Cumulative logit models for ordinal data: a case study involving allergic rhinitis severity scores

Ordered categorical data arise in numerous settings, a common example being pain scores in analgesic trials. The modelling of such data is intrinsically more difficult than the modelling of continuous data due to the constraints on the underlying probabilities and the reduced amount of information that discrete outcomes contain. In this paper we discuss the class of cumulative logit models, which provide a natural framework for ordinal data analysis. We show how viewing the categorical outcome as the discretization of an underlying continuous response allows a natural interpretation of model parameters. We also show how covariates are incorporated into the model and how various types of correlation among repeated measures on the same individual may be accounted for. The models are illustrated using longitudinal allergy data consisting of sneezing scores measured on a four-point scale. Our approach throughout is Bayesian and we present a range of simple diagnostics to aid model building.