Survival and event history analysis a process point of view
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| Format: | Buch |
| Sprache: | English |
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Springer
2008
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| Schriftenreihe: | Statistics for biology and health
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| 020 | |a 9780387202877 |c hbk. |9 978-0-387-20287-7 | ||
| 020 | |a 0387202870 |c hbk. |9 0-387-20287-0 | ||
| 035 | |a (OCoLC)213855657 | ||
| 035 | |a (DE-599)BVBBV035856543 | ||
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| 084 | |a SK 840 |0 (DE-625)143261: |2 rvk | ||
| 100 | 1 | |a Aalen, Odd O. |e Verfasser |0 (DE-588)170647293 |4 aut | |
| 245 | 1 | 0 | |a Survival and event history analysis |b a process point of view |c Odd O. Aalen, Ornulf Borgan, Håkon K. Gjessing |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a xviii, 539 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Statistics for biology and health | |
| 500 | |a Includes bibliographical references (p. 499-520) and indexes | ||
| 650 | 7 | |a Ereignisdatenanalyse |2 swd | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Ereignisdatenanalyse |0 (DE-588)4132103-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ereignisdatenanalyse |0 (DE-588)4132103-0 |D s |
| 689 | 0 | |C b |5 DE-604 | |
| 700 | 1 | |a Borgan, Ørnulf |e Verfasser |0 (DE-588)170587290 |4 aut | |
| 700 | 1 | |a Gjessing, Håkon K. |e Verfasser |0 (DE-588)1038563240 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-68560-1 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018714483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018714483 | ||
Datensatz im Suchindex
| DE-473_call_number | 31/MR 2100 WX 74848 |
|---|---|
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| DE-BY-UBG_katkey | 2931772 |
| DE-BY-UBG_media_number | 013107096276 |
| _version_ | 1811360061098819584 |
| adam_text | Contents
Preface
.
VH
1 An
introduction
to survival and event history analysis
.............. 1
1.1
Survival analysis: basic concepts and examples
.................. 2
1.1.1
What makes survival special: censoring and truncation
..... 3
1.1.2
Survival function and hazard rate
....................... 5
1.1.3
Regression and frailty models
.......................... 7
1.1.4
The past
............................................ 9
1
.
1
.5
Some illustrative examples
............................ 9
1.2
Event history analysis: models and examples
.................... 16
1.2.1
Recurrent event data
.................................. 17
1.2.2
Multistate models
.................................... 18
1.3
Data that do not involve time
................................. 24
1.4
Counting processes
......................................... 25
1.4.1
What is a counting process?
........................... 25
1
.4.2
Survival times and counting processes
.................. 28
1.4.3
Event histories and counting processes
.................. 32
1.5
Modeling event history data
.................................. 33
1.5.1
The multiplicative intensity model
...................... 34
1.5.2
Regression models
................................... 34
1.5.3
Frailty models and first passage time models
............. 35
1.5.4
Independent or dependent data?
