Medical and epidemiological researchers commonly study ordinal measures of symptoms or pathology. Some of these studies involve two correlated ordinal measures. There is often an interest in including both measures in the modeling. It is common to see analyses that consider one of the measures as a predictor in the model for the other measure as outcome. There are, however, issues with these analyses including biased estimate of the probabilities and a decreased power due to multicollinearity (since they share some predictors). These issues create a necessity to examine both variables as simultaneous outcomes, by assessing the marginal probabilities for each outcome (i.e. using a proportional odds model) and the association between the two outcomes (i.e. using a constant global odds model). In this work we extend this model using a parsimonious option when the constraints imposed by assumptions of proportional marginal odds and constant global odds do not hold. We compare approaches by using simulations and by analyzing data on brain infarcts in older adults. Age at death is a marginal predictor of gross infarcts and also a marginal predictor of microscopic infarcts, but does not modify the association between gross and microscopic infarcts.
Keywords: Dale model; Global odds model; brain infarcts; logistic regression; proportional odds.