A Joint Normal-Ordinal(Probit) Model for Ordinal and Continuous Longitudinal Data

Oregon Convention Center 

In biomedical studies, continuous and ordinal longitudinal variables are frequently encountered. In many of these studies it is of interest to estimate the effect of one of these longitudinal variables on the other. Time dependent covariates have however several limitations; they can for example not be applied when the data is not collected at fixed intervals. The issues can be circumvented by implementing joint models. In a joint model, both variables are modeled with a random-effects model, and the random effects are allowed to correlate. We propose a normal-ordinal(probit) joint model. First, we derive closed-form formulas to estimate the manifest correlations between the responses as observed. In addition, we derive the marginal model, where the interpretation is no longer conditional on the random effects. As a consequence, we can make predictions for a subvector of one response conditional on the other response and potentially a subvector of the history of the response . Next, we extend the approach to a high-dimensional case with more than two ordinal and/or continuous longitudinal variables. The methodology will be presented by means of a case study.

Longitudinal data analysis

Joint model

Random effects model

Time dependent effects

Probit link 

Biometrics Section