Nonparametric Identification of the Minimum Effective Dose
- PDF / 434,741 Bytes
- 8 Pages / 504 x 719.759 pts Page_size
- 92 Downloads / 203 Views
Drug Irlformo~ionJorrrndl. Vol. 36. pp. X81 XXX. ? ( W E Printed in the USA. All rights rehcrved.
Copyright Q 1002 Drug Infmnation Associalion Inc.
NONPARAMETRIC IDENTIFICATION OF THE MINIMUM EFFECTIVE DOSE MARKUSNEUHAUSER Senior Lecturer, Department of Mathematics and Statistics, University of Otago, Dunedin. New Zealand
In clinical dose-finding trials the identification of the ttrinirnum effective dose is ittiporrunt. Recenrl!, a nonpuranretric stepdown procedure bmed upon Wilcmon runk sun1 tests WYIS proposed f o r identijjing the minirnrcnr effectiLse dose. However; the recently introduced modified Bnunrgartner- We$-Schindler statistic is veq poirerful nnd, conseyuentl~v,mri?, be used in the step-down procedure instead of the Wilcoxon rank sum. The two stepdowrr closed testing procedures based upon the Wilcoxon arid the modijied BaumgartnerWe$-Schindler statistic, respectively, $rere compared in a Monte Curlo s1ud.y. According to simulation result.7,the procedure based upon the rnodlfied Raumgarrner- We$-Schindler stutistic is more powerful thurr thmt bnsed upon the Mann- Whitney or Wilcoxon test f o r identibing the nrininiicnr elfectivc dose. Key word.7: Wilcoxon rank sum test; M a n n - W h i h e y test: Baumgnrtner-WeiR-Schindler \tatistic; Step-down procedure: Many-one pairwise tests
INTRODUCTION: THE BAUMGARTNER-WEIfi-SCHINDLER STATISTIC I N 1998, BAUMGARTNER ET AL. ( I ) introduced a novel nonparametric two-sample test. The proposed test statistic is 1 B = - * ( B , + B)). 2
where
and R , < . . . < R,, (HI< . . . < H,,,) denote the combined-samples ranks of the ?I (m)values from the first (second) sample in increasing order of magnitude. Large values of B support the alternative that there are differences between the two samples. The test based on the Reprint address: Dr. Markus Neuhauser. Department of Mathematics and Statistic.;. University of Otago, Dunedin, New Zealand (E-mail: mnruhauserQmaths.otago.ac.nL).
88I
882
Mnrkiis Neuhiiuser
asymptotic distribution of R (see reference 1 for details regarding this asymptotic distribution) is at least as powerful as commonly used nonparametric tests such as the Wilcoxon test (1). However, the test can have an inflated type I error rate in case of small sample sizes (2). Furthermore, the test can be extremely anticonservative in the presence of ties when the test statistic is computed using average ranks (3). Consequently, an exact test based upon the permutation distribution of B was proposed (2). I n order to perform a permutation test the test statistic must be computed for the originally observed data. In the following step all possible permutations under the null hypothesis must be generated and the test statistic must be recomputed for each permutation. In the last step, the null hypothesis can be accepted or rejected using the permutation distribution of the test statistic as a guide. The p-value is the probability for the permutations yielding a statistic as supportive or more supportive of the alternative than the original observed test sta
Data Loading...
