Multivariate survival analysis and competing risks:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla.
CRC Press
2012
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| Schriftenreihe: | Texts in statistical science
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXIV, 393 S. graph. Darst. 25 cm |
| ISBN: | 9781439875216 |
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| 100 | 1 | |a Crowder, M. J. |d 1943- |e Verfasser |0 (DE-588)172028469 |4 aut | |
| 245 | 1 | 0 | |a Multivariate survival analysis and competing risks |c Martin Crowder |
| 264 | 1 | |a Boca Raton, Fla. |b CRC Press |c 2012 | |
| 300 | |a XXIV, 393 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 Texts in statistical science | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Failure time data analysis | |
| 650 | 4 | |a Competing risks | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 0 | 7 | |a Multivariate Analyse |0 (DE-588)4040708-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 0 | |a Multivariate Analyse |0 (DE-588)4040708-1 |D s |
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Datensatz im Suchindex
| _version_ | 1804149092320804864 |
|---|---|
| adam_text | Titel: Multivariate survival analysis and competing risks
Autor: Crowder, Martin J
Jahr: 2012
Contents
Preface
xxi
Part I Univariate Survival Analysis
1. Scenario..............................................................3
1.1 Survival Data...................................................3
1.1.1 Waiting Times..........................................3
1.1.2 Discrete Time...........................................4
1.1.3 Censoring..............................................4
1.2 Some Small Data Sets...........................................5
1.2.1 Strengths of Cords......................................5
1.2.2 Cancer Survival.........................................6
1.2.3 Catheter Infection.......................................6
1.3 Inspecting the Data with R......................................7
1.4 Fitting Models with R..........................................9
1.5 Simulating Data with R.........................................9
2. Survival Distributions..............................................11
2.1 Continuous Lifetimes..........................................11
2.2 Some Continuous Survival Distributions.......................12
2.2.1 The Exponential Distribution..........................12
2.2.2 The Weibull Distribution...............................13
2.2.3 The Pareto Distribution................................13
2.2.4 Other Distributions....................................14
2.2.5 The Shape of Hazard...................................14
2.3 Discrete Lifetimes.............................................15
2.4 Some Discrete Survival Distributions..........................16
2.4.1 The Geometric Distribution............................16
2.4.2 The Negative Binomial Distribution....................17
2.5 Mixed Discrete-Continuous Survival Distributions.............17
2.5.1 From Discrete to Continuous...........................18
2.5.2 Rieman-Stieltjes Integrals..............................19
2.6 Reliability Topics..............................................20
2.6.1 Reliability of Systems..................................20
2.6.2 k-out-of-n Systems.....................................21
2.6.3 Survival Aspect........................................21
tx
Contents
2.6.4 Degradation Processes.................................21
2.6.5 Stress and Strength....................................22
2.7 Exercises......................................................22
2.7.1 Survival Distributions.................................22
2.7.2 Reliability of Systems..................................23
2.7.3 Degradation Processes.................................24
2.7.4 Stress and Strength....................................24
2.8 Hints and Solutions...........................................24
2.8.1 Survival Distributions.................................24
2.8.2 Reliability of Systems..................................26
2.8.3 Degradation Processes.................................26
2.8.4 Stress and Strength....................................26
Continuous Time-Parametric Inference.............................29
3.1 Parametric Inference: Frequentist and Bayesian................29
3.1.1 Frequentist Approach..................................29
3.1.2 Bayesian Approach....................................30
3.1.3 Proceed with Caution..................................31
3.2 Random Samples..............................................32
3.2.1 Type-I Censoring......................................33
3.2.2 Type-II Censoring......................................33
3.2.3 Left Truncation........................................34
3.2.4 Probabilities of Observation versus Censoring..........34
3.2.5 Weibull Lifetimes......................................35
3.2.6 Strengths of Cords.....................................36
3.2.7 Survival of Breast Cancer Patients......................38
3.3 Regression Models............................................39
3.3.1 Business Start-Ups.....................................40
3.3.2 Proportional Hazards (PH).............................41
3.3.3 Accelerated Life (AL)..................................42
3.3.4 Proportional Odds (PO) ...............................42
3.3.5 Mean Residual Life (MRL).............................42
3.3.6 Catheter Infection......................................43
3.4 Goodness of Fit................................................44
3.4.1 Enhanced Models......................................45
