Testing Medians of Skewed Distribution: A Case Study

• Activity Number: 109
• Type: Contributed
• Date/Time: Monday, August 4, 2008 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Hongwei Wang*+ and Arvind K. Shah
• Companies: Merck Research Laboratories and Merck Research Laboratories
• Keywords: skewed distribution ; log-transformation ; rank-transformation ; bootstrap ; median ; least absolute error

Abstract

Encountering of positive data with skewed distribution is fairly common in many disciplines where the median is a preferred measure of central tendency and hence for inference. For comparison of medians, three strategies are considered here: 1) ANCOVA on the normalized ranks; 2) ANCOVA on the log-transformed data; 3) Least absolute error regression. The relative performance of three strategies is studied with respect to their attained powers and coverages of 95% confidence intervals using bootstrap approach on a real-life dataset. The dataset comes from three similarly designed clinical trials (n=3083) with c-reactive protein as one of the secondary endpoints. For bootstrapping, various fractions of the data are repeatedly drawn with replacement on which the three methods are applied to test no difference among medians. The conclusions on utilization of the three method are reported.