Plackett, which results in modelling the dependency between the fellow eyes with the global odds ratio. We illustrate the proposed model with data from the Wisconsin Epidemiologic Study of Diabetic Retinopathy, a study that seeks to identify risk factors among younger-onset diabetics.