Regression models for ordinal responses: a review of methods and applications

Epidemiologists are often interested in estimating the risk of several related diseases as well as adverse outcomes, which have a natural ordering of severity or certainty. While most investigators choose to model several dichotomous outcomes (such as very low birthweight versus normal and moderately low birthweight versus normal), this approach does not fully utilize the available information. Several statistical models for ordinal responses have been proposed, but have been underutilized. In this paper, we describe statistical methods for modelling ordinal response data, and illustrate the fit of these models to a large database from a perinatal health programme.

Models considered here include (1) the cumulative logit model, (2) continuation-ratio model, (3) constrained and unconstrained partial proportional odds models, (4) adjacent-category logit model, (5) polytomous logistic model, and (6) stereotype logistic model. We illustrate and compare the fit of these models on a perinatal database, to study the impact of midline episiotomy procedure on perineal lacerations during labour and delivery. Finally, we provide a discussion on graphical methods for the assessment of model assumptions and model constraints, and conclude with a discussion on the choice of an ordinal model. The primary focus in this paper is the formulation of ordinal models, interpretation of model parameters, and their implications for epidemiological research.

This paper presents a synthesized review of generalized linear regression models for analysing ordered responses. We recommend that the analyst performs (i) goodness-of-fit tests and an analysis of residuals, (ii) sensitivity analysis by fitting and comparing different models, and (iii) by graphically examining the model assumptions.