Unified methods for censored longitudinal data and causality
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| Format: | Buch |
| Sprache: | English |
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2003
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| Schriftenreihe: | Springer series in statistics
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Laan, Mark J. van der |d 1967- |e Verfasser |0 (DE-588)128946326 |4 aut | |
| 245 | 1 | 0 | |a Unified methods for censored longitudinal data and causality |c Mark J. van der Laan ; James M. Robins |
| 264 | 1 | |a New York |b Springer |c 2003 | |
| 300 | |a xii, 397 p. |b ill. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Includes bibliographical references (p. 371-387) and indexes | ||
| 650 | 7 | |a Análise de dados longitudinais (pesquisa;planejamento) |2 larpcal | |
| 650 | 4 | |a Estimation, Théorie de l' | |
| 650 | 7 | |a Longitudinaal onderzoek |2 gtt | |
| 650 | 4 | |a Méthode longitudinale | |
| 650 | 7 | |a Statistiek |2 gtt | |
| 650 | 4 | |a Statistique non paramétrique | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Nonparametric statistics | |
| 650 | 4 | |a Longitudinal method | |
| 650 | 4 | |a Estimation theory | |
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| adam_text | MARK J. VAN DER LAAN JAMES M. ROBINS UNIFIED METHODS FOR CENSORED
LONGITUDINAL DATA AND CAUSALITY SPRINGER CONTENTS PREFACE V NOTATION 1 1
INTRODUCTION 8 1.1 MOTIVATION, BIBLIOGRAPHIC HISTORY, AND AN OVERVIEW OF
THE BOOK 8 1.2 TOUR THROUGH THE GENERAL ESTIMATION PROBLEM 16 1.2.1
ESTIMATION IN A HIGH-DIMENSIONAL FULL DATA MODEL 17 1.2.2 THE CURSE OF
DIMENSIONALITY IN THE FULL DATA MODEL 21 1.2.3 COARSENING AT RANDOM 23
1.2.4 THE CURSE OF DIMENSIONALITY REVISITED 27 1.2.5 THE OBSERVED DATA
MODEL 40 1.2.6 GENERAL METHOD FOR CONSTRUCTION OF LOCALLY EFFICIENT
ESTIMATORS 40 1.2.7 COMPARISON WITH MAXIMUM LIKELIHOOD ESTIMATION 45 1.3
EXAMPLE: CAUSAL EFFECT OF AIR POLLUTION ON SHORT-TERM ASTHMA RESPONSE 48
1.4 ESTIMATING FUNCTIONS 55 1.4.1 ORTHOGONAL COMPLEMENT OF A NUISANCE
TANGENT SPACE 55 1.4.2 REVIEW OF EFFICIENCY THEORY 61 1.4.3 ESTIMATING
FUNCTIONS 62 1.4.4 ORTHOGONAL COMPLEMENT OF A NUISANCE TANGENT SPACE IN
AN OBSERVED DATA MODEL 64 VIII CONTENTS 1.4.5 BASIC USEFUL RESULTS TO
COMPUTE PROJECTIONS . . . . 68 1.5 ROBUSTNESS OF ESTIMATING FUNCTIONS 69
