응용통계연구 (The Korean Journal of Applied Statistics)

  • 제28권6호
  • /
  • Pages.1181-1189
  • /
  • 2015
  • /
  • 1225-066X(pISSN)
  • /
  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

일원배치법에서 Umbrella Alternatives에 대한 위치를 이용한 비모수 검정법

Nonparametric Method in One-way Layout for Umbrella Alternatives based on Placement

  • 이혜정 (가톨릭대학교 의생명.건강과학과) ;
  • 김동재 (가톨릭대학교 의생명.건강과학과)
  • Lee, Hyejung (Department of Biomedicine.Health Science, The Catholic University of Korea) ;
  • Kim, Dongjae (Department of Biomedicine.Health Science, The Catholic University of Korea)
  • 투고 : 2015.10.12
  • 심사 : 2015.11.11
  • 발행 : 2015.12.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

임상시험에서 약의 복용량에 따라 처리 효과가 증가하다가, 부작용으로 인해 일정 용량 수준에서 감소하는 추세를 보일 수 있다. 이러한 경향을 우산형 패턴이라 하며, 우산형 패턴의 대립가설에 대한 검정은 이러한 경향이 사전에 예측 가능할 때 유용하다. 이 논문에서는 Orban과 Wolfe (1982)가 제안한 선형 위치(linear placement)를 이용하여 일원배치법에서 우산형 대립가설의 비모수적 검정법을 제안하였다. 또한 Monte Carlo 모의실험을 통하여 기존의 방법들과 검정력(power)을 비교하였다.

The treatment effect in clinical tests depending on dose of the drug; however, it can show a decreasing trend in fixed dose level due to side effects. The trend is known as an umbrella pattern; in addition, the method for the umbrella alternative is quite useful when the tendency is predicted in advance. In this paper, we propose a nonparametric method of umbrella alternatives for a one-way layout by using linear placement described in Orban and Wolfe (1982). The Monte Carlo simulation is adapted to compare the power of proposed procedure with previous methods.

키워드

참고문헌

  1. Alvo, M. (2008). Nonparametric tests of hypotheses for umbrella alternatives, Canadian Journal of Statistics, 36, 143-156. https://doi.org/10.1002/cjs.5550360113
  2. Bhat, S. V. (2009). Simple K-sample rank tests for umbrella alternatives, Research Journal of Mathematics and Statistics, 1, 27-29.
  3. Chen, Y. I. and Wolfe, D. A. (1990). A study of distribution-free tests for umbrella alternatives, Biometrical Journal, 32, 48-57.
  4. Chen, Y. I. and Wolfe, D. A. (1993). Nonparametric procedures for comparing umbrella pattern treatment effects with a control in a one-way layout, Biometrics, 455-465.
  5. Chung, T. S. and Kim, D. (2007). Nonparametric method using placement in one-way layout, The Korean Communications in Statistics, 14, 551-560. https://doi.org/10.5351/CKSS.2007.14.3.551
  6. Hettmansperger, T. P. and Norton, R. M. (1987). Tests for patterned alternatives in k-sample problems, Journal of the American Statistical Association, 82, 292-299.
  7. Jonckheere, A. R. (1954). A distribution-free k-sample test against ordered alternatives, Biometrika, 41, 133-145. https://doi.org/10.1093/biomet/41.1-2.133
  8. Kim, D. (1999). A class of distribution-free treatments versus control tests based on placements, Far East Journal of Theoretical Statistics, 3, 19-33.
  9. Kruskal, W. H. and Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis, Journal of the American statistical Association, 47, 583-621. https://doi.org/10.1080/01621459.1952.10483441
  10. Mack, G. A. and Wolfe, D. A. (1981). K-sample rank tests for umbrella alternatives, Journal of the American Statistical Association, 76, 175-181.
  11. Mann, H. B. and Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other, The Annals of Mathematical Statistics, 18, 50-60. https://doi.org/10.1214/aoms/1177730491
  12. Orban, J. and Wolfe, D. A. (1982). A class of distribution-free-two-sample tests based on placement, Journal of the American Statistical Association, 77, 666-671. https://doi.org/10.1080/01621459.1982.10477870
  13. 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.