Mathematical methods in survival analysis, reliability and quality of life
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
London
ISTE [u.a.]
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Applied stochastic methods series
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| 020 | |a 9781847040213 |9 978-1-84704-021-3 | ||
| 020 | |a 1847040217 |9 1-84704-021-7 | ||
| 020 | |a 9781848210103 |9 978-1-84821-010-3 | ||
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| 245 | 1 | 0 | |a Mathematical methods in survival analysis, reliability and quality of life |c ed. by Catherine Huber ... |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a London |b ISTE [u.a.] |c 2008 | |
| 300 | |a 369 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Applied stochastic methods series | |
| 650 | 4 | |a Failure time data analysis | |
| 650 | 4 | |a Survival analysis (Biometry) | |
| 650 | 0 | 7 | |a Ereignisdatenanalyse |0 (DE-588)4132103-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zuverlässigkeitstheorie |0 (DE-588)4195525-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Zuverlässigkeitstheorie |0 (DE-588)4195525-0 |D s |
| 689 | 0 | 2 | |a Mathematische Methode |0 (DE-588)4155620-3 |D s |
| 689 | 0 | |C b |5 DE-604 | |
| 700 | 1 | |a Huber, Catherine |e Sonstige |4 oth | |
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Datensatz im Suchindex
| DE-BY-UBR_call_number | 02/21.Q0060 |
|---|---|
| DE-BY-UBR_katkey | 3868767 |
| DE-BY-UBR_location | 00 |
| DE-BY-UBR_media_number | 069040997496 |
| _version_ | 1822742694638649344 |
| adam_text | Contents
Preface
......................................... 13
Part
і
......................................... 15
Chapter
1.
Model Selection for Additive Regression in the Presence of
Right-Censoring
................................... 17
Elodie Brunel
and
Fabienne Comte
1.1.
Introduction
................................. 17
1.2.
Assumptions on the model and the collection of approximation spaces
18
1.2.1.
Non-parametric regression model with censored data
...... 18
1.2.2.
Description of the approximation spaces in the univariate case
. 19
1.2.3.
The particular multivariate setting of additive models
...... 20
1.3.
The estimation method
........................... 20
1.3.1.
Transformation of the data
..................... 20
1.3.2.
The mean-square contrast
...................... 21
1.4.
Main result for the adaptive mean-square estimator
.......... 22
1.5.
Practical implementation
......................... 23
1.5.1.
The algorithm
............................. 23
1.5.2.
Univariate examples
......................... 24
1.5.3.
В
¡variate
examples
.......................... 27
1.5.4.
A trivariate example
......................... 28
1.6.
Bibliography
................................ 30
Chapter
2.
Non-parametric Estimation of Conditional Probabilities, Means
and
Quantités
under Bias Sampling
....................... 33
Odile Pons
2.1.
Introduction
................................. 33
2.2.
Non-parametric estimation of
ρ
...................... 34
2.3.
Bias depending on the value of
F
.................... 35
6
Mathematical Methods in Survival Analysis, Reliability and Quality of Life
2.4.
Bias due to truncation on X
........................ 37
2.5.
Truncation of a response variable in a non-parametric regression model
37
2.6.
Double censoring of a response variable in a non-parametric model
. 42
2.7.
Other truncation and censoring of
У
in a non-parametric model
... 44
2.8.
Observation by interval
.......................... 47
2.9.
Bibliography
................................ 48
Chapter
3.
Inference in Transformation Models for Arbitrarily Censored
and Truncated Data
................................. 49
Filia
Vonta
and Catherine Huber
3.1.
Introduction
................................. 49
3.2.
Non-parametric estimation of the survival function
S
......... 50
3.3.
Semi-parametric estimation of the survival function
S
......... 51
3.4.
Simulations
................................. 54
3.5.
Bibliography
................................ 59
Chapter
4.
Introduction of Within-area Risk Factor Distribution in Eco¬
logical
Poisson
Models
............................... 61
Lea
Fortunato,
Chantal Guihenneuc-Jouyaux,
Dominique
Laurier,
Margot
TlRMARCHE, Jacqueline
CLAVEL
and Denis
HÉMON
4.1.
Introduction
................................. 61
4.2.
Modeling framework
............................ 62
4.2.1.
