Table Of ContentSurvival Analysis: State of the Art
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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
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© 1992 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1992
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No part of the material protected by this copyright notice may be reproduced or
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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
