Order-restricted inference for multivariate binary data with application to toxicology

Ori Davidov, Shyamal Peddada

Research output: Contribution to journalArticlepeer-review


In many applications, researchers collect multivariate binary response data under two or more naturally ordered experimental conditions. In such situations, one is often interested in using all binary outcomes simultaneously to detect an ordering among the experimental conditions. To make such comparisons, we develop a general methodology for testing for the multivariate stochastic order between K ≥ 2 multivariate binary distributions. Our proposed test uses order-restricted estimators, which, according to our simulation study, are more efficient than the unrestricted estimators in terms of their mean squared error. We compared the power of the proposed test with that of several alternative tests, including procedures that combine individual univariate tests for order, such as union-intersection tests and a Bonferroni-based test. We also compared the proposed test with an unrestricted Hotelling T 2-type test. Our simulations suggest that the proposed method competes well with these alternatives. The gain in power is often substantial. The proposed methodology is illustrated by applying it to a two-year rodent cancer bioassay data obtained from the U.S. National Toxicology Program. Supplemental materials are available online.

Original languageEnglish
Pages (from-to)1394-1404
Number of pages11
JournalJournal of the American Statistical Association
Issue number496
StatePublished - Dec 2011

Bibliographical note

Funding Information:
Ori Davidov is Associate Professor, Department of Statistics, University of Haifa, Mount Carmel, Haifa 31905, Israel (E-mail: [email protected]). Shyamal Peddada is Senior Investigator, Biostatistics Branch, National Institute of Environmental Health Sciences, Alexander Drive, Research Triangle Park, NC 27709 (E-mail: [email protected]). The research of Ori Davi-dov was partially supported by the Israeli Science Foundation (grant 875/09) and was conducted when visiting Shyamal Das Peddada. This research was supported in part by the Intramural Research Program of the National Institute of Environmental Health Sciences (grant Z01 ES101744-04). We thank Professor Doron Zeilberger (Rutgers University) for pointing out the connection between the number of upper sets and the Dedekind numbers and Drs. Grace Kissling (NIEHS) and Wenge Guo (New Jersey Institute of Technology) for several useful comments that improved the presentation. We would also like to thank the editors and reviewers for constructive comments that helped improve many aspects of the article.


  • Dose-response study
  • Multivariate binary data
  • Order-restricted statistical inference
  • Stochastic order relation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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