1.5.1 ROBUSTNESS OF ESTIMATING FUNCTIONS AGAINST MISSPEC- IFICATION OF
LINEAR CONVEX NUISANCE PARAMETERS. . . 69 1.5.2 DOUBLE ROBUSTNESS OF
OBSERVED DATA ESTIMATING FUNCTIONS 77 1.5.3 UNDERSTANDING DOUBLE
ROBUSTNESS FOR A GENERAL SEMIPARAMETRIC MODEL 79 1.6 DOUBLY ROBUST
ESTIMATION IN CENSORED DATA MODELS. ... 81 1.7 USING CROSS-VALIDATION TO
SELECT NUISANCE PARAMETER MODELS 93 1.7.1 A SEMIPARAMETRIC MODEL
SELECTION CRITERIAN . . . . 94 1.7.2 FORWARD/BACKWARD SELECTION OF A
NUISANCE PARAME- TER MODEL BASED ON CROSS-VALIDATION WITH RESPECT TO THE
PARAMETER OF INTEREST 97 1.7.3 DATA ANALYSIS EXAMPLE: ESTIMATING THE
CAUSAL RELA- TIONSHIP BETWEEN BOILED WATER USE AND DIARRHEA IN
HIV-POSITIVE MEN 99 2 GENERAL METHODOLOGY 102 2.1 THE GENERAL MODEL AND
OVERVIEW 102 2.2 FULL DATA ESTIMATING FUNCTIONS 103 2.2.1 ORTHOGONAL
COMPLEMENT OF THE NUISANCE TAN- GENT SPACE IN THE MULTIVARIATE
GENERALIZED LINEAR REGRESSION MODEL (MGLM) 105 2.2.2 ORTHOGONAL
COMPLEMENT OF THE NUISANCE TANGENT SPACE IN THE MULTIPLICATIVE INTENSITY
MODEL . . . . 107 2.2.3 LINKING THE ORTHOGONAL COMPLEMENT OF THE
NUISANCE TANGENT SPACE TO ESTIMATING FUNCTIONS ILL 2.3 MAPPING INTO
OBSERVED DATA ESTIMATING FUNCTIONS . . . 114 2.3.1 INITIAL MAPPINGS AND
REPARAMETRIZING THE FULL DATA ESTIMATING FUNCTIONS 114 2.3.2 INITIAL
MAPPING INDEXED BY CENSORING AND PROTECTED NUISANCE PARAMETER 124 2.3.3
EXTENDING A MAPPING FOR A RESTRICTED CENSORING MODEL TO A COMPLETE
CENSORING MODEL 125 2.3.4 INVERSE WEIGHTING A MAPPING DEVELOPED FOR A
RESTRICTED CENSORING MODEL 126 2.3.5 BEATING A GIVEN RAL ESTIMATOR 128
2.3.6 ORTHOGONALIZING AN INITIAL MAPPING W.R.T. G: DOUBLE ROBUSTNESS 131
2.3.7 IGNORING INFORMATION ON THE CENSORING MECHANISM IMPROVES
EFFICIENCY 135 2.4 OPTIMAL MAPPING INTO OBSERVED DATA ESTIMATING FUNC-
TIONS 137 CONTENTS IX 2.4.1 THE CORRESPONDING ESTIMATING EQUATION 139
2.4.2 DISCUSSION OF INGREDIENTS OF A ONE-STEP ESTIMATOR . 141 2.5
GUARANTEED IMPROVEMENT RELATIVE TO AN INITIAL ESTIMATING FUNCTION 142
2.6 CONSTRUCTION OF CONFIDENCE INTERVALS 144 2.7 ASYMPTOTICS OF THE
ONE-STEP ESTIMATOR 145 2.7.1 ASYMPTOTICS ASSUMING CONSISTENT ESTIMATION
OF THE CENSORING MECHANISM 146 2.7.2 PROOF OF THEOREM 2.4 150 2.7.3
ASYMPTOTICS ASSUMING THAT EITHER THE CENSORING MECHANISM OR THE FULL
DATA DISTRIBUTION IS ESTIMATED CONSISTENTLY 151 2.7.4 PROOF OF THEOREM
