A joint overdispersed marginalized random-effects model for analyzing two or more longitudinal ordinal responses.

Disease severity is a latent concept which should be observed using a measurement tool; it can be useful in assessing disease status both cross-sectionally and longitudinally. Medsger scale is a valid instrument for assessing the systemic sclerosis severity in which the items are categorized from 0 (normal) to 4 (endstage) for each organ system. We simultaneously analyzed two of the Medsger scale items, namely, general system and skin system as two correlated ordinal responses using an overdispersed marginalized random-effects model for longitudinal ordinal data exhibiting an overdispersion pattern. In general, a random-effects approach is implemented to account for the correlation between these two stochastic processes and to make simultaneous inference; our model also accounts for temporal correlations amongst observations taken on the same subject. Another important aspect of our model is its capacity to handle data overdispersion in order to make reliable inference. Last but not least, it is proved that certain parameters in our joint model have marginal interpretations. We investigate the statistical properties of our estimators through extensive simulation study. Finally, the methodology is applied to a data of systemic sclerosis patients.