Ordinal regression
What question does this help answer?
Whether an exposure or treatment shifts patients along an ordered scale: a symptom grade, a disability score, a Likert response, a stage.
Why not dichotomise
Collapsing an ordered scale into good and bad is the most common approach and it throws away information. A treatment that moves many patients one category better across the whole scale can produce no difference at all in the proportion crossing one arbitrary threshold. Dichotomising also loses power, often a great deal of it, which means a larger and more expensive study for the same answer.
Why not treat it as continuous
Because the spacing is not known to be equal. The distance from mild to moderate is not necessarily the distance from moderate to severe, and a mean of an ordinal scale asserts that it is.
The models
- Proportional odds (cumulative logit): one odds ratio describing the shift across every cutpoint. The usual first choice.
- Partial proportional odds: relaxes the assumption for the variables where it fails.
- Continuation ratio: models the odds of moving beyond each level given having reached it, natural when the categories represent a progression.
- Multinomial logistic: ignores the order entirely, which is a last resort, not a safe default.
What the cumulative splits look like
Checking proportional odds
Fit the cutpoint-specific odds ratios and look at whether they are similar; a formal test is available but has poor power in small samples and excessive power in large ones, so it should not be the only evidence. Where the assumption fails badly, report the cutpoint-specific effects rather than an average that hides them.
Why Mallard may recommend it
Mallard may name ordinal regression when the outcome is a graded scale, and it will resist a proposal to collapse such a scale into two levels without a stated clinical reason for the particular threshold.
What to watch out for
The proportional odds assumption is a real assumption and is often skipped: it says the effect is the same at every cutpoint of the scale, and where it fails the single odds ratio is an average that may describe no part of the scale well. Check it. The other trap is presentational: an ordinal odds ratio is a statement about shifting the whole distribution, and reading it as the odds of one particular category is a misreading that changes the clinical claim.
Clinical example
Question: Does a thrombolytic shift the distribution of disability at 90 days? Analysis: Proportional odds regression across the full ordinal scale, with the assumption checked and the cutpoint-specific odds ratios shown, rather than dichotomising at a favourable-outcome threshold.
- Applications of proportional odds ordinal logistic regression models and continuation ratio models in examining the association of physical inactivity with erectile dysfunction among type 2 diabetic patients (opens in a new tab) · Phys Act Nutr · doi 10.20463/pan.2021.0005
- Estimates, power and sample size calculations for two-sample ordinal outcomes under before-after study designs (opens in a new tab) · Stat Med · doi 10.1002/sim.1383