Regression Models for Ordinal Outcomes

INTRODUCTION

This Guide to Statistics and Methods provides an overview of regression models for ordinal outcomes, including an explanation of why they are used and their limitations.

In an issue of JAMA, Self et al¹ reported a randomized clinical trial that evaluated whether treatment with hydroxychloroquine improved clinical outcomes of adults hospitalized with COVID-19 compared with placebo. The primary outcome was the patient’s clinical status 14 days after randomization, assessed with an ordinal 7-category scale ranging from worst (“death”) to the best (“discharged from the hospital and able to perform normal activities”). The term “ordinal” is applied to an outcome measure for which its mutually exclusive categories can be ordered by their clinical preference. The primary outcome was analyzed with a multivariable ordinal logistic regression model, which is a regression model for an ordinal dependent variable. The authors found that there was not a statistically significant difference between the hydroxychloroquine and placebo groups in clinical status 14 days after randomization.

USE OF REGRESSION MODELS FOR ORDINAL OUTCOMES

Why Are Ordinal Outcomes Used?

Ordinal outcomes are those for which their categories (in this case, specific clinical states at 14 days) can be naturally rank ordered, but the degree of difference between categories may not be quantifiable.² For example, the event “discharged from the hospital and able to perform normal activities” is better than “death,” but there is no numerical quantity to measure how much better. Analyses of ordinal outcomes seek to maximize use of available information by exploiting the inherent rank ordering of their categories.

Important information can be lost if the rank ordering of the outcome categories is ignored. An arbitrary binary dichotomization of an ordinal outcome (ie, collapsing the ordered categories into 2 levels) sacrifices granularity and reduces statistical power.³ In addition, a composite binary outcome—an indicator of whether any event occurs—treats each component event equally and ignores their relative severity. Although binary outcomes are simple to analyze using standard logistic regression models, this loss of information is inconsistent with the principles of ethical conduct of research, which require that investigators maximize the possible benefits of research, including the most efficient use of study data. At the same time, an ordinal outcome should not be analyzed as a continuous variable (eg, using a linear regression model) because an ordinal outcome does not take on numeric values and likely does not satisfy the assumptions required for such models. However, in some situations, quantitative outcomes can be treated as ordinal outcomes for statistical analysis purposes.⁴

Description of Regression Models for Ordinal Outcomes

Ordinal logistic regression models are tailored for the ...