A Permutation Test for Nonindependent Matched Pair Data
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0092-861 5/2001
Copyright 0 2001 Drug Information Association Inc.
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A PERMUTATION TEST FOR NONINDEPENDENT MATCHED PAIR DATA SEUNG-HO KANG,PHD Assistant Professor, Department of Statistics, Ewha Womans University, Seoul, Korea
HYUNGW. KIM, MS Statistical Analyst. Department of Biostatistics. University of Texas, M. D. Anderson Cancer Center, Houston, Texas
CHULW. AHN,PHD Professor, Clinical Epidemiology, University of Texas Medical School, Houston, Texas
The paired t-test and the Wilcoxon signed-rank test are often conducted to compare two continuous outcomes from paired observations. An assumption underlying these tests is that the responses from pair to pair are mutually independent. However, the assumption is violated in certain applications such as site-specific data in periodontal research. An adjustment to the paired t-test to account for the clustering effect has been well developed. But the adjustment relies on either large sample theory or the assumption that the observations being analyzed follow a normal distribution. In this paper, we propose a permutation test for matched pair clustered data which are valid in small samples. We developed and reviewed software to carry out the proposed test. The proposed test is applied to real-life data. Key Words: Paired t-test; Wilcoxon signed-rank test; Intraclass correlation; Dentistry
INTRODUCTION MATCHED PAIRS OF data often arise in medical statistics for comparing two treatments. In clinical trials subjects matched on the basis of characteristics that are associated with the response being studied are randomized to the treatments independently within each matched group. The purpose of matching in clinical trials is to increase the precision of the comparisons among the treatments. The matched pair samples may also represent two sets of measurements on the
Reprint address: Seung-Ho Kang, PhD, Department of Statistics, Ewha Womans University, 1 1- 1, Dae HyunDong, SeoDaeMun-Gu, Seoul, 120-750, Korea. Email: [email protected].
same patient. The most common paired design results when one group is measured twice. Oftentimes the first measurement occurs before treatment and the second measurement occurs after treatment. Continuous outcomes in the paired design are analyzed by using the paired t-test. The paired t-test requires that the observations being analyzed follow a normal distribution. When researchers suspect that the distribution of the variable of interest departs significantly from the normal distribution, nonparametric tests such as the Wilcoxon signed-rank test are often conducted. An important assumption of the tests mentioned above is that the responses from pair to pair are mutually independent. However, this assumption is violated in cluster sam-
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Seurig-Ho Kring, Hyung W. Kim. and Cliul W. Ahn
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pling of data which is frequently encountered where h, is the median of the h
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