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Two‐sample empirical likelihood ratio tests for medians in application to biomarker evaluations
Author(s) -
Yu Jihnhee,
Vexler Albert,
Kim SeongEun,
Hutson Alan D.
Publication year - 2011
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.10108
Subject(s) - statistics , mathematics , empirical likelihood , econometrics , null hypothesis , statistical hypothesis testing , confidence interval
The median is a commonly used parameter to characterize biomarker data. In particular, with two vastly different underlying distributions, comparing medians provides different information than comparing means; however, very few tests for medians are available. We propose a series of two‐sample median‐specific tests using empirical likelihood methodology and investigate their properties. We present the technical details of incorporating the relevant constraints into the empirical likelihood function for in‐depth median testing. An extensive Monte Carlo study shows that the proposed tests have excellent operating characteristics even under unfavourable occasions such as non‐exchangeability under the null hypothesis. We apply the proposed methods to analyze biomarker data from Western blot analysis to compare normal cells with bronchial epithelial cells from a case–control study. The Canadian Journal of Statistics 39: 671–689; 2011. © 2011 Statistical Society of Canada