Survival Analysis with Interval-Censored Data: A Practical Approach with Examples in R, SAS, and BUGS

617 Pages·2018·10.02 MB·English

by  Kris Bogaerts

SURVIVAL ANALYSIS with
INTERVAL-CENSORED DATA
A Practical Approach with
Examples in R, SAS, and BUGS
CHAPMAN & HALL/CRC
Interdisciplinar y Statistics Series
Series editors: N. Keiding, B.J.T. Morgan, C.K. Wikle, P. van der Heijden
Published titles
AGE-PERIOD-COHORT ANALYSIS: NEW MODELS, METHODS, AND
EMPIRICAL APPLICATIONS Y. Yang and K. C. Land
ANALYSIS OF CAPTURE-RECAPTURE DATA R. S. McCrea and B. J. T. Morgan
AN INVARIANT APPROACH TO STATISTICAL ANALYSIS OF SHAPES
S. Lele and J. Richtsmeier
ASTROSTATISTICS G. Babu and E. Feigelson
BAYESIAN ANALYSIS FOR POPULATION ECOLOGY R. King, B. J. T. Morgan,
O. Gimenez, and S. P. Brooks
BAYESIAN DISEASE MAPPING: HIERARCHICAL MODELING IN SPATIAL
EPIDEMIOLOGY, SECOND EDITION A. B. Lawson
BIOEQUIVALENCE AND STATISTICS IN CLINICAL PHARMACOLOGY
S. Patterson and B. Jones
CAPTURE-RECAPTURE METHODS FOR THE SOCIAL AND MEDICAL
SCIENCES
D. Böhning, P. G. M. van der Heijden, and J. Bunge
CLINICAL TRIALS IN ONCOLOGY, THIRD EDITION S. Green, J. Benedetti, A. Smith,
and J. Crowley
CLUSTER RANDOMISED TRIALS R.J. Hayes and L.H. Moulton
CORRESPONDENCE ANALYSIS IN PRACTICE, THIRD EDITION M. Greenacre
THE DATA BOOK: COLLECTION AND MANAGEMENT OF RESEARCH DATA
M. Zozus
DESIGN AND ANALYSIS OF QUALITY OF LIFE STUDIES IN CLINICAL TRIALS,
SECOND EDITION D.L. Fairclough
DYNAMICAL SEARCH L. Pronzato, H. Wynn, and A. Zhigljavsky
FLEXIBLE IMPUTATION OF MISSING DATA S. van Buuren
GENERALIZED LATENT VARIABLE MODELING: MULTILEVEL, LONGITUDI-
NAL, AND STRUCTURAL EQUATION MODELS A. Skrondal and S. Rabe-Hesketh
GRAPHICAL ANALYSIS OF MULTI-RESPONSE DATA K. Basford and J. Tukey
INTRODUCTION TO COMPUTATIONAL BIOLOGY: MAPS, SEQUENCES, AND
GENOMES M. Waterman
MARKOV CHAIN MONTE CARLO IN PRACTICE W. Gilks, S. Richardson, and
D. Spiegelhalter
Published titles
MEASUREMENT ERROR ANDMISCLASSIFICATION IN STATISTICS AND EPIDE-
MIOLOGY: IMPACTS AND BAYESIAN ADJUSTMENTS P. Gustafson
MEASUREMENT ERROR: MODELS, METHODS, AND APPLICATIONS
J. P. Buonaccorsi
MEASUREMENT ERROR: MODELS, METHODS, AND APPLICATIONS
J. P. Buonaccorsi
MENDELIAN RANDOMIZATION: METHODS FOR USING GENETIC VARIANTS
IN CAUSAL ESTIMATION S.Burgess and S.G. Thompson
META-ANALYSIS OF BINARY DATA USINGPROFILE LIKELIHOOD D. Böhning,
R. Kuhnert, and S. Rattanasiri
MISSING DATA ANALYSIS IN PRACTICE T. Raghunathan
MODERN DIRECTIONAL STATISTICS C. Ley and T. Verdebout
POWER ANALYSIS OF TRIALS WITH MULTILEVEL DATA M. Moerbeek and
S. Teerenstra
SPATIAL POINT PATTERNS: METHODOLOGY AND APPLICATIONS WITH R
A. Baddeley, E Rubak, and R. Turner
STATISTICAL ANALYSIS OF GENE EXPRESSION MICROARRAY DATA T. Speed
STATISTICAL ANALYSIS OF QUESTIONNAIRES: A UNIFIED APPROACH
BASED ON R AND STATA F. Bartolucci, S. Bacci, and M. Gnaldi
STATISTICAL AND COMPUTATIONAL PHARMACOGENOMICS R. Wu and M. Lin
STATISTICS IN MUSICOLOGY J. Beran
STATISTICS OF MEDICAL IMAGING T. Lei
STATISTICAL CONCEPTS AND APPLICATIONS IN CLINICAL MEDICINE
J. Aitchison, J.W. Kay, and I.J. Lauder
STATISTICAL AND PROBABILISTIC METHODS IN ACTUARIAL SCIENCE
P.J. Boland
STATISTICAL DETECTION AND SURVEILLANCE OF GEOGRAPHIC CLUSTERS
P. Rogerson and I. Yamada
STATISTICAL METHODS IN PSYCHIATRY AND RELATED FIELDS:
LONGITUDINAL, CLUSTERED, AND OTHER REPEATED MEASURES DATA
R. Gueorguieva
STATISTICS FOR ENVIRONMENTAL BIOLOGY AND TOXICOLOGY A. Bailer
and W. Piegorsch
STATISTICS FOR FISSION TRACK ANALYSIS R.F. Galbraith
SURVIVAL ANALYSIS WITH INTERVAL-CENSORED DATA: A PRACTICAL
APPROACH WITH EXAMPLES IN R, SAS, AND BUGS
K. Bogaerts, A. Komárek, and E. Lesaffre