........................ 36
1.6
Exercises
................................................. 37
2
Stochastic processes in event history analysis
...................... 41
2.1
Stochastic processes in discrete time
........................... 43
2.1.1
Martingales in discrete time
........................... 43
2.1.2
Variation processes
................................... 44
2
Л
.3
Stopping times and transformations
..................... 45
2.1.4
The Doob decomposition
.............................. 47
2.2
Processes in continuous time
................................. 48
xjj
Contents
2.2.1
Martingales
in continuous time
......................... 48
2.2.2
Stochastic integrals
................................... 50
2.2.3
The Doob-Meyer decomposition
....................... 52
2.2.4
The
Poisson
process
.................................. 52
2.2.5
Counting processes
................................... 53
2.2.6
Stochastic integrals for counting process martingales
...... 55
2.2.7
The innovation theorem
............................... 56
2.2.8
Independent censoring
................................ 57
2.3
Processes with continuous sample paths
........................ 61
2.3.1
The Wiener process and Gaussian martingales
........... 61
2.3.2
Asymptotic theory for martingales: intuitive discussion
.... 62
2.3.3
Asymptotic theory for martingales: mathematical
formulation
......................................... 63
2.4
Exercises
................................................. 66
3
Nonparametric analysis of survival and event history data
.......... 69
3.1
The
Nelson-Aalen
estimator
.................................. 70
3.1.1
The survival data situation
............................. 71
3.1.2
The multiplicative intensity model
...................... 76
3.1.3
Handling of ties
..................................... 83
3.1.4
Smoothing the Nelson-
Aalen
estimator
.................. 85
3.1.5
The estimator and its small sample properties
............. 87
3.1.6
Large sample properties
............................... 89
3.2
The Kaplan-Meier estimator
................................. 90
3.2.1
The estimator and confidence intervals
.................. 90
3.2.2
Handling tied survival times
........................... 94
3.2.3
Median and mean survival times
........................ 95
3.2.4
Product-integral representation
......................... 97
3.2.5
Excess mortality and relative survival
................... 99
3.2.6
Martingale representation and statistical properties
........103
3.3
Nonparametric tests
.........................................104
3.3.1
The two-sample case
.................................105
3.3.2
Extension to more than two samples
....................109
3.3.3
Stratified tests
.......................................110
3.3.4
Handling of tied observations
..........................
Ill
3.3.5
Asymptotics
........................................112
3.4
The empirical transition matrix
...............................114
3.4.1
Competing risks and cumulative incidence functions
.......114
3.4.2
An illness-death model
...............................117
3.4.3
The general case
.....................................120
3.4.4
Martingale representation and large sample properties
.....123
3.4.5
Estimation of («^variances
............................124
3.5
Exercises
.................................................126
Contents
Regression
models..............................................
131
4.1 Relative
risk regression
......................................133
4.1.1
Partial likelihood and inference for regression coefficients
.. 134
4.1.2
Estimation of cumulative hazards and survival probabilities
.141
4.1.3
Martingale residual processes and model check
...........142
4.1.4
Stratified models
.........
^
...........................148
4.1.5
Large sample properties of
β
..........................149
4.1.6
Large sample properties of estimators of cumulative
hazards and survival functions
.........................152
4.2
Additive regression models
..................................154
4.2.1
Estimation in the additive hazard model
.................157
4.2.2
Interpreting changes over time
.........................163
4.2.3
Martingale tests and a generalized log-rank test
...........164
4.2.4
Martingale residual processes and model check
...........167
4.2.5
Combining the Cox and the additive models
..............171
4.2.6
Adjusted monotone survival curves for comparing groups
.. 172
4.2.7
Adjusted Kaplan-Meier curves under dependent censoring
.. 175
4.2.8
Excess mortality models and the relative survival function
.. 179
4.2.9
Estimation of Markov transition probabilities
.............181
4.3
Nested case-control studies
..................................190
4.3.1
A general framework for nested-case control sampling
.....192
4.3.2
Two important nested case-control designs
...............194
4.3.3
Counting process formulation of nested case-control
sampling
...........................................195
4.3.4
Relative risk regression for nested case-control data
.......196
4.3.5
Additive regression for nested case-control data: results
.... 200
4.3.6
Additive regression for nested case-control data: theory
.... 202
4.4
Exercises
.................................................203
Parametric counting process models
..............................207
5.1
Likelihood inference
........................................208
5.1.1
Parametric models for survival times
....................208
5.1.2
Likelihood for censored survival times
..................209
5.1.3
Likelihood for counting process models
.................210
5.1.4
The maximum likelihood estimator and related tests
.......213
5.1.5
Some applications
...................................214
5.2
Parametric regression models
.................................223
5.2.1
Poisson
regression
...................................223
5.3
Proof of large sample properties
..............................226
5.4
Exercises
.................................................228
Unobserved heterogeneity: The odd effects of frailty
...............231
6.1
What is randomness in survival models?
