A bayesian analysis of bivariate ordered categorical responses using a latent variable regression model: Application to diabetic retinopathy data

Latent variable distribution models are frequently utilized for analyzing bivariate ordered categorical
response data. In this context, choosing the bivariate normal distribution as the underlying latent
distribution, which leads to the bivariate cumulative probit model, is the most common strategy for
analyzing theses data sets. However, when the conditional distribution of the available bivariate
response has an asymmetric form, other convenient asymmetric bivariate distributions may lead to a
better fit. In this paper, we use an asymmetric bivariate cumulative latent variable distribution model for
analyzing bivariate ordered categorical response data. For estimating the model parameters, we use
two strategies: maximum likelihood and Bayesian approaches. We also use the proposed model for
analyzing the data from 623 diabetic patients to identify some of the most important risk indicators of
diabetic retinopathy among them. The obtained results revealed that patients’ age at diagnosis,
duration of diabetes, HbA1c, method of diabetes control, macular edema, and presence of hypertension
and renal disease are significantly associated with the severity of diabetic retinopathy. In conclusion,
both the maximum likelihood and Bayesian analyses resulted in similar significant risk indicators.
However, it seems that the Bayesian analysis gives us smaller standard errors compared to the
maximum likelihood approach