VISUALIZING DATA PATTERNS WITH MICROMAPS D.B. Carr and L.W. Pickle

Chapman & Hall/CRC
Interdisciplinary Statistics Series
SURVIVAL ANALYSIS with
INTERVAL-CENSORED DATA
A Practical Approach with
Examples in R, SAS, and BUGS
Kris Bogaerts
Arnošt Komárek
Emmanuel Lesaffre
CRC Press
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Version Date: 20171012
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Contents
List of Tables xvii
List of Figures xxi
Notation xxvii
Preface xxix
I Introduction 1
1 Introduction 3
1.1 Survival concepts . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Types of censoring . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Right censoring . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Interval and left censoring . . . . . . . . . . . . . . . . 4
1.2.3 Some special cases of interval censoring . . . . . . . . 5
1.2.4 Doubly interval censoring . . . . . . . . . . . . . . . . 7
1.2.5 Truncation . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Ignoring interval censoring . . . . . . . . . . . . . . . . . . . 8
1.4 Independent noninformative censoring . . . . . . . . . . . . . 13
1.4.1 Independent noninformative right censoring . . . . . . 13
1.4.2 Independent noninformative interval censoring . . . . 14
1.5 Frequentist inference . . . . . . . . . . . . . . . . . . . . . . 15
1.5.1 Likelihood for interval-censored data . . . . . . . . . . 15
1.5.2 Maximum likelihood theory . . . . . . . . . . . . . . . 17
1.6 Data sets and research questions . . . . . . . . . . . . . . . . 20
1.6.1 Homograft study . . . . . . . . . . . . . . . . . . . . . 20
1.6.2 Breast cancer study . . . . . . . . . . . . . . . . . . . 22
1.6.3 AIDS clinical trial . . . . . . . . . . . . . . . . . . . . 22
1.6.4 Sensory shelf life study. . . . . . . . . . . . . . . . . . 23
1.6.5 Survey on mobile phone purchases . . . . . . . . . . . 25
1.6.6 Mastitis study . . . . . . . . . . . . . . . . . . . . . . 27
1.6.7 Signal Tandmobiel study . . . . . . . . . . . . . . . . 28
1.7 Censored data in R and SAS . . . . . . . . . . . . . . . . . . 30
1.7.1 R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
vii
viii Contents
1.7.2 SAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2 Inference for right-censored data 35
2.1 Estimation of the survival function . . . . . . . . . . . . . . . 35
2.1.1 Nonparametric maximum likelihood estimation . . . . 35
2.1.2 R solution . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.3 SAS solution . . . . . . . . . . . . . . . . . . . . . . . 40
2.2 Comparison of two survival distributions . . . . . . . . . . . 41
2.2.1 Review of significance tests . . . . . . . . . . . . . . . 41
2.2.2 R solution . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.2.3 SAS solution . . . . . . . . . . . . . . . . . . . . . . . 45
2.3 Regression models . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3.1 Proportional hazards model . . . . . . . . . . . . . . . 46
2.3.1.1 Model description and estimation . . . . . . 46
2.3.1.2 Model checking. . . . . . . . . . . . . . . . . 47
2.3.1.3 R solution . . . . . . . . . . . . . . . . . . . 50
2.3.1.4 SAS solution . . . . . . . . . . . . . . . . . . 52
2.3.2 Accelerated failure time model . . . . . . . . . . . . . 53
2.3.2.1 Model description and estimation . . . . . . 53
2.3.2.2 Model checking. . . . . . . . . . . . . . . . . 55
2.3.2.3 R solution . . . . . . . . . . . . . . . . . . . 56
2.3.2.4 SAS solution . . . . . . . . . . . . . . . . . . 58
II Frequentist methods for interval-censored data 61
3 Estimating the survival distribution 63
3.1 Nonparametric maximum likelihood . . . . . . . . . . . . . . 63