Aggregated model
.......................... 62
4.2.2.
Prior distributions
.......................... 65
4.3.
Simulation framework
........................... 65
4.4.
Results
.................................... 66
4.4.1.
Strong association between relative risk and risk factor, corre¬
lated within-area means and variances (mean-dependent case)
. 67
4.4.2.
Sensitivity to within-area distribution of the risk factor
..... 68
4.4.3.
Application: leukemia and indoor radon exposure
........ 69
4.5.
Discussion
................................. 71
4.6.
Bibliography
................................ 72
Chapter
5.
Semi-Markov Processes and Usefulness in Medicine
...... 75
Eve Mathieu-Dupas,
Claudine
Gras-Aygon and Jean-Pierre
DaurÈS
5.1.
Introduction
................................. 75
5.2.
Methods
................................... 76
5.2.1.
Model description and notation
................... 76
5.2.2.
Construction of health indicators
.................. 79
5.3.
An application to
HIV
control
...................... 82
5.3.1.
Context
................................ 82
5.3.2.
Estimation method
.......................... 82
Contents 7
5.3.3.
Results: new indicators of health state
............... 84
5.4.
An application to breast cancer
...................... 86
5.4.1.
Context
................................ 86
5.4.2.
Age and stage-specific prevalence
................. 87
5.4.3.
Estimation method
.......................... 88
5.4.4.
Results: indicators of public health
................. 88
5.5.
Discussion
................................. 89
5.6.
Bibliography
................................ 89
Chapter
6.
Bivariate Cox Models
......................... 93
Michel Broniatowski,
Alexandre
Depire
and Ya acov Ritov
6.1.
Introduction
................................. 93
6.2.
A dependence model for duration data
.................. 93
6.3.
Some useful facts in bivariate dependence
................ 95
6.4.
Coherence
.................................. 98
6.5.
Covariates and estimation
......................... 102
6.6.
Application: regression of Spearman s rho on covariates
....... 104
6.7.
Bibliography
................................ 106
Chapter
7.
Non-parametric Estimation of a Class of Survival Functionals
109
Belkacem Abdous
7.1.
Introduction
................................. 109
7.2.
Weighted local polynomial estimates
...................
Ill
7.3.
Consistency of local polynomial fitting estimators
........... 114
7.4.
Automatic selection of the smoothing parameter
............ 116
7.5.
Bibliography
................................ 119
Chapter
8.
Approximate Likelihood in Survival Models
........... 121
Henning Läuter
8.1.
Introduction
................................. 121
8.2.
Likelihood in proportional hazard models
................ 122
8.3.
Likelihood in parametric models
..................... 122
8.4.
Profile likelihood
.............................. 123
8.4.1.
Smoothness classes
......................... 124
8.4.2.
Approximate likelihood function
.................. 125
8.5.
Statistical arguments
............................ 127
8.6.
Bibliography
................................ 129
PARTII
........................................ 131
Chapter
9.
Cox Regression with Missing Values of a Covariate having a
Non-proportional Effect on Risk of Failure
................... 133
Jean-François DUPUY
and Eve Leconte
8
Mathematical Methods in Survival Analysis, Reliability and Quality of Life
9.1.
Introduction
................................. 133
9.2.
Estimation in the Cox model with missing covariate values: a short
review
.................................... 136
9.3.
Estimation procedure in the stratified Cox model with missing stra¬
tum indicator values
............................ 139
9.4.
Asymptotic theory
............................. 141
9.5.
A simulation study
............................. 145
9.6.
Discussion
................................. 147
9.7.
Bibliography
................................ 149
Chapter
10.
Exact Bayesian Variable Sampling Plans for Exponential Dis¬
tribution under
Туре
-I
Censoring
......................... 151
Chien-Tai Lin, Yen-Lung HUANG and
N.
Balakrishnan
10.1.
Introduction
................................. 151
10.2.
Proposed sampling plan and
Bayes
risk
................. 152
10.3.
Numerical examples and comparison
.................. 156
10.4.
Bibliography
................................ 161
Chapter
11.
Reliability of Stochastic Dynamical Systems Applied to Fa¬
tigue Crack Growth Modeling
........................... 163
Julien Chiquet
and Nikolaos Limnios
11.1.
Introduction
................................. 163
11.2.
