Proportional odds (ordinal logistic) regression
Compares an ordered score between groups while adjusting for other variables, giving one common odds ratio across the cut-points of the score.
Clinical example
The modified Rankin Scale at 90 days after stroke, compared between two treatments while adjusting for age and stroke severity.
When to use it
- The outcome is an ordered score with a few categories, such as the mRS or a pain category.
- You need to adjust for other variables.
- You want to use the full order of the categories instead of cutting the score into two groups.
Assumptions to check
Proportional odds
One odds ratio applies across all cut-points of the score. Check it, and report how.
Check first
- Proportional odds assumption
What to report
- Common odds ratio with 95% CI
- The variables you adjusted for, and why
- The distribution of the score in each group
Common mistakes
Be careful treating a score as a measurement
The steps of an ordinal score aren't necessarily equal. Means and t-tests assume they are.
Don't dichotomize a measurement
Cutting a continuous variable into high and low ("BP above 140") throws away information and power, and the cut-off is often arbitrary.
Check the proportional odds assumption
The model assumes one odds ratio applies across all cut-points of the score. Check it, and report how.
Alternatives
| If your situation is… | Use |
|---|---|
| Two groups, no adjustment needed | Mann-Whitney U test (Wilcoxon rank-sum test) |
| Three or more groups, no adjustment needed | Kruskal-Wallis test |
In your software
# R
library(ordinal)
d$mrs <- factor(d$mrs, ordered = TRUE)
fit <- clm(mrs ~ treatment + age, data = d)
summary(fit)
PLUM mrs BY treatment WITH age
/LINK=LOGIT
/PRINT=FIT PARAMETER SUMMARY TPARALLEL.