3.1.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.2 Asymptotic results . . . . . . . . . . . . . . . . . . . . 67
3.1.3 R solution . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1.4 SAS solution . . . . . . . . . . . . . . . . . . . . . . . 71
3.2 Parametric modelling . . . . . . . . . . . . . . . . . . . . . . 77
3.2.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.2 Model selection . . . . . . . . . . . . . . . . . . . . . . 78
3.2.3 Goodness of fit . . . . . . . . . . . . . . . . . . . . . . 78
3.2.4 R solution . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.2.5 SAS solution . . . . . . . . . . . . . . . . . . . . . . . 82
3.3 Smoothing methods . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.1 Logspline density estimation . . . . . . . . . . . . . . 85
3.3.1.1 A smooth approximation to the density . . . 85
3.3.1.2 Maximum likelihood estimation . . . . . . . 86
3.3.1.3 R solution . . . . . . . . . . . . . . . . . . . 87
3.3.2 Classical Gaussian mixture model . . . . . . . . . . . 90
Contents ix
3.3.3 Penalized Gaussian mixture model . . . . . . . . . . . 93
3.3.3.1 R solution . . . . . . . . . . . . . . . . . . . 99
3.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . 104
4 Comparison of two or more survival distributions 105
4.1 Nonparametric comparison of survival curves . . . . . . . . . 105
4.1.1 Weighted log-rank test: derivation . . . . . . . . . . . 107
4.1.2 Weighted log-rank test: linear form . . . . . . . . . . . 109
4.1.3 Weighted log-rank test: derived from the linear
transformation model . . . . . . . . . . . . . . . . . . 109
4.1.4 Weighted log-rank test: the G(cid:37),γ family . . . . . . . . 111
4.1.5 Weighted log-rank test: significance testing . . . . . . 112
4.1.6 R solution . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.1.7 SAS solution . . . . . . . . . . . . . . . . . . . . . . . 123
4.2 Sample size calculation . . . . . . . . . . . . . . . . . . . . . 127
4.3 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . 128
5 The proportional hazards model 131
5.1 Parametric approaches . . . . . . . . . . . . . . . . . . . . . 132
5.1.1 Maximum likelihood estimation . . . . . . . . . . . . . 132
5.1.2 R solution . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.1.3 SAS solution . . . . . . . . . . . . . . . . . . . . . . . 135
5.2 Towards semiparametric approaches . . . . . . . . . . . . . . 136
5.2.1 Piecewise exponential baseline survival model . . . . . 137
5.2.1.1 Model description and estimation . . . . . . 137
5.2.1.2 R solution . . . . . . . . . . . . . . . . . . . 138
5.2.1.3 SAS solution . . . . . . . . . . . . . . . . . . 140
5.2.2 SemiNonParametric approach . . . . . . . . . . . . . . 141
5.2.2.1 Model description and estimation . . . . . . 141
5.2.2.2 SAS solution . . . . . . . . . . . . . . . . . . 142
5.2.3 Spline-based smoothing approaches . . . . . . . . . . . 144
5.2.3.1 Two spline-based smoothing approaches . . . 144
5.2.3.2 R solution . . . . . . . . . . . . . . . . . . . 146
5.2.3.3 SAS solution . . . . . . . . . . . . . . . . . . 147
5.3 Semiparametric approaches . . . . . . . . . . . . . . . . . . . 149
5.3.1 Finkelstein’s approach . . . . . . . . . . . . . . . . . . 149
5.3.2 Farrington’s approach . . . . . . . . . . . . . . . . . . 150
5.3.3 Iterative convex minorant algorithm . . . . . . . . . . 153
5.3.4 Grouped proportional hazards model . . . . . . . . . . 153
5.3.5 Practical applications . . . . . . . . . . . . . . . . . . 154
5.3.5.1 Two examples . . . . . . . . . . . . . . . . . 154
5.3.5.2 R solution . . . . . . . . . . . . . . . . . . . 155
5.3.5.3 SAS solution . . . . . . . . . . . . . . . . . . 158