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Estimation Under Order Restrictions

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Modeling Dose-Response Microarray Data in Early Drug Development Experiments Using R

Part of the book series: Use R! ((USE R))

Abstract

Chapter 2 covers the basic setting on which we focus in the first part of this book, i.e., the one in which a response variable Y is expected to increase or decrease monotonically with respect to increasing levels of a predictor variable x which in biomedical applications is usually the dose or concentration of a drug. We assume that the mean response is given by

$$E(Y \vert x) = \mu (x),$$

where μ( ) is an unknown monotone function. In Chap. 2, we focus on the estimation problem under order restriction using isotonic regression.

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References

  • Barlow, R. E., Bartholomew, D. J., Bremner, M. J., & Brunk, H. D. (1972). Statistical inference under order restriction. New York: Wiley.

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  • De Leeuw, J., Hornik, K., Mair, P. (2009). Isotone optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods. Journal of Statistical Software, 32(5), 1–24.

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Author information

Authors and Affiliations

  1. Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Center for Statistics (CenStat), Hasselt University, Diepenbeek, Belgium

    Ziv Shkedy & Marc Aerts

  2. Biostatistics and Programming, Jansenn Pharmaceutical Companies of Johnson & Johnson, Raritan, NJ, USA

    Dhammika Amaratunga

Authors
  1. Ziv Shkedy
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  2. Dhammika Amaratunga
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  3. Marc Aerts
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Corresponding author

Correspondence to Ziv Shkedy .

Editor information

Editors and Affiliations

  1. , VMRD, Pfizer Animal Health, Hoge Wei 1, Zaventem, 1930, Belgium

    Dan Lin

  2. Center for Statistics, Hasselt University, Agoralaan 1, Diepenbeek, 3590, Belgium

    Ziv Shkedy

  3. , Department of Statistics and, School of Mathematical Sciences, Ramat Aviv, Tel Aviv, 69978, Israel

    Daniel Yekutieli

  4. Johnson & Johnson, Route 202 1000, Raritan, 08869, New Jersey, USA

    Dhammika Amaratunga

  5. , Biostatistics and Programming Center of, Janssen Pharmaceutica, Turnhoutseweg 30, Beerse, 2340, Belgium

    Luc Bijnens

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© 2012 Springer-Verlag Berlin Heidelberg

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Shkedy, Z., Amaratunga, D., Aerts, M. (2012). Estimation Under Order Restrictions. In: Lin, D., Shkedy, Z., Yekutieli, D., Amaratunga, D., Bijnens, L. (eds) Modeling Dose-Response Microarray Data in Early Drug Development Experiments Using R. Use R!. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24007-2_2

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