Mathematical Methods in Survival Analysis, Reliability and Quality of Life. Edited by Catherine Huber Nikolaos Limnios Mounir Mesbah Mikhail Nikulin

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1 Mathematical Methods in Survival Analysis, Reliability and Quality of Life Edited by Catherine Huber Nikolaos Limnios Mounir Mesbah Mikhail Nikulin

2 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 John Wiley & Sons, Inc. 6 Fitzroy Square 111 River Street London W1T 5DX Hoboken, NJ UK USA 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 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: Failure time data analysis. 2. Survival analysis (Biometry) I. Huber, Catherine. QA276.M '46--dc British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.

3 Contents Preface PART I Chapter 1. Model Selection for Additive Regression in the Presence of Right-Censoring Elodie BRUNEL and Fabienne COMTE 1.1. Introduction Assumptions on the model and the collection of approximation spaces Non-parametric regression model with censored data Description of the approximation spaces in the univariate case The particular multivariate setting of additive models The estimation method Transformation of the data The mean-square contrast Main result for the adaptive mean-square estimator Practical implementation The algorithm Univariate examples Bivariate examples A trivariate example Bibliography Chapter 2. Non-parametric Estimation of Conditional Probabilities, Means and Quantiles under Bias Sampling Odile PONS 2.1. Introduction Non-parametric estimation of p Bias depending on the value of Y

4 6 Mathematical Methods in Survival Analysis, Reliability and Quality of Life 2.4. Bias due to truncation on X Truncation of a response variable in a non-parametric regression model Double censoring of a response variable in a non-parametric model Other truncation and censoring of Y in a non-parametric model Observation by interval Bibliography Chapter 3. Inference in Transformation Models for Arbitrarily Censored and Truncated Data Filia VONTA and Catherine HUBER 3.1. Introduction Non-parametric estimation of the survival function S Semi-parametric estimation of the survival function S Simulations Bibliography Chapter 4. Introduction of Within-area Risk Factor Distribution in Ecological Poisson Models Léa FORTUNATO, Chantal GUIHENNEUC-JOUYAUX, Dominique LAURIER, Margot TIRMARCHE, Jacqueline CLAVEL and Denis HÉMON 4.1. Introduction Modeling framework Aggregated model Prior distributions Simulation framework Results Strong association between relative risk and risk factor, correlated within-area means and variances (mean-dependent case) Sensitivity to within-area distribution of the risk factor Application: leukemia and indoor radon exposure Discussion Bibliography Chapter 5. Semi-Markov Processes and Usefulness in Medicine Eve MATHIEU-DUPAS, Claudine GRAS-AYGON and Jean-Pierre DAURÈS 5.1. Introduction Methods Model description and notation Construction of health indicators An application to HIV control Context Estimation method

5 Contents Results: new indicators of health state An application to breast cancer Context Age and stage-specific prevalence Estimation method Results: indicators of public health Discussion Bibliography Chapter 6. Bivariate Cox Models Michel BRONIATOWSKI, Alexandre DEPIRE and Ya acov RITOV 6.1. Introduction A dependence model for duration data Some useful facts in bivariate dependence Coherence Covariates and estimation Application: regression of Spearman s rho on covariates Bibliography Chapter 7. Non-parametric Estimation of a Class of Survival Functionals 109 Belkacem ABDOUS 7.1. Introduction Weighted local polynomial estimates Consistency of local polynomial fitting estimators Automatic selection of the smoothing parameter Bibliography Chapter 8. Approximate Likelihood in Survival Models Henning LÄUTER 8.1. Introduction Likelihood in proportional hazard models Likelihood in parametric models Profile likelihood Smoothness classes Approximate likelihood function Statistical arguments Bibliography PART II Chapter 9. Cox Regression with Missing Values of a Covariate having a Non-proportional Effect on Risk of Failure Jean-François DUPUY and Eve LECONTE

6 8 Mathematical Methods in Survival Analysis, Reliability and Quality of Life 9.1. Introduction Estimation in the Cox model with missing covariate values: a short review Estimation procedure in the stratified Cox model with missing stratum indicator values Asymptotic theory A simulation study Discussion Bibliography Chapter 10. Exact Bayesian Variable Sampling Plans for Exponential Distribution under Type-I Censoring Chien-Tai LIN, Yen-Lung HUANG and N. BALAKRISHNAN Introduction Proposed sampling plan and Bayes risk Numerical examples and comparison Bibliography Chapter 11. Reliability of Stochastic Dynamical Systems Applied to Fatigue Crack Growth Modeling Julien CHIQUET and Nikolaos LIMNIOS Introduction Stochastic dynamical systems with jump Markov process Estimation Numerical application Conclusion Bibliography Chapter 12. Statistical Analysis of a Redundant System with One Standby Unit Vilijandas BAGDONAVIČIUS, Inga MASIULAITYTE and Mikhail NIKULIN Introduction The models The tests Limit distribution of the test statistics Bibliography Chapter 13. A Modified Chi-squared Goodness-of-fit Test for the Threeparameter Weibull Distribution and its Applications in Reliability Vassilly VOINOV, Roza ALLOYAROVA and Natalie PYA Introduction Parameter estimation and modified chi-squared tests

