The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Nonparametric Stratified Test Based on the Jonckheere-Terpstra Trend Statistic

Jonckheere-Terpstra 추세 검정통계량에 근거한 비모수적 층화분석법

  • Cho, Do-Yeon (Department of Biostatistics, Graduate School, The Catholic University of Korea) ;
  • Yang, Soo (College of Nursing, The Catholic University of Korea) ;
  • Song, Hae-Hiang (Department of Biostatistics, Graduate School, The Catholic University of Korea)
  • 조도연 (가톨릭대학교 대학원 의학통계학과) ;
  • 양수 (가톨릭대학교 간호대학) ;
  • 송혜향 (가톨릭대학교 대학원 의학통계학과)
  • Received : 20100800
  • Accepted : 20101000
  • Published : 2010.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Clinical trials are often carried out as multi-center studies because the patients enrolled for a trial study are very limited in one particular hospital. In these circumstances, the use of an ordinary Jonckheere (1954) and Terpstra (1952) test for testing trend among several independent treatment groups is invalid. We propose a the stratified Jonckheere-Terpstra test based on van Elteren (1960)'s stratified test of Wilcoxon (1945) statistics and an application of our method is demonstrated through example data. A simulation study compares the efficiency of stratified and unstratified Jonckheere-Terpstra trend tests.

각 의료기관에서 수집될 수 있는 환자수가 한정되어 있는 질병의 경우에는 주로 다기관연구로써 임상연구가 진행된다. Jonckheere (1954)와 Terpstra (1952)의 추세 검정법으로 분석해야 하는 독립된 여러 군의 자료를 다기관에서 수집한 경우에 이질성을 고려하여 각 연구기관을 하나의 층으로 보아 층화분석법으로 분석하지 않으면 옳지 않은 결론에 도달할 수가 있다. 본 논문에서는 van Elteren (1960)이 제시한 Wilcoxon (1945) 검정통계량의 층화분석법을 이용하여 Jonckheere (1954)와 Terpstra (1952)의 추세 검정통계량에 근거한 층화분석법을 제시한다. 예제 자료에 이 층화분석법을 적용하며 효율성을 모의실험으로 알아본다.

Keywords

References

  1. Bajorski, P. and Petkau, J. (1999). Nonparametric two-sample comparisons of changes on ordinal responses, Journal of the American Statistical Association, 94, 970–978.
  2. Cochran, W. G. (1968). The effectivness of adjustment by sub-classification in removing bias in observational studies, Biometerics, 24, 295–313. https://doi.org/10.2307/2528036
  3. van Elteren, P. H. (1960). On the combination of independent two sample tests of wilcoxon, Bulletin of International Statistical Institute, 37, 351–361.
  4. Hajek, J. and Sidak, Z. (1967). Theory of Rank Test, Academic Press, New York.
  5. Hollander, M. and Wolfe, D. A. (1999). Nonparametric Statistical Methods, John Wiley & Sons,New York.
  6. Jonckheere, A .R. (1954). A distribution-free k-sample test against ordered alternatives, Biometrika, 41, 133–145.
  7. Lehmann, E. L. (1998). Nonparametrics: Statistical Methods Based on Ranks, Holden-Day, San Francisco.
  8. Mann, H. B and Whitney, D. R. (1947). On a test of whether one of two random variable is stochastically larger than the other, Annals of Mathematical Statistical, 18, 50–60.
  9. Palta, M. (1983). The effects of a stratified analysis of censored data, Communication in Statistics-Simulation and Computation, 12, 273–290.
  10. Terpstra, T. J. (1952). The asymptotic normality and consistency of kendall's test against trend when ties are present in one ranking, Indagationes Mathematicae, 14, 327–333.
  11. Tryon, P. V. and Hettmansperger T. P. (1973). A class of non-parametric tests for homogeneity aganist ordered alternatives, The Annals of Statistics, 1, 1061–1070.
  12. Wilcoxon, F. (1945). Individual comparisons by ranking methods, Biometrics, 1, 80–83.
  13. Yang, S. (1992). Effects of fluid intake, dietary fiber supplement and abdominal muscle exercises on antipsychotic drug-induced constipation in schizophrenics, Journal of Catholic Medical College, 45, 1501–1514.
  14. Zhang, Z. (1996). Weighted combination of wilcoxon tests with interlaboratory lifetime data, Sankhyaa Indian Journal of Statistics Series A, 58, 311–327.