Sample Size Determination in Clinical Trials with Multiple Endpoints
This book integrates recent methodological developments for calculating the sample size and power in trials with more than one endpoint considered as multiple primary or co-primary, offering an important reference work for statisticians working in this ar
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Takashi Sozu Tomoyuki Sugimoto Toshimitsu Hamasaki Scott R. Evans
Sample Size Determination in Clinical Trials with Multiple Endpoints 123
SpringerBriefs in Statistics
More information about this series at http://www.springer.com/series/8921
Takashi Sozu Tomoyuki Sugimoto Toshimitsu Hamasaki Scott R. Evans •
•
Sample Size Determination in Clinical Trials with Multiple Endpoints
123
Toshimitsu Hamasaki National Cerebral and Cardiovascular Center Osaka Japan
Takashi Sozu Faculty of Engineering Tokyo University of Science Tokyo Japan Tomoyuki Sugimoto Hirosaki University Graduate School of Science and Technology Hirosaki Japan
ISSN 2191-544X SpringerBriefs in Statistics ISBN 978-3-319-22004-8 DOI 10.1007/978-3-319-22005-5
Scott R. Evans Harvard T.H. Chan School of Public Health Harvard University Boston, MA USA
ISSN 2191-5458
(electronic)
ISBN 978-3-319-22005-5
(eBook)
Library of Congress Control Number: 2015946106 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Continuous Co-primary Endpoints . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Test Statistics and Power . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Known Variance . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Unknown Variance . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Sample Size Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Behavior of the Type I Error Rate, Power and Sample Size . 2.4.1 Type I Error Rate . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2
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