Permutation Testing for Isotonic Inference on Association Studies in Genetics
The purpose of this book is to illustrate a new statistical approach to test allelic association and genotype-specific effects in the genetic study of diseases. There are some parametric and non-parametric methods available for this purpose. We deal with
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Rosa Arboretti Livio Corain Dario Mazzaro Luigi Salmaso •
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Permutation Testing for Isotonic Inference on Association Studies in Genetics
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Rosa Arboretti Department of Territory and Agri-Foresta University of Padova Agripolis-viale dell’Universita’, 16 35020 Legnaro (PD) Italy e-mail: [email protected]
Dario Mazzaro Generali Group Assicurazioni Generali s.p.a Via Marocchesa, 14 31021 Mogliano Veneto (TV) Italy e-mail: [email protected]
Livio Corain Department of Management and Engineering University of Padova Straoella San Nicola 3 36100 Vicenza Italy e-mail: [email protected]
Luigi Salmaso Department of Management and Engineering University of Padova Stradella San Nicola 3 36100 Vicenza Italy e-mail: [email protected]
ISSN 2191-544X ISBN 978-3-642-20583-5 DOI 10.1007/978-3-642-20584-2
e-ISSN 2191-5458 e-ISBN 978-3-642-20584-2
Springer Heidelberg Dordrecht London New York Ó Luigi Salmaso 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar, Berlin/Figueres Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Association Studies in Genetics. . . . . . . . . . . . . 2.1 Case–Control Studies in Genetics . . . . . . . . 2.2 Other Methods . . . . . . . . . . . . . . . . . . . . . 2.3 Case–Control Design Study . . . . . . . . . . . . 2.4 The Problem of Allelic Association Analysis References . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3
The Nonparametric Permutation Methodology . . . . . . . 3.1 Basic Concepts of the Theory of Permutation Tests. . 3.2 Sampling Inspection of Permutation Space . . . . . . . . 3.3 The Nonparametric Combination of Dependent Tests References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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