3.4.2 Uniform Residuals.....................................45
3.4.3 Cox-Snell Residuals...................................46
3.4.4 Right-Censored Times.................................46
3.4.5 Other Residuals........................................46
3.4.6 Tests on Residuals.....................................47
3.5 Frailty and Random Effects....................................47
3.5.1 Frailty.................................................47
3.5.2 Recovering the Frailty Distribution.....................48
3.5.3 Discrete Random Effects and Frailty....................49
3.5.4 Accommodating Zero Frailty...........................51
Contents xi
3.6 Time-Dependent Covariates...................................51
3.7 Exercises......................................................53
3.7.1 Regression Models.....................................53
3.7.2 Residuals..............................................53
3.7.3 Discrete Frailty........................................54
3.8 Hints and Solutions...........................................55
3.8.1 Regression Models.....................................55
3.8.2 Residuals..............................................55
4. Continuous Time: Non- and Semi-Parametric Methods.............57
4.1 Random Samples..............................................57
4.1.1 The Kaplan-Meier Estimator...........................57
4.1.2 Strengths of Cords.....................................59
4.1.3 The Integrated and Cumulative Hazard Functions......60
4.1.4 Interval-Censored Data................................60
4.2 Explanatory Variables.........................................62
4.2.1 Cox s Proportional Hazards Model.....................62
4.2.2 Cox s Partial Likelihood...............................62
4.2.3 Inference..............................................63
4.2.4 Computation..........................................64
4.2.5 Catheter Infection......................................64
4.3 Some Further Aspects.........................................65
4.3.1 Stratification...........................................65
4.3.2 Tied Lifetimes.........................................66
4.3.3 The Baseline Survivor Function........................66
4.3.4 The Log-Rank Test.....................................67
4.3.5 Schoenfeld Residuals..................................68
4.3.6 Time-Dependent Covariates...........................68
4.3.7 Interval-Censored Data................................69
4.4 Task Completion Times........................................69
4.5 Accelerated Life Models.......................................72
4.6 Exercises......................................................75
4.6.1 Random Samples......................................75
4.6.2 Partial Likelihood......................................75
4.6.3 Applications...........................................75
4.6.4 Accelerated Life Models...............................76
4.7 Hints and Solutions...........................................76
4.7.1 Random Samples......................................76
4.7.2 Accelerated Life Models...............................76
5. Discrete Time.......................................................77
5.1 Random Samples: Parametric Methods........................77
5.1.1 Geometric Lifetimes...................................77
5.1.2 Career Promotions.....................................78
5.1.3 Probabilities of Observation versus Censoring..........80
xii Contents
5.2 Random Samples: Non- and Semi-Parametric Estimation......81
5.2.1 Career Promotions.....................................82
5.2.2 Large-Sample Theory..................................83
5.3 Explanatory Variables.........................................84
5.3.1 Likelihood Function...................................84
5.3.2 Geometric Waiting Times..............................85
5.3.3 The Driving Test.......................................85
5.3.4 Proportional Hazards..................................87
5.3.5 Proportional Odds.....................................87
5.3.6 The Driving Test.......................................89
5.3.7 The Baseline Odds.....................................89
5.4 Interval-Censored Data........................................90
5.4.1 Cancer Survival Data..................................90
5.5 Frailty and Random Effects....................................92
5.5.1 Geometric Distribution................................92
5.5.2 Random Effects........................................93
5.5.3 Beta-Geometric Distribution...........................93
5.5.4 Cycles to Pregnancy...................................94
5.5.5 The Driving Test.......................................95
5.6 Exercises......................................................95
5.6.1 Random Samples......................................95
5.6.2 Explanatory Variables..................................96
5.6.3 Gamma and Beta Distributions.........................96
5.7 Hints and Solutions...........................................97
5.7.1 Random Samples......................................97
Part II Multivariate Survival Analysis
6. Multivariate Data and Distributions...............................101
6.1 Some Small Data Sets.........................................101
6.1.1 Repeated Response Times.............................101
6.1.2 Paired Response Times...............................102
6.1.3 Lengths and Strengths of Fibres.......................102
6.1.4 Household Energy Usage.............................102
6.2 Multivariate Survival Distributions...........................105
6.2.1 Joint and Marginal Distributions......................105