.......................233
6.2
The proportional frailty model
................................234
6.2.1
Basic properties
.....................................234
Contents
6.2.2
The Gamma frailty distribution
.........................235
6.2.3
The PVF family of frailty distributions
..................238
6.2.4
Lévy-type
frailty distributions
..........................242
6.3
Hazard and frailty of survivors
...............................243
6.3.1
Results for the PVF distribution
........................243
6.3.2
Cure models
........................................244
6.3.3
Asymptotic distribution of survivors
....................245
6.4
Parametric models derived from frailty distributions
.............246
6.4.1
A model based on Gamma frailty: the Burr distribution
___246
6.4.2
A model based on PVF frailty
..........................247
6.4.3
The Weibull distribution derived from stable frailty
.......248
6.4.4
Frailty and estimation
................................249
6.5
The effect of frailty on hazard ratio
...........................250
6.5.1
Decreasing relative risk and crossover
..................250
6.5.2
The effect of discontinuing treatment
...................253
6.5.3
Practical implications of artifacts
......................255
6.5.4
Frailty models yielding proportional hazards
.............257
6.6
Competing risks and false protectivity
.........................260
6.7
A frailty model for the speed of a process
......................262
6.8
Frailty and association between individuals
....................264
6.9
Case study: A frailty model for testicular cancer
................265
6.10
Exercises
.................................................268
Multìvariate
frailty models
.....................................271
7.1
Censoring in the multivariate case
.............................272
7.1.1
Censoring for recurrent event data
......................273
7.1.2
Censoring for clustered survival data
....................274
7.2
Shared frailty models
.......................................275
7.2.1
Joint distribution
.....................................276
7.2.2
Likelihood
..........................................276
7.2.3
Empirical
Bayes
estimate of individual frailty
............278
7.2.4
Gamma distributed frailty
.............................279
7.2.5
Other frailty distributions suitable for the shared frailty
model
..............................................284
7.3
Frailty and counting processes
................................286
7.4
Hierarchical multivariate frailty models
.......................288
7.4.1
A multivariate model based on
Lévy-type
distributions
.....289
7.4.2
A multivariate stable model
............................290
7.4.3
The PVF distribution with
m
= 1.......................290
7.4.4
A invariate
model
....................................290
7.4.5
A simple genetic model
...............................291
7.5
Case study: A hierarchical frailty model for testicular cancer
......293
7.6
Random effects models for transformed times
...................296
7.6.1
Likelihood function
..................................296
7.6.2
General case
........................................298
Contents
7.6.3
Comparing frailty and random effects models
............299
7.7
Exercises
.................................................299
Marginal and dynamic models for recurrent events and clustered
survival data
...................................................301
8.1
Intensity models and rate models
..............................302
8.1.1
Dynamic covariates
..................................304
8.1.2
Connecting intensity and rate models in the additive case
... 305
8.2
Nonparametric statistical analysis
.............................308
8.2.1
A marginal Nelson-
Aalen
estimator for clustered survival
data
................................................308
8.2.2
A dynamic
Nelson-Aalen
estimator for recurrent event data
. 309
8.3
Regression analysis of recurrent events and clustered survival data
.311
8.3.1
Relative risk models
..................................313
8.3.2
Additive models
.....................................315
8.4
Dynamic path analysis of recurrent event data
...................324
8.4.1
General considerations
................................325
8.5
Contrasting dynamic and frailty models
........................331
8.6
Dynamic models
-
theoretical considerations
...................333
8.6.1
A dynamic view of the frailty model for
Poisson
processes
. 333
8.6.2
General view on the connection between dynamic
and frailty models
....................................334
8.6.3
Are dynamic models well defined?
......................336
8.7
Case study: Protection from natural infections
with enterotoxigenic Escherichia
coli
..........................340
8.8
Exercises
.................................................346
Causality
......................................................347
9.1
Statistics and causality
......................................347
9.1.1
Schools of statistical causality
.........................349
9.1.2
Some philosophical aspects
............................351
9.1.3
Traditional approaches to causality in epidemiology
.......353
9.1.4
The great theory still missing?
