Testing proportionality in the proportional odds model fitted with GEE

Generalized estimating equations (GEE) methodology as proposed by Liang and Zeger has received widespread use in the analysis of correlated binary data. Miller et al. and Lipsitz et al. extended GEE to correlated nominal and ordinal categorical data; in particular, they used GEE for fitting McCullagh's proportional odds model. In this paper, we consider robust (that is, empirically corrected) and model-based versions of both a score test and a Wald test for assessing the assumption of proportional odds in the proportional odds model fitted with GEE. The Wald test is based on fitting separate multiple logistic regression models for each dichotomization of the response variable, whereas the score test requires fitting just the proportional odds model. We evaluate the proposed tests in small to moderate samples by simulating data from a series of simple models. We illustrate the use of the tests on three data sets from medical studies.