2.5 152 2.8 THE OPTIMAL INDEX 153 2.8.1 FINDING THE OPTIMAL ESTIMATING
FUNCTION AMONG A GIVEN CLASS OF ESTIMATING FUNCTIONS 159 2.9 ESTIMATION
OF THE OPTIMAL INDEX 166 2.9.1 REPARAMETRIZING THE REPRESENTATIONS OF
THE OPTIMAL FULL DATA FUNCTION 167 2.9.2 ESTIMATION OF THE OPTIMAL FULL
DATA STRUCTURE ESTIMATING FUNCTION 169 2.10 LOCALLY EFFICIENT ESTIMATION
WITH SCORE-OPERATOR REPRE- SENTATION 170 MONOTONE CENSORED DATA 172 3.1
DATA STRUCTURE AND MODEL 172 3.1.1 CAUSE-SPECIFIC CENSORING 175 3.2
EXAMPLES 176 3.2.1 RIGHT-CENSORED DATA ON A SURVIVAL TIME 176 3.2.2
RIGHT-CENSORED DATA ON QUALITY-ADJUSTED SURVIVAL TIME 177 3.2.3
RIGHT-CENSORED DATA ON A SURVIVAL TIME WITH REPORTING DELAY 179 3.2.4
UNIVARIATELY RIGHT-CENSORED MULTIVARIATE FAILURE TIME DATA 181 3.3
INVERSE PROBABILITY CENSORING WEIGHTED (IPCW) ESTIMA- TORS 183 3.3.1
IDENTIFIABILITY CONDITION 183 3.3.2 ESTIMATION OF A MARGINAL
MULTIPLICATIVE INTENSITY MODEL 184 3.3.3 EXTENSION TO PROPORTIONAL RATE
MODELS 191 3.3.4 PROJECTING ON THE TANGENT SPACE OF THE COX PROPORTIONAL
HAZARDS MODEL OF THE CENSORING MECHANISM 192 3.4 OPTIMAL MAPPING INTO
ESTIMATING FUNCTIONS 195 CONTENTS 3.5 ESTIMATION OF Q 196 3.5.1
REGRESSION APPROACH: ASSUMING THAT THE CENSORING MECHANISM IS CORRECTLY
SPECIFIED 197 3.5.2 MAXIMUM LIKELIHOOD ESTIMATION ACCORDING TO A
MULTIPLICATIVE INTENSITY MODEL: DOUBLY ROBUST . . 198 3.5.3 MAXIMUM
LIKELIHOOD ESTIMATION FOR DISCRETE MODELS: DOUBLY ROBUST 200 3.5.4
REGRESSION APPROACH: DOUBLY ROBUST 201 3.6 ESTIMATION OF THE OPTIMAL
INDEX 204 3.6.1 THE MULTIVARIATE GENERALIZED REGRESSION MODEL . . 205
3.6.2 THE MULTIVARIATE GENERALIZED REGRESSION MODEL WHEN COVARIATES ARE
ALWAYS OBSERVED 206 3.7 MULTIVARIATE FAILURE TIME REGRESSION MODEL 208
3.8 SIMULATION AND DATA ANALYSIS FOR THE NONPARAMETRIC FULL DATA MODEL
211 3.9 RIGOROUS ANALYSIS OF A BIVARIATE SURVIVAL ESTIMATE ... 217 3.9.1
PROOF OF THEOREM 3.2 221 3.10 PREDICTION OF SURVIVAL ; 224 3.10.1
GENERAL METHODOLOGY 225 3.10.2 PREDICTION OF SURVIVAL WITH REGRESSION
TREES . . . 230 CROSS-SECTIONAL DATA AND RIGHT-CENSORED DATA COM- BINED
232 4.1 MODEL AND GENERAL DATA STRUCTURE 232 4.2 CAUSE SPECIFIC
MONITORING SCHEMES 234 4.2.1 OVERVIEW 235 4.3 THE OPTIMAL MAPPING INTO
OBSERVED DATA ESTIMATING FUNCTIONS 236 4.3.1 IDENTIFIABILITY CONDITION
239 4.3.2 ESTIMATION OF A PARAMETER ON WHICH WE HAVE CURRENT STATUS DATA
