Quantile regression
What question does this help answer?
Whether the typical patient's outcome differs, when the outcome is skewed; or whether an effect is concentrated in the upper or lower part of the distribution, such as among the longest hospital stays.
Why not a transformation or a rank test
Log-transforming the outcome changes the question to a ratio of geometric means. A rank test gives a p-value with no adjusted effect estimate, and it is not a comparison of medians unless the two distributions have the same shape. Quantile regression gives an adjusted difference in the outcome's own units.
Reading the coefficient
A coefficient is the difference in the chosen quantile of the outcome between patients who differ in the exposure and share the other covariate values. Estimating several quantiles and plotting the effect across them shows whether an exposure shifts the whole distribution or only one end of it. Name the primary quantile in advance.
Confidence intervals
Standard errors depend on how densely the data sit around the chosen quantile, which is hard to estimate in small or heavily tied samples. Bootstrap percentile intervals are a common and defensible choice.
Sizing
No form in Mallard's sizing catalog fits. Sizing needs the expected density of the outcome around the median and is done by simulation.
Why Mallard may recommend it
Mallard may name median regression when a continuous outcome is strongly skewed and the median is the summary the question is really about.
What to watch out for
An adjusted median difference is a CONDITIONAL quantity: it compares medians among patients with the same covariate values, and unlike an adjusted mean difference it does not average up to the difference between the two groups' overall medians. Say which one the question needs. Outcomes with many ties, such as length of stay in whole days, make the median move in steps and the standard errors unreliable, so look at the data and prefer bootstrap intervals before trusting any p-value.
Clinical example
Question: Does an enhanced-recovery pathway shorten length of stay after colectomy? Analysis: Median regression of length of stay on pathway, adjusted for age and comorbidity, reporting the adjusted median difference in days with a bootstrap confidence interval, and the 75th and 90th percentiles as secondary quantiles.
- Quantile regression and its applications: a primer for anesthesiologists (opens in a new tab) · Anesth Analg · doi 10.1213/ANE.0000000000004017
- Quantile regression: opportunities and challenges from a user's perspective (opens in a new tab) · Am J Epidemiol · doi 10.1093/aje/kwu178