Counting processes and survival analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ u.a.
Wiley
2005
|
| Series: | Wiley-interscience
Wiley series in probability and mathematical statistics |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 429 S. graph. Darst. |
| ISBN: | 0471769886 9780471769880 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface
vii
0.
The Applied
Setting
1
ОЛ
Introduction,
1
0.2
A Data Set and Some Examples,
2
1.
The Counting Process and Martingale Framework
15
1.1
Introduction,
15
1.2
Stochastic Processes and Stochastic Integrals,
15
1.3
The Martingale
M
= N -
A,
25
1.4
The Doob-Meyer Decomposition: Applications to Quadratic Variation,
31
1.5
The Martingale Transform
ƒ
HdM,
42
1.6
Bibliographic Notes,
48
2.
Local Square
Integrable
Martingales
51
2.1
Introduction,
51
2.2
Localization of Stochastic Processes and the Doob-Meyer
Decomposition,
52
2.3
The Martingale
N -
A Revisited,
60
2.4
Stochastic Integrals with Respect to Local Martingales,
65
2.5
Continuous Compensators,
74
2.6
Compensators with Discontinuities,
79
2.7
Summary,
83
2.8
Bibliographic Notes,
88
3.
Finite Sample Moments and Large Sample Consistency
оГ
Tests and Estimators
89
3.1
Introduction,
89
xi
χϋ
CONTENTS
3.2 Nonparametric
Estimation
of the Survival Distribution,
91
3.3
Some Finite Sample Properties of Linear Rank Statistics,
107
3.4
Consistency of the Kaplan-Meier Estimator,
112
3.5
Bibliographic Notes,
121
4.
Censored Data Regression Models and Their Application
125
4.1
Introduction,
125
4.2
The Proportional Hazards and Multiplicative Intensity Models,
126
4.3
Partial Likelihood Inference,
136
4.4
Applications of Partial Likelihood Methods,
153
4.5
Martingale Residuals,
163
4.6
Applications of Residual Methods,
178
4.7
Bibliographic Notes,
197
5.
Martingale Central Limit Theorem
201
5.1
Preliminaries and Motivation,
201
5.2
Convergence of Martingale Difference Arrays,
205
5.3
Weak Convergence of the Process, Uin
215
5.4
Bibliographic Notes,
228
6.
Large Sample Results of the Kaplan-Meier Estimator
229
6.1
Introduction,
229
6.2
A Large Sample Result for Kaplan-Meier and Weighted Logrank
Statistics,
229
6.3
Confidence Bands for the Survival Distribution,
235
6.4
Bibliographic Notes,
252
7.
Weighted Logrank Statistics
255
7.1
Introduction,
255
7.2
Large Sample Null Distribution,
256
7.3
Consistency of Tests of the Class /C,
265
7.4
Efficiencies of Tests of the Class /C,
267
7.5
Some Versatile Test Procedures,
277
7.6
Bibliographic Notes,
284
8.
Distribution Theory for Proportional Hazards Regression
287
8.1
Introduction,
287
8.2
The Partial Likelihood Score Statistic,
289
CONTENTS
ХІІІ
8.3
Estimators of the Regression Parameters and the Cumulative Hazard
Function,
296
8.4
The Asymptotic Theory for Simple Models,
303
8.5
Asymptotic Relative Efficiency of Partial Likelihood Inference in the
Proportional Hazards Model,
311
8.6
Bibliographic Notes,
316
Appendix A. Some Results from
Stieltjes
Integration
and Probability Theory
317
Appendix B. An Introduction to Weak Convergence
331
Appendix C. The Martingale Central Limit Theorem:
Some Preliminaries
343
Appendix D. Data
359
Appendix E. Exercises
385
Bibliography
401
Notation
413
Author Index
417
Subject Index
421
|
| adam_txt |
Contents
Preface
vii
0.
The Applied
Setting
1
ОЛ
Introduction,
1
0.2
A Data Set and Some Examples,
2
1.
The Counting Process and Martingale Framework
15
1.1
Introduction,
15
1.2
Stochastic Processes and Stochastic Integrals,
15
1.3
The Martingale
M
= N -
A,
25
1.4
The Doob-Meyer Decomposition: Applications to Quadratic Variation,
31
1.5
The Martingale Transform
ƒ
HdM,
42
1.6
Bibliographic Notes,
48
2.
Local Square
Integrable
Martingales
51
2.1
Introduction,
51
2.2
Localization of Stochastic Processes and the Doob-Meyer
Decomposition,
52
2.3
The Martingale
N -
A Revisited,
60
2.4
Stochastic Integrals with Respect to Local Martingales,
65
2.5
Continuous Compensators,
74
2.6
Compensators with Discontinuities,
79
2.7
Summary,
83
2.8
Bibliographic Notes,
88
3.