6.2.2 Conditional Distributions.............................105
6.2.3 Dependence and Association.........................105
6.2.4 Hazard Functions and Failure Rates...................106
6.2.5 Gumbel s Bivariate Exponential.......................107
6.3 Exercises.....................................................108
6.3.1 Joint and Marginal Distributions......................108
6.3.2 Dependence and Association.........................108
6.4 Hints and Solutions..........................................109
Contents xiii
6.4.1 Joint and Marginal Distributions......................109
6.4.2 Dependence and Association.........................109
7. Some Models and Methods........................................Ill
7.1 The Multivariate Log-Normal Distribution....................Ill
7.2 Applications.................................................112
7.2.1 Household Energy Usage.............................112
7.2.2 Repeated Response Times.............................113
7.3 Bivariate Exponential.........................................114
7.3.1 Discrete-Tune Version.................................114
7.4 Bivariate Exponential.........................................115
7.4.1 Discrete-Tune Version.................................116
7.5 Some Other Bivariate Distributions...........................116
7.5.1 Block and Basu (1974) ................................116
7.5.2 Lawrance and Lewis (1983)...........................116
7.5.3 Arnold and Brockett (1983)............................117
7.5.4 Cowan (1987).........................................117
7.5.5 Yet More Distributions................................117
7.6 Non- and Semi-Parametric Methods..........................118
7.7 Exercises.....................................................120
8. Frailty, Random Effects, and Copulas..............................121
8.1 Frailty: Construction.........................................121
8.2 Some Frailty-Generated Distributions........................122
8.2.1 Multivariate Burr.....................................122
8.2.2 Multivariate Weibull..................................123
8.2.3 Distribution 3.........................................124
8.2.4 Multivariate Beta-Geometric..........................125
8.2.5 Multivariate Gamma-Poisson.........................126
8.2.6 Marshall-Olkin Families..............................126
8.3 Applications.................................................127
8.3.1 Paired Response Times...............................127
8.3.2 Household Energy Usage.............................129
8.3.3 Cycles to Pregnancy..................................130
8.4 Copulas: Structure...........................................131
8.5 Further Details...............................................133
8.6 Applications.................................................135
8.6.1 Clayton Copula.......................................135
8.7 Exercises.....................................................136
8.7.1 Frailty-Generated Distributions.......................136
8.7.2 Applications..........................................137
8.7.3 Copulas..............................................137
8.8 Hints and Solutions..........................................138
8.8.1 Copulas..............................................138
xiv Contents
9. Repeated Measures................................................139
9.1 Pure Frailty Models: Applications............................139
9.1.1 Lengths and Strengths of Fibres.......................140
9.1.2 Visual Acuity.........................................141
9.2 Models with Serial Correlation: Application..................143
9.2.1 Repeated Response Times.............................144
9.3 Matched Pairs................................................145
9.4 Discrete Time: Applications..................................146
9.4.1 Proportional Odds....................................146
9.4.2 Beta-Geometric Model................................147
9.4.3 Bird Recapture........................................147
9.4.4 Antenatal Knowledge.................................149
9.5 Milestones: Applications.....................................152
9.5.1 Educational Development............................152
9.5.2 Pill Dissolution Rates.................................153
9.5.3 Timber Slip...........................................153
9.5.4 Loan Default.........................................154
9.6 Exercises.....................................................156
9.6.1 Bird Recapture Data..................................156
9.6.2 Some Background for the Bivariate
Beta Distribution.....................................156
9.6.3 Antenatal Data.......................................157
9.6.4 Binomial Waiting Times...............................158
9.6.5 Milestones Data......................................158
10. Recurrent Events...................................................161
10.1 Some Recurrence Data.......................................161
10.2 The Event Rate...............................................163
10.3 Basic Recurrence Processes...................................165
10.3.1 Poisson Processes....................................165
10.3.2 Renewal Processes....................................166
10.3.3 Recurrence of Medical Condition.....................166
10.3.4 Simulation...........................................167
10.4 More Elaborate Models......................................168
10.4.1 Poisson Process.......................................168
10.4.2 Intensity Functions...................................168
10.5 Other Fields of Application..................................169