Stochastic dynamical systems with jump Markov process
....... 165
11.3.
Estimation
.................................. 168
11.4.
Numerical application
........................... 170
11.5.
Conclusion
................................. 175
11.6.
Bibliography
................................ 175
Chapter
12.
Statistical Analysis of a Redundant System with One Stand¬
by Unit
......................................... 179
Vilijandas
Bagdonavičius,
Inga Masiulaityte
and Mikhail Nikulin
12.1.
Introduction
................................. 179
12.2.
The models
................................. 180
12.3.
The tests
................................... 181
12.4.
Limit distribution of the test statistics
.................. 182
12.5.
Bibliography
................................ 187
Chapter
13.
A Modified Chi-squared Goodness-of-fit Test for the Three-
parameter Weibull Distribution and its Applications in Reliability
..... 189
Vassilly Voinov,
Roza Alloyarova
and Natalie Pya
13.1.
Introduction
................................. 189
13.2.
Parameter estimation and modified chi-squared tests
.......... 191
Contents 9
13.3. Power
estimation
.............................. 194
13.4. Neyman-Pearson
classes..........................
194
13.5.
Discussion
................................. 197
13.6.
Conclusion
................................. 198
13.7. Appendix.................................. 198
13.8.
Bibliography
................................ 201
Chapter
14.
Accelerated Life Testing when the Hazard Rate Function has
Cup Shape
...................................... 203
Vilijandas
Bagdonavičius,
Luc Clerjaud and Mikhail Nikulin
14.1.
Introduction
................................. 203
14.2.
Estimation in the AFT-GW model
.................... 204
14.2.1.
AFT model
.............................. 204
14.2.2.
AFT-Weibull, AFT-lognormal and AFT-GW models
....... 205
14.2.3.
Plans of ALT experiments
...................... 205
14.2.4.
Parameter estimation: AFT-GW model
.............. 206
14.3.
Properties of estimators: simulation results for the AFT-GW model
. 207
14.4.
Some remarks on the second plan of experiments
........... 211
14.5.
Conclusion
................................. 213
14.6.
Appendix
.................................. 213
14.7.
Bibliography
................................ 215
Chapter
15.
Point Processes in Software Reliability
.............. 217
James Ledoux
15.1.
Introduction
................................. 217
15.2.
Basic concepts for repairable systems
.................. 219
15.3.
Self-exciting point processes and black-box models
.......... 221
15.4.
White-box models and Markovian arrival processes
.......... 225
15.4.1.
A Markovian arrival model
..................... 226
15.4.2.
Parameter estimation
......................... 228
15.4.3.
Reliability growth
.......................... 232
15.5.
Bibliography
................................ 234
Part III
....................................... 237
Chapter
16.
Likelihood Inference for the Latent Markov
Rasch
Model
. . 239
Francesco Bartolucci, Fulvia
Pennoni
and Monia Lupparelli
16.1.
Introduction
................................. 239
16.2.
Latent class
Rasch
model
......................... 240
16.3.
Latent Markov
Rasch
model
....................... 241
16.4.
Likelihood inference for the latent Markov
Rasch
model
....... 243
16.4.1.
Log-likelihood maximization
.................... 244
10
Mathematical Methods in Survival Analysis, Reliability and Quality of Life
16.4.2.
Likelihood ratio testing of hypotheses on the parameters
.... 245
16.5.
An application
............................... 246
16.6.
Possible extensions
............................. 247
16.6.1.
Discrete response variables
..................... 248
16.6.2.
Multivariate longitudinal data
.................... 248
16.7.
Conclusions
................................. 251
16.8.
Bibliography
................................ 252
Chapter
17.
Selection of Items Fitting a Rasch Model
............. 255
Jean-Benoit Hardouin andMounir Mesbah
17.1.
Introduction
................................. 255
17.2.
Notations and assumptions
........................ 256
17.2.1.
Notations
............................... 256
17.2.2.
Fundamental assumptions of the Item Response Theory
(IRT)
. 256
17.3.
The Rasch model and the multidimensional marginally sufficient
Rasch model
................................. 256
17.3.1.
The Rasch model
........................... 256
17.3.2.
The multidimensional marginally sufficient Rasch model
.... 257
17.4.
The
Raschfit
procedure
.......................... 258
17.5.