.........................353
9.2
Graphical models for event history analysis
.....................354
9.2.1
Time-dependent covariates
............................356
9.3
Local characteristics
-
dynamic model
.........................361
9.3.1
Dynamic path analysis
-
a general view
.................363
9.3.2
Direct and indirect effects
-
a general concept
............365
9.4
Granger-Schweder causality and local dependence
...............367
9.4.1
Local dependence
....................................367
9.4.2
A general definition of Granger-Schweder causality
.......370
9.4.3
Statistical analysis of local dependence
..................371
9.5
Counterfactual causality
.....................................373
9.5.1
Standard survival analysis and counterfactuals
............376
9.5.2
Censored and missing data
............................377
xvi Contents
9.5.3 Dynamic
treatment regimes
............................378
9.5.4
Marginal versus joint modeling
........................380
9.6
Marginal modeling
.........................................380
9.6.1
Marginal structural models
............................380
9.6.2
G-computation: A Markov modeling approach
............382
9.7
Joint modeling
.............................................383
9.7.1
Joint modeling as an alternative to marginal structural
models
.............................................384
9.7.2
Modeling dynamic systems
............................385
9.8
Exercises
.................................................385
10
First passage time models: Understanding the shape of the hazard
rate
...........................................................387
10.1
First hitting time; phase type distributions
......................389
10.1.1
Finite birth-death process with absorbing state
............389
10.1.2
First hitting time as the time to event
....................390
10.1.3
The risk distribution of survivors
.......................392
10.1.4
Reversibility and progressive models
....................393
10.2
Quasi-stationary distributions
................................395
10.2.1
Infinite birth-death process (infinite random walk)
.........397
10.2.2
Interpretation
........................................398
10.3
Wiener process models
......................................399
10.3.1
The inverse Gaussian hitting time distribution
............400
10.3.2
Comparison of hazard rates
............................402
10.3.3
The distribution of survivors
..........................404
10.3.4
Quasi-stationary distributions for the Wiener process
with absorption
......................................405
10.3.5
Wiener process with a random initial value
...............407
10.3.6
Wiener process with lower absorbing and upper reflecting
barriers
............................................408
10.3.7
Wiener process with randomized drift
..................408
10.3.8
Analyzing the effect of covariates for the randomized
Wiener process
......................................410
10.4
Diffusion process models
....................................416
10.4.1
The Kolmogorov equations and a formula for the hazard
rate
...............................................418
10.4.2
An equation for the quasi-stationary distribution
..........419
10.4.3
The Ornstein-Uhlenbeck process
.......................421
10.5
Exercises
.................................................424
11
Diffusion and Levy process models for dynamic frailty
.............425
11.1
Population versus individual survival
..........................426
11.2
Diffusion models for the hazard
..............................428
11.2.1
A simple Wiener process model
........................428
Contents xvji
11.2.2 The
hazard
rate as the square of an Ornstein-Uhlenbeck
process
............................................430
11.2.3
More general diffusion processes
.......................431
11.3
Models based on Levy processes
..............................432
11.4
Levy processes and subordinators
.............................433
11.4.1
Laplace exponent
....................................433
11.4.2
Compound
Poisson
processes and the PVF process
.......434
11.4.3
Other examples of subordinators
.......................435
1
1
.4.4
Levy measure
.......................................436
11.5
A Levy process model for the hazard
..........................438
11.5.1
Population survival
..................................440
11.5.2
The distribution of
h
conditional on no event
.............440
11.5.3
Standard frailty models
...............................441
11.5.4
Moving average
.....................................441
11.5.5
Accelerated failure times
.............................443
11.6
Results for the PVF processes
................................444
11.6.1
Distribution of survivors for the PVF processes
...........445
11.6.2
Moving average and the PVF process
...................446
11.7
Parameterization and estimation
..............................448
11.8
Limit results and quasi-stationary distributions
..................450
11.8.1
Limits for the PVF process
............................452
11.9
Exercises
.................................................453
A Markov processes and the product-integral
.......................457
A.