10.5.1 Repair and Warranty Data............................169
10.5.2 Sports Data...........................................169
10.5.3 Institution Data......................................170
10.5.4 Alternating Periods...................................170
10.6 Event Counts................................................171
10.6.1 Continuous Time: Poisson Process....................171
10.6.2 Discrete Time.........................................172
10.6.3 Multivariate Negative Binomial.......................172
Contents xv
10.7 Quasi-Life Tables.............................................174
10.7.1 Estimation...........................................174
10.8 Exercises.....................................................176
10.9 Hints and Solutions..........................................177
11. Multi-State Processes..............................................179
11.1 Markov Chain Models.......................................179
11.1.1 Discrete Time.........................................179
11.1.2 Continuous Time.....................................180
11.1.3 Hidden Markov Chains...............................181
11.1.4 Estimation............................................182
11.2 The Wiener Process..........................................183
11.3 Wear and Tear and Lack of Care..............................184
11.4 Cumulative Models..........................................185
11.4.1 Compound Poisson Process...........................186
11.4.2 Compound Birth Process.............................188
11.4.3 Gamma Process......................................188
11.4.4 Customer Lifetime Value.............................190
11.5 Some Other Models and Applications........................190
11.5.1 Empirical Equation Models...........................190
11.5.2 Models for the Stress Process.........................192
11.5.3 Stress-Strength Models...............................193
11.5.4 Other Models and Applications.......................193
11.6 Exercises.....................................................194
11.6.1 Markov Chains.......................................194
11.6.2 Wiener Process.......................................195
11.6.3 Cumulative Damage Models..........................197
11.6.4 Compound Poisson Process...........................197
11.6.5 Compound Birth Process.............................197
11.6.6 Gamma Process......................................198
11.7 Hints and Solutions..........................................198
11.7.1 Markov Chains.......................................198
11.7.2 Wiener Process.......................................198
11.7.3 Cumulative Damage Models..........................199
11.7.4 Compound Poisson Process...........................199
11.7.5 Compound Birth Process.............................199
Part III Competing Risks
12. Continuous Failure Times and Their Causes.......................203
12.1 Some Small Data Sets........................................203
12.1.1 Gubbins..............................................203
12.1.2 Catheter Infection....................................203
12.1.3 Superalloy Testing....................................204
12.2 Basic Probability Functions: Continuous Time................204
12.2.1 Exponential Mixture..................................206
xvi Contents
12.3 Hazard Functions............................................207
12.3.1 Exponential Mixture..................................207
12.3.2 Lemma...............................................208
12.3.3 Weibull Sub-Hazards.................................208
12.4 Proportional Hazards........................................209
12.4.1 Weibull Sub-Hazards.................................209
12.4.2 Theorem.............................................210
12.5 Regression Models...........................................211
12.5.1 Proportional Hazards (PH)...........................211
12.5.2 Accelerated Life (AL).................................211
12.5.3 Proportional Odds (PO)..............................211
12.5.4 Mean Residual Life (MRL)............................212
12.6 Examples....................................................212
12.6.1 Exponential Mixture..................................212
12.7 Exercises.....................................................214
12.8 Hints and Solutions..........................................214
13. Continuous Time: Parametric Inference............................215
13.1 The Likelihood for Competing Risks.........................215
13.1.1 Forms of the Likelihood Function.....................215
13.1.2 Uncertainty about C..................................216
13.1.3 Uncertainty about T..................................216
13.1.4 Maximum Likelihood Estimates......................217
13.1.4.1 Weibull Sub-Hazards........................217
13.1.4.2 Exponential Mixture........................217
13.2 Model Checking.............................................218
13.2.1 Goodness of Fit.......................................218
13.2.2 Uniform Residuals...................................218
13.3 Inference.....................................................219
13.4 Some Applications...........................................221
13.4.1 Gubbins..............................................221
13.4.2 Survival Times of Mice...............................222
13.4.3 Fracture Toughness...................................224
13.4.4 Length of Hospital Stay...............................225
13.5 Some Examples of Hazard Modelling........................226
13.5.1 Exponential Mixture..................................226