A fast version of
Raschfit......................... 259
17.5.1.
Estimation of the parameters under the fixed effects Rasch model
259
17.5.2.
Principle of Raschfit-fast
...................... 260
17.5.3.
A model where the new item is explained by the same latent
trait as the kernel
........................... 260
17.5.4.
A model where the new item is not explained by the same latent
trait as the kernel
........................... 260
17.5.5.
Selection of the new item in the scale
............... 261
17.6.
A small set of simulations to compare
Raschfit
and Raschfit-fast
... 261
17.6.1.
Parameters of the simulation study
................. 261
17.6.2.
Results and computing time
..................... 264
17.7.
A large set of simulations to compare Raschfit-fast, MSP and
HCA/CCPROX
............................... 269
17.7.1.
Parameters of the simulations
.................... 269
17.7.2.
Discussion
.............................. 270
17.8.
The
Stata
module Raschfif
....................... 270
17.9.
Conclusion
................................. 271
n.lO.Bibliography
................................ 273
Chapter
18.
Analysis of Longitudinal HrQoL using Latent Regression in
the Context of Rasch Modeling
.......................... 275
Silvia Bacci
18.1.
Introduction
................................. 275
18.2.
Global models for longitudinal data analysis
.............. 276
Contents 11
18.3.
A
latent
regression
Rasch
model for
longitudinal
data analysis
.... 278
18.3.1.
Model structure
............................ 278
18.3.2.
Correlation structure
......................... 280
18.3.3.
Estimation
.............................. 281
18.3.4.
Implementation with
SAS
...................... 281
18.4.
Case study: longitudinal HrQoL of terminal cancer patients
...... 283
18.5.
Concluding remarks
............................ 287
18.6.
Bibliography
................................ 289
Chapter
19.
Empirical Internal Validation and Analysis of a Quality of
Life Instrument in French Diabetic Patients during an Educational Inter¬
vention
......................................... 291
Judith Chwalow, Keith Meadows, Mounir Mesbah, Vincent
Coliche
and
Etienne Mollet
19.1.
Introduction
................................. 291
19.2.
Material and methods
........................... 292
19.2.1.
Health care providers and patients
................. 292
19.2.2.
Psychometric validation of the DHP
................ 293
19.2.3.
Psychometric methods
........................ 293
19.2.4.
Comparative analysis of quality of life by treatment group
. . . 294
19.3.
Results
.................................... 295
19.3.1.
Internal validation of the DHP
................... 295
19.3.2.
Comparative analysis of quality of life by treatment group
. . . 303
19.4.
Discussion
................................. 304
19.5.
Conclusion
................................. 305
19.6.
Bibliography
................................ 306
19.7.
Appendices
................................. 309
Part IV
........................................ 315
Chapter
20.
Deterministic Modeling of the Size of the HIV/AIDS Epidemic
in Cuba
........................................ 317
Rachid Lounes,
Hector de
Arazoza, Y.H. Hsieh and Jose
Joanes
20.1.
Introduction
................................. 317
20.2.
The models
................................. 319
20.2.1.
The k2X model
........................... 322
20.2.2.
The k2Y model
............................ 322
20.2.3.
The
λ·2ΧΥ
model
.......................... 323
20.2.4.
The k2-^Y model
.......................... 324
20.3.
The underreporting rate
.......................... 324
20.4.
Fitting the models to Cuban data
..................... 325
20.5.
Discussion and concluding remarks
................... 326
20.6.
Bibliography
................................ 330
12
Mathematical Methods in Survival Analysis, Reliability and Quality of Life
Chapter
21.
Some Probabilistic Models Useful in Sport Sciences
...... 333
Léo Gerville-Réache,
Mikhail Nikulin,
Sébastien Orazio,
Nicolas Paris
and
Virginie Ro S A
21.1.
Introduction
................................. 333
21.2.
Sport jury analysis: the Gauss-Markov approach
............ 334
21.2.1.
Gauss-Markov model
........................ 334
21.2.2.
Test for non-objectivity of a variable
................ 334
21.2.3.
Test of difference between skaters
................. 335
21.2.4.
Test for the less precise judge
.................... 336
21.3.
Sport performance analysis: the fatigue and fitness approach
..... 337
21.3.1.
Model characteristics
........................ 337
21.3.2.