241 4.3.3 ESTIMATION OF A PARAMETER ON WHICH WE HAVE RIGHT- CENSORED
DATA 243 4.3.4 ESTIMATION OF A JOINT-DISTRIBUTION PARAMETER ON WHICH WE
HAVE CURRENT STATUS DATA AND RIGHT- CENSORED DATA 244 4.4 ESTIMATION OF
THE OPTIMAL INDEX IN THE MGLM 245 4.5 EXAMPLE: CURRENT STATUS DATA WITH
TIME-DEPENDENT COVARIATES 246 4.5.1 REGRESSION WITH CURRENT STATUS DATA
248 4.5.2 PREVIOUS WORK AND COMPARISON WITH OUR RESULTS . 250 4.5.3 AN
INITIAL ESTIMATOR 251 4.5.4 THE LOCALLY EFFICIENT ONE-STEP ESTIMATOR 252
4.5.5 IMPLEMENTATION ISSUES 253 4.5.6 CONSTRUCTION OF CONFIDENCE
INTERVALS 255 CONTENTS XI 4.5.7 A DOUBLY ROBUST ESTIMATOR 256 4.5.8
DATA-ADAPTIVE SELECTION OF THE LOCATION PARAMETER 257 4.5.9 SIMULATIONS
257 4.5.10 EXAMPLE 1: NO UNMODELED COVARIATE 258 4.5.11 EXAMPLE 2:
UNMODELED COVARIATE 258 4.5.12 DATA ANALYSIS: CALIFORNIA PARTNERS STUDY
. . . . 260 4.6 EXAMPLE: CURRENT STATUS DATA ON A PROCESS UNTIL DEATH
262 MULTIVARIATE RIGHT-CENSORED MULTIVARIATE DATA 266 5.1 GENERAL DATA
STRUCTURE 266 5.1.1 MODELING THE CENSORING MECHANISM 268 5.1.2 OVERVIEW
270 5.2 MAPPING INTO OBSERVED DATA ESTIMATING FUNCTIONS . . . 271 5.2.1
THE INITIAL MAPPING INTO OBSERVED ESTIMATING DATA FUNCTIONS 271 5.2.2
GENERALIZED DABROWSKA ESTIMATOR OF THE SURVIVAL FUNCTION IN THE
NONPARAMETRIC FULL DATA MODEL . . 273 5.2.3 SIMULATION STUDY OF THE
GENERALIZED DABROWKA ESTIMATOR 275 5.2.4 THE PROPOSED MAPPING INTO
OBSERVED DATA ESTIMAT- ING FUNCTIONS 276 5.2.5 CHOOSING THE FULL DATA
ESTIMATING FUNCTION IN MGLM 282 5.3 BIVARIATE RIGHT-CENSORED FAILURE
TIME DATA 282 5.3.1 INTRODUCTION 282 5.3.2 LOCALLY EFFICIENT ESTIMATION
WITH BIVARIATE RIGHT- CENSORED DATA 286 5.3.3 IMPLEMENTATION OF THE
LOCALLY EFFICIENT ESTIMATOR . 290 5.3.4 INVERSION OF THE INFORMATION
OPERATOR 292 5.3.5 ASYMPTOTIC PERFORMANCE AND CONFIDENCE INTERVALS 293
5.3.6 ASYMPTOTICS 294 5.3.7 SIMULATION METHODS AND RESULTS FOR THE
NONPARAMET- RIC FULL DATA MODEL 299 5.3.8 DATA ANALYSIS: TWIN AGE AT
APPENDECTOMY . . . . 302 UNIFIED APPROACH FOR CAUSAL INFERENCE AND
CENSORED DATA 311 6.1 GENERAL MODEL AND METHOD OF ESTIMATION 311 6.2
CAUSAL INFERENCE WITH MARGINAL STRUCTURAL MODELS . . . . 318 6.2.1
CLOSED FORM FORMULA FOR THE INVERSE OF THE NONPARAMETRIC INFORMATION
OPERATOR IN CAUSAL INFERENCE MODELS 324 6.3 DOUBLE ROBUSTNESS IN POINT
TREATMENT MSM 326 6.4 MARGINAL STRUCTURAL MODEL WITH RIGHT-CENSORING . .
