Abstract

Latent variable, bivariate ordinal response, asymmetric distribution, maximum likelihood estimation, Bayesian estimation, diabetic retinopathy.

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.