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Two-Sample Rank-Sum Test for Order Restricted Randomized Designs

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Robust Rank-Based and Nonparametric Methods

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 168))

Abstract

This paper develops a new nonparametric test for the location shift between two populations based on order restricted randomized design (ORRD). The ORRD exploits the use of subjective, imprecise or rough information among experimental units to create a blocking factor. The blocking factor, in a given set of H experimental units, is constructed by ranking the units from smallest to largest and then assigning them into H ranking classes (judgment blocks). The design then uses a restricted randomization to assign the treatment regimes to experimental units across these judgment blocks. This randomization scheme induces a positive correlation structure among within-set response measurements. The positive correlation structure then acts as a variance reduction technique in the inference of a contrast parameter in an ORRD. The paper develops a rank-sum test to test the difference between two treatment medians. It is shown that the test performs better than its competitors regardless of the accuracy of the ranking information of within-set units. The paper also constructs point and interval estimators for the contrast parameter. For set sizes H > 2, there are more than one ORRDs. The paper constructs an optimal design that maximizes the asymptotic Pitman efficacy of the proposed test among all possible ORRDs. The proposed test is applied to ACTG 320 clinical trial data.

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Author information

Authors and Affiliations

  1. PTC Therapeutics INC., 674 Roosevelt Avenue, Piscataway, NJ, 08854, USA

    Yiping Sun

  2. The Ohio State University, 404 Cockins Hall, 1958 Neil Avenue, Columbus, OH, 43210, USA

    Omer Ozturk

Authors
  1. Yiping Sun
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  2. Omer Ozturk
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Corresponding author

Correspondence to Omer Ozturk .

Editor information

Editors and Affiliations

  1. Department of Statistics, Rutgers University, New Brunswick, New Jersey, USA

    Regina Y. Liu

  2. Department Statistics, Western Michigan University, Kalamazoo, Michigan, USA

    Joseph W. McKean

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Sun, Y., Ozturk, O. (2016). Two-Sample Rank-Sum Test for Order Restricted Randomized Designs. In: Liu, R., McKean, J. (eds) Robust Rank-Based and Nonparametric Methods. Springer Proceedings in Mathematics & Statistics, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-319-39065-9_8

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