Finite Sample Moments and Large Sample Consistency
оГ
Tests and Estimators
89
3.1
Introduction,
89
xi
χϋ
CONTENTS
3.2 Nonparametric
Estimation
of the Survival Distribution,
91
3.3
Some Finite Sample Properties of Linear Rank Statistics,
107
3.4
Consistency of the Kaplan-Meier Estimator,
112
3.5
Bibliographic Notes,
121
4.
Censored Data Regression Models and Their Application
125
4.1
Introduction,
125
4.2
The Proportional Hazards and Multiplicative Intensity Models,
126
4.3
Partial Likelihood Inference,
136
4.4
Applications of Partial Likelihood Methods,
153
4.5
Martingale Residuals,
163
4.6
Applications of Residual Methods,
178
4.7
Bibliographic Notes,
197
5.
Martingale Central Limit Theorem
201
5.1
Preliminaries and Motivation,
201
5.2
Convergence of Martingale Difference Arrays,
205
5.3
Weak Convergence of the Process, Uin\
215
5.4
Bibliographic Notes,
228
6.
Large Sample Results of the Kaplan-Meier Estimator
229
6.1
Introduction,
229
6.2
A Large Sample Result for Kaplan-Meier and Weighted Logrank
Statistics,
229
6.3
Confidence Bands for the Survival Distribution,
235
6.4
Bibliographic Notes,
252
7.
Weighted Logrank Statistics
255
7.1
Introduction,
255
7.2
Large Sample Null Distribution,
256
7.3
Consistency of Tests of the Class /C,
265
7.4
Efficiencies of Tests of the Class /C,
267
7.5
Some Versatile Test Procedures,
277
7.6
Bibliographic Notes,
284
8.
Distribution Theory for Proportional Hazards Regression
287
8.1
Introduction,
287
8.2
The Partial Likelihood Score Statistic,
289
CONTENTS
ХІІІ
8.3
Estimators of the Regression Parameters and the Cumulative Hazard
Function,
296
8.4
The Asymptotic Theory for Simple Models,
303
8.5
Asymptotic Relative Efficiency of Partial Likelihood Inference in the
Proportional Hazards Model,
311
8.6
Bibliographic Notes,
316
Appendix A. Some Results from
Stieltjes
Integration
and Probability Theory
317
Appendix B. An Introduction to Weak Convergence
331
Appendix C. The Martingale Central Limit Theorem:
Some Preliminaries
343
Appendix D. Data
359
Appendix E. Exercises
385
Bibliography
401
Notation
413
Author Index
417
Subject Index
421 |
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| index_date | 2024-07-02T21:42:45Z |
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| language | English |
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| series2 | Wiley-interscience Wiley series in probability and mathematical statistics |
| spelling | Fleming, Thomas R. Verfasser (DE-588)103147966X aut Counting processes and survival analysis Thomas R. Fleming ; David P. Harrington Hoboken, NJ u.a. Wiley 2005 XIII, 429 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-interscience Wiley series in probability and mathematical statistics Martingales (Mathématiques) Processus ponctuels Temps entre défaillances, Analyse des Failure time data analysis Martingales (Mathematics) Point processes Martingaltheorie (DE-588)4168982-3 gnd rswk-swf Lebensdauer (DE-588)4034837-4 gnd rswk-swf Lebensdauer (DE-588)4034837-4 s Martingaltheorie (DE-588)4168982-3 s DE-604 Harrington, David P. Verfasser aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016676869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fleming, Thomas R. Harrington, David P. Counting processes and survival analysis Martingales (Mathématiques) Processus ponctuels Temps entre défaillances, Analyse des Failure time data analysis Martingales (Mathematics) Point processes Martingaltheorie (DE-588)4168982-3 gnd Lebensdauer (DE-588)4034837-4 gnd |
| subject_GND | (DE-588)4168982-3 (DE-588)4034837-4 |
| title | Counting processes and survival analysis |
| title_auth | Counting processes and survival analysis |
| title_exact_search | Counting processes and survival analysis |
| title_exact_search_txtP | Counting processes and survival analysis |
| title_full | Counting processes and survival analysis Thomas R. Fleming ; David P. Harrington |
| title_fullStr | Counting processes and survival analysis Thomas R. Fleming ; David P. Harrington |
| title_full_unstemmed | Counting processes and survival analysis Thomas R. Fleming ; David P. Harrington |
| title_short | Counting processes and survival analysis |
| title_sort | counting processes and survival analysis |
| topic | Martingales (Mathématiques) Processus ponctuels Temps entre défaillances, Analyse des Failure time data analysis Martingales (Mathematics) Point processes Martingaltheorie (DE-588)4168982-3 gnd Lebensdauer (DE-588)4034837-4 gnd |
| topic_facet | Martingales (Mathématiques) Processus ponctuels Temps entre défaillances, Analyse des Failure time data analysis Martingales (Mathematics) Point processes Martingaltheorie Lebensdauer |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016676869&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT flemingthomasr countingprocessesandsurvivalanalysis AT harringtondavidp countingprocessesandsurvivalanalysis |