. . 329 XII CONTENTS 6.4.1 DOUBLY ROBUST ESTIMATORS IN MARGINAL
STRUCTURAL MODELS WITH RIGHT-CENSORING 334 6.4.2 DATA ANALYSIS: SPARCS
338 6.4.3 A SIMULATION FOR ESTIMATORS OF A TREATMENT-SPECIFIC SURVIVAL
FUNCTION 343 6.5 STRUCTURAL NESTED MODEL WITH RIGHT-CENSORING 347 6.5.1
THE ORTHOGONAL COMPLEMENT OF A NUISANCE TANGENT SPACE IN A STRUCTURAL
NESTED MODEL WITHOUT CENSORING 353 6.5.2 A CLASS OF ESTIMATING FUNCTIONS
FOR THE MARGINAL STRUCTURAL NESTED MODEL 357 6.5.3 ANALYZING DYNAMIC
TREATMENT REGIMES 359 6.5.4 SIMULATION FOR DYNAMIC REGIMES IN POINT
TREATMENT STUDIES 360 6.6 RIGHT-CENSORING WITH MISSINGNESS 362 6.7
INTERVAL CENSORED DATA 366 6.7.1 INTERVAL CENSORING AND RIGHT-CENSORING
COMBINED . 368 REFERENCES 371 AUTHOR INDEX 388 SUBJECT INDEX 394 EXAMPLE
INDEX 397
|
| any_adam_object | 1 |
| author | Laan, Mark J. van der 1967- |
| author_GND | (DE-588)128946326 |
| author_facet | Laan, Mark J. van der 1967- |
| author_role | aut |
| author_sort | Laan, Mark J. van der 1967- |
| author_variant | m j v d l mjvd mjvdl |
| building | Verbundindex |
| bvnumber | BV014639939 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278.8.L33 2003 |
| callnumber-search | QA278.8.L33 2003 |
| callnumber-sort | QA 3278.8 L33 42003 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 252 SK 845 |
| ctrlnum | (OCoLC)50280137 (DE-599)BVBBV014639939 |
| dewey-full | 519.5/421 519.5/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/4 21 519.5/4 |
| dewey-search | 519.5/4 21 519.5/4 |
| dewey-sort | 3519.5 14 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV014639939 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T16:57:40Z |
| institution | BVB |
| isbn | 0387955569 |
| language | English |
| lccn | 2002030239 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009942583 |
| oclc_num | 50280137 |
| open_access_boolean | |
| owner | DE-29 DE-N2 DE-19 DE-BY-UBM DE-521 |
| owner_facet | DE-29 DE-N2 DE-19 DE-BY-UBM DE-521 |
| physical | xii, 397 p. ill. : 24 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spellingShingle | Laan, Mark J. van der 1967- Unified methods for censored longitudinal data and causality Análise de dados longitudinais (pesquisa;planejamento) larpcal Estimation, Théorie de l' Longitudinaal onderzoek gtt Méthode longitudinale Statistiek gtt Statistique non paramétrique Statistik Nonparametric statistics Longitudinal method Estimation theory Längsschnittuntersuchung (DE-588)4034036-3 gnd Datenanalyse (DE-588)4123037-1 gnd Schätzung (DE-588)4193791-0 gnd Semiparametrisches Modell (DE-588)4232479-8 gnd |
| subject_GND | (DE-588)4034036-3 (DE-588)4123037-1 (DE-588)4193791-0 (DE-588)4232479-8 |
| title | Unified methods for censored longitudinal data and causality |
| title_auth | Unified methods for censored longitudinal data and causality |
| title_exact_search | Unified methods for censored longitudinal data and causality |
| title_full | Unified methods for censored longitudinal data and causality Mark J. van der Laan ; James M. Robins |
| title_fullStr | Unified methods for censored longitudinal data and causality Mark J. van der Laan ; James M. Robins |
| title_full_unstemmed | Unified methods for censored longitudinal data and causality Mark J. van der Laan ; James M. Robins |
| title_short | Unified methods for censored longitudinal data and causality |
| title_sort | unified methods for censored longitudinal data and causality |
| topic | Análise de dados longitudinais (pesquisa;planejamento) larpcal Estimation, Théorie de l' Longitudinaal onderzoek gtt Méthode longitudinale Statistiek gtt Statistique non paramétrique Statistik Nonparametric statistics Longitudinal method Estimation theory Längsschnittuntersuchung (DE-588)4034036-3 gnd Datenanalyse (DE-588)4123037-1 gnd Schätzung (DE-588)4193791-0 gnd Semiparametrisches Modell (DE-588)4232479-8 gnd |
| topic_facet | Análise de dados longitudinais (pesquisa;planejamento) Estimation, Théorie de l' Longitudinaal onderzoek Méthode longitudinale Statistiek Statistique non paramétrique Statistik Nonparametric statistics Longitudinal method Estimation theory Längsschnittuntersuchung Datenanalyse Schätzung Semiparametrisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009942583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT laanmarkjvander unifiedmethodsforcensoredlongitudinaldataandcausality AT robinsjamesm unifiedmethodsforcensoredlongitudinaldataandcausality |