1
Hazard, survival, and the product-integral
......................458
A.2 Markov chains, transition intensities, and the Kolmogorov
equations
.................................................461
A.2.1 Discrete time-homogeneous Markov chains
..............463
A.2.2 Continuous time-homogeneous Markov chains
...........465
A.2.3 The Kolmogorov equations for homogeneous Markov
chains
.............................................467
A.2.4 Inhomogeneous Markov chains and the product-integral
___468
A.2.5 Common multistate models
............................471
A.3 Stationary and quasi-stationary distributions
....................475
A.3.
1
The stationary distribution of a discrete Markov chain
.....475
A.3.2 The quasi-stationary distribution of a Markov chain
with an absorbing state
...............................477
A.4 Diffusion processes and stochastic differential equations
..........479
A.4.1 The Wiener process
..................................480
A.4.2 Stochastic differential equations
........................482
A.4.3 The Ornstein-Uhlenbeck process
.......................484
A.4.4 The infinitesimal generator and the Kolmogorov equations
for a diffusion process
................................486
A.4.5 The Feynman-Kac formula
............................488
A.5 Levy processes and subordinators
.............................490
xviii Contents
A.5.1
The Levy process
..................■..................491
A.5.2
The Laplace exponent................................
493
В
Vector-valued counting processes, martingales and stochastic
integrals
......................................................495
B.I Counting processes, intensity processes and martingales
..........495
B.2 Stochastic integrals
.........................................496
B.3 Martingale central limit theorem
..............................497
References
.........................................................499
Author index
.......................................................521
Index
.............................................................529
|
| any_adam_object | 1 |
| author | Aalen, Odd O. Borgan, Ørnulf Gjessing, Håkon K. |
| author_GND | (DE-588)170647293 (DE-588)170587290 (DE-588)1038563240 |
| author_facet | Aalen, Odd O. Borgan, Ørnulf Gjessing, Håkon K. |
| author_role | aut aut aut |
| author_sort | Aalen, Odd O. |
| author_variant | o o a oo ooa ø b øb h k g hk hkg |
| building | Verbundindex |
| bvnumber | BV035856543 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274 |
| callnumber-search | QA274 |
| callnumber-sort | QA 3274 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | MR 2100 QH 252 SK 840 |
| ctrlnum | (OCoLC)213855657 (DE-599)BVBBV035856543 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035856543 |
| illustrated | Illustrated |
| indexdate | 2024-09-27T16:26:41Z |
| institution | BVB |
| isbn | 9780387202877 0387202870 |
| language | English |
| lccn | 2008927364 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018714483 |
| oclc_num | 213855657 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11 DE-473 DE-BY-UBG DE-384 |
| owner_facet | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11 DE-473 DE-BY-UBG DE-384 |
| physical | xviii, 539 S. graph. Darst. 25 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Statistics for biology and health |
| spellingShingle | Aalen, Odd O. Borgan, Ørnulf Gjessing, Håkon K. Survival and event history analysis a process point of view Ereignisdatenanalyse swd Stochastic processes Ereignisdatenanalyse (DE-588)4132103-0 gnd |
| subject_GND | (DE-588)4132103-0 |
| title | Survival and event history analysis a process point of view |
| title_auth | Survival and event history analysis a process point of view |
| title_exact_search | Survival and event history analysis a process point of view |
| title_full | Survival and event history analysis a process point of view Odd O. Aalen, Ornulf Borgan, Håkon K. Gjessing |
| title_fullStr | Survival and event history analysis a process point of view Odd O. Aalen, Ornulf Borgan, Håkon K. Gjessing |
| title_full_unstemmed | Survival and event history analysis a process point of view Odd O. Aalen, Ornulf Borgan, Håkon K. Gjessing |
| title_short | Survival and event history analysis |
| title_sort | survival and event history analysis a process point of view |
| title_sub | a process point of view |
| topic | Ereignisdatenanalyse swd Stochastic processes Ereignisdatenanalyse (DE-588)4132103-0 gnd |
| topic_facet | Ereignisdatenanalyse Stochastic processes |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018714483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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