Survival Analysis: State of the Art PDF
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Survival Analysis: State of the Art NATO ASI Series Advanced Science Institutes Series A Series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical Kluwer Academic Publishers and PhYSical Sciences Dordrecht, Boston and London D Behavioural and Social Sciences E Applied Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris and Tokyo I Global Environmental Change NATO-PCO-DATA BASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords and/or abstracts) to more than 30000 contributions from international scientists published in all sections of the NATO ASI Series. Access to the NATO-PCO-DATA BASE is possible in two ways: - via online FILE 128 (NATO-PCO-DATA BASE) hosted by ESRIN, Via Galileo Galilei, 1-00044 Frascati, Italy. - via CD-ROM "NATO-PCO-DATA BASE" with user-friendly retrieval software in English, French and German (© WTV GmbH and DATAWARE Technologies Inc. 1989). The CD-ROM can be ordered through any member of the Board of Publishers or through NATO-PCO, Overijse, Belgium. Series E: Applied Sciences -Vol. 211 Survival Analysis: State of the Art edited by John P. Klein and Prem K. Goel Department of Statistics, The Ohio State University, Columbus, Ohio, US. .A. Springer-Science+Business Media, B.v. Proceedings of the NATO Advanced Research Workshop on Survival Analysis and Related Topics Columbus, Ohio, U.S.A. 23-28 June 1991 Library of Congress Cataloging-in-Publication Data NATO Advaneed Researeh Workshop an Survival Analys,s and Related Topies (1991 Columbus. Ohio) Surv,val analys,s state of the art I edlted by John P. Kle,n ana Prem K. Goe 1. p. em. -- (NATO ASI serles. Ser,es E, Appllea se,enees ; val. 211> ·Proeeed,ngs of the NATO Advaneed Researeh Workshop an Surv,val Analys,s ana Relatea Top,es, Columbus, Ohio, U.S.A .• 23-28 June 1991 .• Ineludes ,naex. ISBN 978-90-481-4133-3 ( a 1k . pa per) ,. Fa"ur. t,me data analvs,s--Congresses. 2. Surv,val analys,s (8iometryl--Congresses. I. Kle,n, John P., 1950- II. Gaei. Prem K. • 1943- III. Title. IV. Ser,e •• NATO ASI ser,es. Ser,e. E. Appliea se,enees ; no. 211. CA276.A1N37 1991 519.5--ae20 92-734 CIP ISBN 978-90-481-4133-3 ISBN 978-94-015-7983-4 (eBook) DOI 10.1007/978-94-015-7983-4 AII Rights Reserved © 1992 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1992 Softcover reprint of the hardcover 1s t edition 1992 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photo copying, recording or by any information storage and retrieval system, without written permission from the copyright owner. CONTENTS Preface ix Part 1 - Bayesian Approach to Reliability and Survival Analysis Life Testing and Reliability Estimation Under Asymmetric Loss 3 A. P. Basu and R. D. Thompson Discussant -P. W. Laud Bayesian Computations In Survival Models Via the Gibbs Sampler 11 L. Kuo and A. F. M. Smith Discussants -So M. MacEachern and M. West Bayesian Nonparametric Survival Analysis: A Comparison of the Kaplan-Meier and Berliner-Hill Estimators 25 B. M. Hill Discussant-S. M. MacEachern Modelling Time-Varying Hazards and Covariate Effects 47 M. West Discussant -L. M. Berliner Part 2 - Bio-Medical Applications of Survival Analysis Analysis of Trials with Treatment -Individual Interactions 65 J. Cuzick and B. Trejo Discussants -N. Flournoy and P. D. Sasieni Assessment of Dependence In the Life Times of Twins 77 P. Hougaard, B. Harvald, andN. Holm Discussants -M. A. Islam & K. P. Singh, and N. Flournoy Estimating Random Effects In the Framingham Heart Study 99 J. P. Klein, M. L. Moeschberger, Y. H. Li and S. T. Wang Discussant -N. Flournoy Survival Analysis in Genetics: Danish Twin Data Applied To a Gerontological Question 121 J. W. Vaupel, B. Harvald and N. V. Holm, A. I. Yashin and L. Xiu Discussant -H. H. Dayal Part 3 - Engineering Applications of Survival Analysis Some Issues in the Collection and Analysis of Field Reliability Data 141 J. F. Lawless and J.D. Kalbfleisch Discussant - S. Blumenthal Bayesian Modelling For Fatigue Crack Curves 153 P. Palettas and P. K. Goel Discussant -P. W. Laud vi Part 4 - Inference for Survival Models