Testing for order among <i>K</i> populations: theory and examples

Davidov, Ori; Herman, Amir

doi:10.1002/cjs.10041

Cited by 13 publications

(13 citation statements)

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“…The appropriateness of these approaches, particularly for small sample sizes common in toxicology, is hard to decide, since k ranking and pairwise ranking procedures were compared. As an alternative to the Shirley's test, recently, Davidov and Herman (2010) proposed a test procedure for H F 0 that can be accommodated for any stochastic ordering. The test is based on a maximally selectedχ 2 statistics, which are based on projections of the empirical distribution functions on convex cones and Brownian bridges.…”

Section: Discussionmentioning

confidence: 99%

Evaluation of Toxicological Studies Using a Nonparametric Shirley-Type Trend Test for Comparing Several Dose Levels with a Control Group

Konietschke

Hothorn

2012

Statistics in Biopharmaceutical Research

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Program uses Shirley's test for the evaluation of endpoints in hematology, clinical chemistry, and urinalysis, which are assumed to be skewed distributed. Until now, no algorithm for Shirley's test for general unbalanced designs has been devised. A Shirley-type procedure is provided for estimating multiplicity-adjusted p-values or simultaneous confidence intervals for any continuous or discrete distributions and possible heterogeneous variances. Routine evaluation can be performed using the open-source R package nparcomp. The use of simultaneous confidence intervals for the relative effect is recommended, since these scale-invariant intervals allow one to claim the statistical significance of multiple endpoints as well as their biological relevance.

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Section: Discussionmentioning

confidence: 99%

Evaluation of Toxicological Studies Using a Nonparametric Shirley-Type Trend Test for Comparing Several Dose Levels with a Control Group

Konietschke

Hothorn

2012

Statistics in Biopharmaceutical Research

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“…However, the assumption of shift model and lack of protection against the lack of trend result in no inclusion of this test into comparisons. There is also a plethora of tests for testing homogeneity against increasing trend which are based on likelihood ratio; see, for instance, Robertson et al (1988), Wang (1996), El Barmi and Mukerjee (2005), and Davidov and Herman (2010). Since, they have no built-in protection guaranteeing safe use in application to against + we do not include them as well.…”

Section: An Overview Of Competitive Solutionsmentioning

confidence: 98%

Data-Driven Tests for Trend

Wyłupek

2013

Communications in Statistics - Theory and Methods

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This article proposes a new nonparametric test for the ordered alternatives problem in the k-sample setting for null hypothesis of lack of trend. This article further elaborates upon and extends the results of Ledwina and Wyłupek (2012a) obtained for k = 2. Simulations show that the new test has high and stable power and is able to control the Type I error to satisfactory extent, thus solving the problem posed in Terpstra and Magel (2003). Our theoretical results say that asymptotic errors of both kinds do not exceed significance level, thus implying that the test is asymptotically unbiased.

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“…A by‐product of our testing methodology is a general approach to detecting the minimal toxic dose. A non‐parametric procedure for detecting the minimal toxic dose was first developed in Davidov and Herman (2010), who used a maximally selected chi‐bar test. It turns out that using the ODC‐based tests considerably improves on their procedure.…”

Section: The Multisample Problemmentioning

confidence: 99%

“…El‐Barmi and Mukerjee (2005) used one‐sided Kolmogorov–Smirnov statistics and Bonferroni adjustments for hypothesis testing. Using the same estimated DFs Davidov and Herman (2010) developed a more powerful test based on maximally selected chi‐bar statistics.…”

Section: Introductionmentioning

confidence: 99%

Ordinal Dominance Curve Based Inference for Stochastically Ordered Distributions

Davidov

Herman

2012

Journal of the Royal Statistical Society Series B: Statistical Methodology

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In a variety of applications researchers collect data that are sampled under ordered experimental conditions. In such situations it is reasonable to assume that outcomes are ordered stochastically by the level of the treatment. For example a toxicologist may want to assess the effect of a toxin on the reproductive system by studying the number of offspring produced by an animal as a function of the dose that it received. A variety of scientific questions arise in such a context. The most basic is whether a dose-response relationship is present. If so, determining the minimal toxic dose is of great interest. The strength of the ordering between groups i < j may be assessed by the probabilities P.X i X j / or monotone functions thereof. Large probabilities indicate a strong ordering. We find that such (and other) questions are naturally addressed by studying the ordinal dominance curve and the area under the curve (AUC). We develop new, non-parametric, order-restricted estimators for the AUCs in K 2 samples and investigate them in detail. We show that the restricted estimators are strongly consistent and have lower meansquared error compared with the unrestricted estimators. In the two-sample case estimators are considerably improved in those situations where the data are highly variable and/or sample sizes are small, and where the AUC is close to its boundary value. Note that these are precisely the conditions under which estimating the AUC is difficult. Simulations indicate that in the multisample case estimators are improved under a much broader set of conditions with substantial reductions in mean-squared error. These estimators provide a basis for a family of distribution-free tests for the usual stochastic order in K 2 samples. Limiting distributions are derived. An accurate and simple approximation to the tail area is given for K D 2. Simulation studies show that the new tests perform well compared with existing alternatives. The methodology proposed is illustrated by applying it to an aquatic toxicology study where it is used to determine the minimal toxic dose more accurately.

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Testing for order among K populations: theory and examples

Cited by 13 publications

References 57 publications

Evaluation of Toxicological Studies Using a Nonparametric Shirley-Type Trend Test for Comparing Several Dose Levels with a Control Group

Evaluation of Toxicological Studies Using a Nonparametric Shirley-Type Trend Test for Comparing Several Dose Levels with a Control Group

Data-Driven Tests for Trend

Ordinal Dominance Curve Based Inference for Stochastically Ordered Distributions

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