Mathematical Methods In Survival Analysis, Reliability And Quality Of Life

This page intentionally left blank Mathematical Methods in Survival Analysis, Reliability and Quality of Life This page intentionally left blank Mathematical Methods in Survival Analysis, Reliability and Quality of Life Edited by Catherine Huber Nikolaos Limnios Mounir Mesbah Mikhail Nikulin First published in Great Britain and the United States in 2008 by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 6 Fitzroy Square London W1T 5DX UK John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.iste.co.uk www.wiley.com © ISTE Ltd, 2008 The rights of Catherine Huber, Nikolaos Limnios, Mounir Mesbah and Mikhail Nikulin to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Cataloging-in-Publication Data Mathematical methods in survival analysis, reliability and quality of life / edited by Catherine Huber ... [et al.]. p. cm. Includes bibliographical references and index. ISBN: 978-1-84821-010-3 1. Failure time data analysis. 2. Survival analysis (Biometry) I. Huber, Catherine. QA276.M342 2008 519.5'46--dc22 2007046232 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: 978-1-84821-010-3 Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire. Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 PART I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Chapter 1. Model Selection for Additive Regression in the Presence of Right-Censoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elodie B RUNEL and Fabienne C OMTE 17 1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Assumptions on the model and the collection of approximation spaces 1.2.1. Non-parametric regression model with censored data . . . . . . 1.2.2. Description of the approximation spaces in the univariate case . 1.2.3. The particular multivariate setting of additive models . . . . . . 1.3. The estimation method . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1. Transformation of the data . . . . . . . . . . . . . . . . . . . . . 1.3.2. The mean-square contrast . . . . . . . . . . . . . . . . . . . . . . 1.4. Main result for the adaptive mean-square estimator . . . . . . . . . . 1.5. Practical implementation . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1. The algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2. Univariate examples . . . . . . . . . . . . . . . . . . . .