7 Contents Power estimation Neyman-Pearson classes Discussion Conclusion Appendix Bibliography Chapter 14. Accelerated Life Testing when the Hazard Rate Function has Cup Shape Vilijandas BAGDONAVIČIUS, Luc CLERJAUD and Mikhail NIKULIN Introduction Estimation in the AFT-GW model AFT model AFT-Weibull, AFT-lognormal and AFT-GW models Plans of ALT experiments Parameter estimation: AFT-GW model Properties of estimators: simulation results for the AFT-GW model Some remarks on the second plan of experiments Conclusion Appendix Bibliography Chapter 15. Point Processes in Software Reliability James LEDOUX Introduction Basic concepts for repairable systems Self-exciting point processes and black-box models White-box models and Markovian arrival processes A Markovian arrival model Parameter estimation Reliability growth Bibliography PART III Chapter 16. Likelihood Inference for the Latent Markov Rasch Model Francesco BARTOLUCCI, Fulvia PENNONI and Monia LUPPARELLI Introduction Latent class Rasch model Latent Markov Rasch model Likelihood inference for the latent Markov Rasch model Log-likelihood maximization

8 10 Mathematical Methods in Survival Analysis, Reliability and Quality of Life Likelihood ratio testing of hypotheses on the parameters An application Possible extensions Discrete response variables Multivariate longitudinal data Conclusions Bibliography Chapter 17. Selection of Items Fitting a Rasch Model Jean-Benoit HARDOUIN and Mounir MESBAH Introduction Notations and assumptions Notations Fundamental assumptions of the Item Response Theory (IRT) The Rasch model and the multidimensional marginally sufficient Rasch model The Rasch model The multidimensional marginally sufficient Rasch model The Raschfit procedure A fast version of Raschfit Estimation of the parameters under the fixed effects Rasch model Principle of Raschfit-fast A model where the new item is explained by the same latent trait as the kernel A model where the new item is not explained by the same latent trait as the kernel Selection of the new item in the scale A small set of simulations to compare Raschfit and Raschfit-fast Parameters of the simulation study Results and computing time A large set of simulations to compare Raschfit-fast, MSP and HCA/CCPROX Parameters of the simulations Discussion The Stata module Raschfit Conclusion Bibliography Chapter 18. Analysis of Longitudinal HrQoL using Latent Regression in the Context of Rasch Modeling Silvia BACCI Introduction Global models for longitudinal data analysis

9 Contents A latent regression Rasch model for longitudinal data analysis Model structure Correlation structure Estimation Implementation with SAS Case study: longitudinal HrQoL of terminal cancer patients Concluding remarks Bibliography Chapter 19. Empirical Internal Validation and Analysis of a Quality of Life Instrument in French Diabetic Patients during an Educational Intervention Judith CHWALOW, Keith MEADOWS, Mounir MESBAH, Vincent COLICHE and Étienne MOLLET Introduction Material and methods Health care providers and patients Psychometric validation of the DHP Psychometric methods Comparative analysis of quality of life by treatment group Results Internal validation of the DHP Comparative analysis of quality of life by treatment group Discussion Conclusion Bibliography Appendices PART IV Chapter 20. Deterministic Modeling of the Size of the HIV/AIDS Epidemic in Cuba Rachid LOUNES, Héctor DE ARAZOZA, Y.H. HSIEH and Jose JOANES Introduction The models The k 2 X model The k 2 Y model The k 2 XY model XY The k 2 X+Y model The underreporting rate Fitting the models to Cuban data Discussion and concluding remarks Bibliography

10 12 Mathematical Methods in Survival Analysis, Reliability and Quality of Life Chapter 21. Some Probabilistic Models Useful in Sport Sciences Léo GERVILLE-RÉACHE, Mikhail NIKULIN, Sébastien ORAZIO, Nicolas PARIS and Virginie ROSA Introduction Sport jury analysis: the Gauss-Markov approach Gauss-Markov model Test for non-objectivity of a variable Test of difference between skaters Test for the less precise judge Sport performance analysis: the fatigue and fitness approach Model characteristics Monte Carlo simulation Results Sport equipment analysis: the fuzzy subset approach Statistical model used Sensorial analysis step Results Sport duel issue analysis: the logistic simulation approach Modeling by logistic regression Numerical simulations Results Sport epidemiology analysis: the accelerated degradation approach Principle of degradation in reliability analysis Accelerated degradation model Conclusion Bibliography Appendices A. European Seminar: Some Figures A.1. Former international speakers invited to the European Seminar A.2. Former meetings supported by the European Seminar A.3. Books edited by the organizers of the European Seminar A.4. Institutions supporting the European Seminar (names of colleagues) 355 B. Contributors Index