13.5.2 Gumbel s Bivariate Exponential......................227
13.5.3 Bivariate Makeham Distribution......................227
13.5.4 Kimber and Grace: The Dream Team..................227
13.5.5 A Clinical Trial.......................................229
13.6 Masked Systems.............................................231
13.7 Exercises.....................................................233
13.7.1 Applications.........................................233
14. Latent Lifetimes...................................................235
14.1 Basic Probability Functions...................................235
Contents xvii
14.1.1 Tsiatis s Lemma......................................235
14.1.2 Gumbel s Bivariate Exponential......................236
14.2 Some Examples..............................................238
14.2.1 Freund s Bivariate Exponential.......................238
14.2.2 Frailty Models........................................238
14.2.3 Multivariate Burr (MB)...............................239
14.2.4 Multivariate Weibull (MW)...........................239
14.2.5 A Stochastic Process Model...........................241
14.2.6 Other Applications...................................241
14.3 Further Aspects..............................................242
14.3.1 Latent Failure Times versus Hazard Functions........242
14.3.2 Marginals versus Sub-Distributions...................242
14.3.3 Peterson s Bounds....................................243
14.4 Independent Risks...........................................244
14.4.1 Gail s Theorem.......................................245
14.4.2 Other Applications...................................247
14.5 The Makeham Assumption...................................247
14.5.1 Proportional Hazards.................................248
14.6 A Risk-Removal Model......................................249
14.7 A Degradation Process.......................................250
14.7.1 Wiener Process.......................................251
14.7.2 Compound Poisson and Compound Birth
Processes............................................251
14.7.3 Gamma Process......................................251
14.8 Exercises.....................................................251
14.9 Hints and Solutions..........................................252
15. Continuous Time: Non- and Semi-Parametric Methods............253
15.1 The Kaplan-Meier Estimator.................................253
15.1.1 Survival Times of Mice...............................255
15.2 Actuarial Approach..........................................257
15.3 Proportional Hazards and Partial Likelihood.................259
15.3.1 The Proportional Hazards (PH) Model................259
15.3.2 The Partial Likelihood................................259
15.3.3 A Clinical Trial.......................................260
15.4 The Baseline Survivor Functions.............................261
15.5 Other Methods and Applications.............................262
16. Discrete Lifetimes.................................................265
16.1 Basic Probability Functions...................................265
16.1.1 Geometric Mixture...................................266
16.2 Latent Lifetimes and Sub-Odds Functions....................267
16.2.1 Sub-Odds Theorem...................................268
16.3 Some Examples..............................................271
16.3.1 Discrete Version of Gumbel...........................271
16.3.2 Discrete Version of Freund............................272
xviii Contents
16.3.3 Discrete Version of Marshall-Olkin...................273
16.3.4 Mixture Models......................................273
16.4 Parametric Estimation........................................274
16.4.1 Likelihood Function..................................275
16.4.2 Discrete Marshall-Olkin..............................275
16.4.3 Psychiatric Wards....................................276
16.5 Non-Parametric Estimation from Random Samples...........277
16.5.1 Gubbins..............................................279
16.5.2 Interval-Censored Data...............................281
16.5.3 Superalloy Testing....................................281
16.6 Asymptotic Distribution of Non-Parametric Estimators.......283
16.7 Proportional Odds and Partial Likelihood....................284
16.7.1 Psychiatric Wards....................................285
16.8 Exercises.....................................................286
16.9 Hints and Solutions..........................................286
17. Latent Lifetimes: Identifiability Crises.............................287
17.1 The Cox-Tsiatis Impasse.....................................287
17.1.1 Tsiatis s Theorem.....................................287
17.1.2 Gumbel s Bivariate Exponential......................289
17.2 More General Identifiablility Results.........................290
17.2.1 Miller s Theorem.....................................290
17.2.2 The LPQ Theorem....................................291
17.2.3 The Marshall-Olkin Distribution.....................295
17.3 Specified Marginals..........................................296
17.4 Discrete Lifetimes............................................299
17.4.1 Discrete Freund......................................301
17.4.2 Discrete Marshall-Olkin..............................301
17.4.3 A Test for Independence of Risks.....................301
17.5 Regression Case..............................................302
17.5.1 Heckman and Honore s Theorem.....................302
17.5.2 Gumbel s Bivariate Exponential......................303
17.6 Censoring of Survival Data...................................304
