Confidence Interval for skewed distribution in outcome of change or difference between methods

BackgroundWhen we have pre and post measurements on same subjects and the outcome of interest is change or to compare the reliability across two methods, then it is required to present mean change and the 95% Confidence Interval (CI) for the change. However, when the distribution of the ‘change’ is skewed, then it is not possible to calculate CI using normal approximation. This study was to demonstrate an appropriate method in such situations.MethodsHypothetical data was considered. Difference of two methods was obtained that included positive and negative values and 95% CI using normal approximation with log transformation, Hodges–Lehmann CI, shifting the origin with log transformation and the Bootstrap CI was obtained.ResultsData consisted of 399 observations. The mean (sd) of the outcome was 96.9 (465.6). The 95% CI using the normal approximation with log transformation was obtained as (245.8, 307.5) with only 194 observations while Bootstrap CI was calculated as (54.1, 139.4) using all observations.ConclusionWhen the outcome of interest is to compare the ‘change’ which is skewed, then we discourage the log transformed normal approximation method or adding constant and taking log transformation method to calculate CI and encourage researchers to use Bootstrap CIs.