Monte Carlo simulation
....................... 338
21.3.3.
Results
................................ 339
21.4.
Sport equipment analysis: the fuzzy subset approach
......... 339
21.4.1.
Statistical model used
........................ 340
21.4.2.
Sensorial
analysis step
........................ 341
21.4.3.
Results
................................ 342
21.5.
Sport duel issue analysis: the logistic simulation approach
...... 343
21.5.1.
Modeling by logistic regression
.................. 344
21.5.2.
Numerical simulations
........................ 345
21.5.3.
Results
................................ 345
21.6.
Sport epidemiology analysis: the accelerated degradation approach
. 347
21.6.1.
Principle of degradation in reliability analysis
.......... 347
21.6.2.
Accelerated degradation model
................... 348
21.7.
Conclusion
................................. 350
21.8.
Bibliography
................................ 350
Appendices
...................................... 353
A. European Seminar: Some Figures
...................... 353
A.I. Former international speakers invited to the European Seminar
. . 353
A.2. Former meetings supported by the European Seminar
....... 353
A.3. Books edited by the organizers of the European Seminar
...... 354
A.4. Institutions supporting the European Seminar (names of colleagues)
355
B. Contributors
.................................. 357
Index
.......................................... 367
Reliability and survival analysis are important
applications of stochastic mathematics (probability,
statistics and stochastic processes) that are usually
covered separately in spite of the similarity of the
mathematical theory involved.
This book aims to redress this situation: it includes
21
chapters divided into four parts: survival analysis,
reliability, quality of life and related topics. Many of
these chapters are based on papers that were presented
at the European Seminar on Mathematical Methods for
Survival Analysis, Reliability and Quality of Life in
2006.
Catherine Huber is an Emeritus Professor at the
Université de
Paris
René
Descartes, France.
Nikolaos Li
m n
ios
is a Professor at the University of
Technology of
Compiègne,
France.
Mounir Mesbah is a Professor at the
Université
Pierre
et
Marie Curie, Paris
6,
France.
Mikhail Nikuiin is a Professor at the
Université
Victor
Segalen, Bordeaux
2,
France,
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV022490534 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276 |
| callnumber-search | QA276 |
| callnumber-sort | QA 3276 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 252 |
| ctrlnum | (OCoLC)182573444 (DE-599)BVBBV022490534 |
| dewey-full | 519.5/46 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/46 |
| dewey-search | 519.5/46 |
| dewey-sort | 3519.5 246 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV022490534 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T20:06:38Z |
| institution | BVB |
| isbn | 9781847040213 1847040217 9781848210103 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015697754 |
| oclc_num | 182573444 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | 369 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | ISTE [u.a.] |
| record_format | marc |
| series2 | Applied stochastic methods series |
| spellingShingle | Mathematical methods in survival analysis, reliability and quality of life Failure time data analysis Survival analysis (Biometry) Ereignisdatenanalyse (DE-588)4132103-0 gnd Zuverlässigkeitstheorie (DE-588)4195525-0 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4132103-0 (DE-588)4195525-0 (DE-588)4155620-3 (DE-588)4143413-4 |
| title | Mathematical methods in survival analysis, reliability and quality of life |
| title_auth | Mathematical methods in survival analysis, reliability and quality of life |
| title_exact_search | Mathematical methods in survival analysis, reliability and quality of life |
| title_full | Mathematical methods in survival analysis, reliability and quality of life ed. by Catherine Huber ... |
| title_fullStr | Mathematical methods in survival analysis, reliability and quality of life ed. by Catherine Huber ... |
| title_full_unstemmed | Mathematical methods in survival analysis, reliability and quality of life ed. by Catherine Huber ... |
| title_short | Mathematical methods in survival analysis, reliability and quality of life |
| title_sort | mathematical methods in survival analysis reliability and quality of life |
| topic | Failure time data analysis Survival analysis (Biometry) Ereignisdatenanalyse (DE-588)4132103-0 gnd Zuverlässigkeitstheorie (DE-588)4195525-0 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Failure time data analysis Survival analysis (Biometry) Ereignisdatenanalyse Zuverlässigkeitstheorie Mathematische Methode Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015697754&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015697754&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hubercatherine mathematicalmethodsinsurvivalanalysisreliabilityandqualityoflife |