Statistical Analysis Of a Weibull Process With Left-Censored Data 173 M. Engelhardt and L. J. Bain Discussant - S. Blumenthal Kernel Density Estimation from Record-Breaking Data 197 S. Gulati and W. J. Padgett Discussant - S. Blumenthal Semiparametric Estimation Of Parametric Hazard Rates 211 N. L. Hjort Discussants -S. Leurgans and M. West Cox-Type Regression Analysis for Large Numbers of Small Groups of Correlated Failure Time Observations 237 E. W. Lee, L. J. Wei and D. A. Amato Discussant -S. Leurgans Information Bounds For the Additive and Multiplicative Intensity Models 249 P. D. Sasieni Discussant -I. McKeague Part 5 - Left Truncation and Censoring Survival Analysis For Left Censored Data 269 G. Gomez, O. Julia and F. Utzet Discussant -M. L. Moeschberger Regression Analysis for Discrete and Continuous Truncated and Eventually Censored Data 289 S. Gross and C. Huber-Carol Discussant -T. Costigan Independent Delayed Entry 309 N. Keiding Discussant -M. L. Moeschberger Part 6 - Models for Survival Analysis Periodic Inspections in a Longitudinal Study: Viewing Occult Tumors Through a Filter 329 E. Arjas and P. Haara Discussant -S. Leurgans Survival Under Multiple Time Scales in Dynamic Environments 345 N. Singpurwalla Discussant -P. W. Laud Nonparametric Identifiability of Marginal Survival Distributions in the Presence of Dependent Competing Risks and a Prognostic Covariate 355 E. V. Slud Discussant -I. McKeague vii Part 7 - Multivariate Failure Time Analysis Frailty Models For Multiple Event Times 371 D. Oakes A Nonparametric Approach To Dependence For Bivariate Censored Data 381 O. Pons, A. Kaddour and E. de Turckheim Marginal and Conditional Models for the Analysis of Multivariate Failure Time Data 393 R. L. Prentice and J. Cai Multivariate Failure Time Analysis: Discussion of Papes by Oakes; Pons, Kaddour and De Turckheim; and Prentice and Cai 407 B. Turnbull Rejoinders -D. Oakes; O. Pons, A. Kaddour andE. de Turckheim; and R. L. Prentice and J. Cai Part 8 - Social Science Applications of Survival Analysis Survivor Functions as Dependent Variables In Demographic Analysis 423 K. Namboodiri Discussant -H. H. Dayal Relation Between The Rate Of Return To Tenure, Earnings Growth and Job Switching 435 R. J. Olsen Discussant -H. H. Dayal List of Contributors 449 Index 451 Preface Survival analysis is a highly active area of research with applications spanning the physical, engineering, biological, and social sciences. In addition to statisticians and biostatisticians, researchers in this area include epidemiologists, reliability engineers, demographers and economists. The economists survival analysis by the name of duration analysis and the analysis of transition data. We attempted to bring together leading researchers, with a common interest in developing methodology in survival analysis, at the NATO Advanced Research Workshop. The research works collected in this volume are based on the presentations at the Workshop. Analysis of survival experiments is complicated by issues of censoring, where only partial observation of an individual's life length is available and left truncation, where individuals enter the study group if their life lengths exceed a given threshold time. Application of the theory of counting processes to survival analysis, as developed by the Scandinavian School, has allowed for substantial advances in the procedures for analyzing such experiments. The increased use of computer intensive solutions to inference problems in survival analysis~ in both the classical and Bayesian settings, is also evident throughout the volume. Several areas of research have received special attention in the volume. The first area of emphasis is that of multivariate models in survival analysis. Much of the work in this area involves the use of so called frailty models. In these models an unobserved random proportionality factor is applied to the time dependent intensity. The techniques developed were used to model multiple events which may occur on the same individual, such as times from remission to relapse in an acute disease phase, to model the onset times of different