A note on interval estimation of the relative difference in data with matched pairs.

Abstract

For controlled comparative trials with matched pairs, in an attempt to improve the asymptotic interval estimator of the relative difference proposed elsewhere, I develop two asymptotic closed-form interval estimators with use of the logarithmic transformation and an idea used for deriving Fieller's theorem, respectively. I use Monte Carlo simulation to compare the performance of these three interval estimators. Findings reveal that when the number of pairs is as small as 20, the asymptotic interval estimator with use of the logarithmic transformation can actually perform quite well and is generally preferable to the other two asymptotic interval estimators with respect to both the coverage probability and the average length of the resulting confidence intervals. When the number of pairs is large (n > or = 100), results show that the three interval estimators considered here are all appropriate for use; they are essentially equivalent in a variety of situations.