A tutorial on selecting and interpreting predictive models for ordinal health-related outcomes

Ordinal variables are very often objects of study in health sciences. However, due to the lack of dissemination of models suited for ordinal variables, users often adopt other practices that result in the loss of statistical power. In this tutorial, different models from the family of logistic regression models are introduced as alternatives to handle and interpret ordinal outcomes. The models that were considered include: ordinal regression model (ORM), continuation ratio model (CRM), adjacent category model (ACM), gen- eralised ordered logit model, sequential model, multinomial logit model, partial propor- tional odds model, partial continuation ratio model and stereotype ordered regression model. By using the relationship of hospital length of stay in a public hospital in Mexico with patient characteristics as an example, the models were used to describe the nature of such relationship and to predict the length of stay category to which a patient is most likely to belong. After an initial analysis, the ORM, CRM and ACM proved to be unsuitable for our data due to the transgression of the parallel regression assumption. The rest of the models were estimated in STATA. The results suggested analogous directionality of the parameter estimates between models, although the interpretation of the odds ratios varied from one model to another. Performance measurements indicated that the models had similar prediction performance. Therefore, when there is an interest in exploiting the ordinal nature of an outcome, there is no reason to maintain practices that ignore such nature since the models discussed here proved to be computationally inexpensive and easy to estimate, analyse and interpret.