diseases in an individual, to allow for heterogeneity of risk beyond that explained by known covariates in a clinical trial, to explore the feasibility of Freis hypothesis, using data on Danish twins, that individuals are born with genetically determined life spans, and to explore the effects of a common environmental or genetic factors on cardiovascular disease using data on siblings from the Framingham Heart Study. Estimation techniques proposed for these models included semiparametric estimation using an EM algorithm based on either a profile or rank likelihood, extensions of standard counting process methodology to multiple occurrence data, as well as the rigorous construction of efficient estimation based on the influence function. Other work on multivariate survival analysis focused on a nonparametric approach based on generalization of the standard Nelson-Aalen estimator of the cumulative intensity to more than one dimension and the development of tests for independence conditional on observable covariates. The second area of emphasis was the use of Bayesian methodology in survival analysis. Recent advances in this area presented at the workshop included the application of the Gibbs sampler to survival experiments, the use of Bayesian updating in the estimation of piecewise proportional hazards models where the parameters 'evolve' over time, the demonstration that some Bayesian nonparametric estimation outperform the usual Product-Limit estimator of the survival function, the construction of more appropriate asymmetric loss functions for use in reliability applications, and the application of Bayes methodology to modeling Fatigue Crack Propagation. The third area of emphasis was the development of statistical methods to accommodate left censoring and either right or left truncation. These techniques are useful for modeling AIDS incidence, as well as delayed entry into a study. The properties of a Kaplan-Meier estimator for left censored data were developed, a Cox model based on the retro-hazard was developed for the right-truncated left-censored data, and fundamental work on the use of filtered counting processes for survival data with delayed entry was ix x presented. Finally, the fourth area of emphasis was the applications of the survival analysis methodology to various areas disciplines. The present volume represents recent advances in this highly active area of statistical research. The collection is based on the invited papers at the NATO Advanced Research Workshop held at The Ohio State University, Columbus, Ohio, from June 23-28, 1991. The financial support for this workshop was provided by the NATO Advanced Research Workshop Program, the National Institute of Health, under grant 1 R13 CA54325, the National Science Foundation, under grant DMS-9018052, the Department of Statistics, the Department ofP reventive Medicine, the College ofM athematical and Physical Sciences, the College of Medicine, and the Office of The Vice-President For Research at The Ohio State University, as well as the OSU Comprehensive Cancer Center which is funded by PHS Grant 2 P30 Ca 16058-16A1. Without their generous support, it would have been impossible to organize the workshop. We are grateful to the other members of the Program Committee, Neils Keiding (University of Copenhagen) and Adrian F.M. Smith (Imperial College), who were helpful in putting together an impressive list of invited speakers. We highly appreciate the efforts of the invited speakers and discussants, who created an excellent learning environment at the workshop in addition to a high standard of scientific content of the presentations. Special thanks to the faculty and students of the Department of Statistics who helped with the local arrangements for the workshop. Finally, this volume would not have been possible without the long and hard hours put in by Myrtle Pfouts in the word processing of the manuscripts. This effort is most genuinely appreciated. John P. Klein Prem K. Goel Columbus, November 21, 1991 PART 1 BAYESIAN APPROACH TO RELIABILITY AND SURVIVAL ANALYSIS
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