17.7 Parametric Identifiability.....................................306
Part IV Counting Processes in Survival Analysis
18. Some Basic Concepts..............................................311
18.1 Probability Spaces............................................311
18.2 Conditional Expectation......................................312
18.3 Filtrations....................................................314
18.4 Martingales in Discrete Time.................................315
18.4.1 Likelihood Ratios.....................................316
18.5 Martingales in Continuous Time.............................317
18.6 Counting Processes..........................................319
18.7 Product Integrals.............................................320
Contents xix
19. Survival Analysis..................................................323
19.1 A Single Lifetime............................................323
19.1.1 The Intensity Process.................................323
19.1.2 Parametric Likelihood Function......................324
19.2 Independent Lifetimes.......................................325
19.3 Competing Risks.............................................326
19.4 Right-Censoring.............................................328
20. Non- and Semi-Parametric Methods...............................331
20.1 Survival Tunes...............................................331
20.2 Competing Risks.............................................333
20.3 Large-Sample Results........................................334
20.3.1 Consistency..........................................334
20.3.2 Asymptotic Normality................................334
20.3.3 Confidence Intervals.................................334
20.4 Hypothesis Testing...........................................335
20.4.1 Single-Sample Case...................................335
20.4.2 Several Samples......................................336
20.5 Regression Models...........................................338
20.5.1 Intensity Models and Time-Dependent Covariates___338
20.5.2 Proportional Hazards Model.........................339
20.5.3 Martingale Residuals.................................339
Appendix A: Terms, Notations, and Abbreviations....................341
Appendix B: Basic Likelihood Methods...............................343
Appendix C: Some Theory for Partial Likelihood.....................347
Appendix D: Numerical Optimisation of Functions...................351
References.............................................................355
Epilogue to First Edition...............................................375
Index..................................................................377
|
| any_adam_object | 1 |
| author | Crowder, M. J. 1943- |
| author_GND | (DE-588)172028469 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Biologie Mathematik Medizin |
| format | Book |
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| id | DE-604.BV040128548 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:17:32Z |
| institution | BVB |
| isbn | 9781439875216 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024985765 |
| oclc_num | 797323969 |
| open_access_boolean | |
| owner | DE-521 DE-91G DE-BY-TUM DE-83 |
| owner_facet | DE-521 DE-91G DE-BY-TUM DE-83 |
| physical | XXIV, 393 S. graph. Darst. 25 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Texts in statistical science |
| spelling | Crowder, M. J. 1943- Verfasser (DE-588)172028469 aut Multivariate survival analysis and competing risks Martin Crowder Boca Raton, Fla. CRC Press 2012 XXIV, 393 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Includes bibliographical references and index Failure time data analysis Competing risks Multivariate analysis MATHEMATICS / Probability & Statistics / General bisacsh Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Ereignisdatenanalyse (DE-588)4132103-0 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Ereignisdatenanalyse (DE-588)4132103-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024985765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crowder, M. J. 1943- Multivariate survival analysis and competing risks Failure time data analysis Competing risks Multivariate analysis MATHEMATICS / Probability & Statistics / General bisacsh Multivariate Analyse (DE-588)4040708-1 gnd Ereignisdatenanalyse (DE-588)4132103-0 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4132103-0 |
| title | Multivariate survival analysis and competing risks |
| title_auth | Multivariate survival analysis and competing risks |
| title_exact_search | Multivariate survival analysis and competing risks |
| title_full | Multivariate survival analysis and competing risks Martin Crowder |
| title_fullStr | Multivariate survival analysis and competing risks Martin Crowder |
| title_full_unstemmed | Multivariate survival analysis and competing risks Martin Crowder |
| title_short | Multivariate survival analysis and competing risks |
| title_sort | multivariate survival analysis and competing risks |
| topic | Failure time data analysis Competing risks Multivariate analysis MATHEMATICS / Probability & Statistics / General bisacsh Multivariate Analyse (DE-588)4040708-1 gnd Ereignisdatenanalyse (DE-588)4132103-0 gnd |
| topic_facet | Failure time data analysis Competing risks Multivariate analysis MATHEMATICS / Probability & Statistics / General Multivariate Analyse Ereignisdatenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024985765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT crowdermj multivariatesurvivalanalysisandcompetingrisks |