Verfügbarkeit: Survival and event history analysis

Survival and event history analysis: a process point of view

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Bibliographische Detailangaben
Hauptverfasser:	Aalen, Odd O. (VerfasserIn), Borgan, Ørnulf (VerfasserIn), Gjessing, Håkon K. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York, NY Springer 2008
Schriftenreihe:	Statistics for biology and health
Schlagworte:	Ereignisdatenanalyse Stochastic processes
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references (p. 499-520) and indexes
Beschreibung:	xviii, 539 S. graph. Darst. 25 cm
ISBN:	9780387202877 0387202870

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Datensatz im Suchindex

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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
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spelling	Aalen, Odd O. Verfasser (DE-588)170647293 aut Survival and event history analysis a process point of view Odd O. Aalen, Ornulf Borgan, Håkon K. Gjessing New York, NY Springer 2008 xviii, 539 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Statistics for biology and health Includes bibliographical references (p. 499-520) and indexes Ereignisdatenanalyse swd Stochastic processes Ereignisdatenanalyse (DE-588)4132103-0 gnd rswk-swf Ereignisdatenanalyse (DE-588)4132103-0 s b DE-604 Borgan, Ørnulf Verfasser (DE-588)170587290 aut Gjessing, Håkon K. Verfasser (DE-588)1038563240 aut Erscheint auch als Online-Ausgabe 978-0-387-68560-1 Digitalisierung UB Regensburg application/pdf 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 Inhaltsverzeichnis
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
work_keys_str_mv	AT aalenoddo survivalandeventhistoryanalysisaprocesspointofview AT borganørnulf survivalandeventhistoryanalysisaprocesspointofview AT gjessinghakonk survivalandeventhistoryanalysisaprocesspointofview

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