Joint analysis of repeatedly observed continuous and ordinal measures of disease severity

In biomedical studies often multiple measures of disease severity are recorded over time. Although correlated, such measures are frequently analysed separately of one another. Joint analysis of the outcomes variables has several potential advantages over separate analyses. However, models for response variables of different types (discrete and continuous) are challenging to define and to fit. Herein we propose correlated probit models for joint analysis of repeated measurements on ordinal and continuous variables measuring the same underlying disease severity over time. We demonstrate how to rewrite the models so that maximum-likelihood estimation and inference can be performed with standard software. Simulation studies are performed to assess efficiency gains in fitting the responses together rather than separately and to guide response variable selection for future studies. Data from a depression clinical trial are used for illustration.