Regression with Linear Predictors
This text provides, in a non-technical language, a unified treatment of regression models for different outcome types, such as linear regression, logistic regression, and Cox regression. This is done by focusing on the many common aspects of these models,
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Per Kragh Andersen • Lene Theil Skovgaard
Regression with Linear Predictors With 171 illustrations by Therese Graversen
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Per Kragh Andersen University of Copenhagen Dept. Biostatistics Øster Farimagsgade 5 DK-1014 Copenhagen K Denmark [email protected]
Lene Theil Skovgaard University of Copenhagen Dept. Biostatistics Øster Farimagsgade 5 DK-1014 Copenhagen K Denmark [email protected]
Series Editors M. Gail National Cancer Institute Bethesda, MD 20892, USA K. Krickeberg Le Chatelet F-63270 Manglieu, France J. Samet Department of Preventive Medicine Keck School of Medicine University of Southern California 1441 Eastlake Ave. Room 4436, MC 9175 Los Angeles, CA 90089
A. Tsiatis Department of Statistics North Carolina State University Raleigh, NC 27695, USA W. Wong Department of Statistics Stanford University Stanford, CA 94305-4065, USA
ISSN 1431-8776 ISBN 978-1-4419-7169-2 e-ISBN 978-1-4419-7170-8 DOI 10.1007/978-1-4419-7170-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010931468 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
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Preface This is a book about regression analysis, that is, the situation in statistics where the distribution of a response (or outcome) variable is related to explanatory variables (or covariates). This is an extremely common situation in the application of statistical methods in many fields, and linear regression, logistic regression, and Cox proportional hazards regression are frequently used for quantitative, binary, and survival time outcome variables, respectively. Several books on these topics have appeared and for that reason one may well ask why we embark on writing still another book on regression. We have two main reasons for doing this: 1. First, we want to highlight similarities among linear, logistic, proportional hazards, and other regression models that include a linear predictor. These models are often treated entirely separately in texts in spite of the fact that all operations on the models dealing with the linear predictor are precisely the same, including handling of categorical and quantitative covariates, test
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