Calculation of Confidence Intervals for Differences in Medians Between Groups and Comparison of Methods

Continuous data that are not normally distributed are typically presented in terms of median and interquartile range (IQR) for each group. High-quality anesthesia journals often require that confidence intervals are calculated and presented for all estimated associations of interest reported within a manuscript submission, and therefore, methods for calculating confidence intervals for differences in medians are vital. It is informative to present the difference in medians along with a confidence interval to provide insight about the magnitude of variability for the estimated difference. In a clinical research example using the American College of Surgeons National Surgical Quality Improvement Program (ACS NSQIP) Pediatric database, we demonstrate how to estimate confidence intervals for the difference in medians using 3 different statistical methods: the Hodges-Lehmann estimator, bootstrap resampling with replacement, and quantile regression modeling on the median (median regression). We discuss specific recommendations regarding the methods according to the objectives of the study as well as the distribution of the data as it pertains to the assumptions of the respective methods. Quantile regression allows for covariate adjustment, which may be an advantage in situations where differences in medians between groups may be due to confounding.