Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer
2015
|
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXV, 582 S. Ill., graph. Darst. |
| ISBN: | 9783319194240 |
Internformat
MARC
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| 020 | |a 9783319194240 |c Print |9 978-3-319-19424-0 | ||
| 035 | |a (OCoLC)924750688 | ||
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| 100 | 1 | |a Harrell, Frank E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Regression modeling strategies |b with applications to linear models, logistic and ordinal regression, and survival analysis |c Frank E. Harrell, jr. |
| 250 | |a 2nd ed. | ||
| 264 | 1 | |a Cham [u.a.] |b Springer |c 2015 | |
| 300 | |a XXV, 582 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 650 | 0 | 7 | |a Regressionsmodell |0 (DE-588)4127980-3 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-028201757 | ||
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
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| DE-BY-FWS_katkey | 653115 |
| DE-BY-FWS_media_number | 083000517947 |
| _version_ | 1806176845763182592 |
| adam_text | Contents
typographical Conventions.........................................xxv
1 Introduction......................................................
I d (lypot hrsis 1 rst inn. Estimation, and Prediction......... 1
! .2 Examples of Uses of Predictive; Multivariable Modeling.. 3
i .3 Predict ion vs. Classification.............................. 4
Id Planning for Modeling....................................... 6
1.4.1 Emphasizing Continuous Variables ................... 8
l.o Choice of the Model......................................... 8
Lb Further Reading.............................................. 11
2 General Aspects of Fitting Regression Models................. 13
2d Notation for Multivariable Regression Models............... 13
2.2 Model Formulations ........................................ 14
2.3 Interpreting Model Parameters.............................. 15
2.3d Nominal Predictors................................. 16
2.3.2 Interactions....................................... 16
2.3.3 Example: Inference for a Simple Model.............. 17
2.4 Relaxing Linearity Assumption for Continuous Predictors . . 18
2.4.1 Avoiding Categorization............................ 18
2.4.2 Simple Nonlinear Terms............................. 21
2.4.3 Splines for Estimating Shape of Regression
Function and Determining Predictor
Transformations.................................... 22
2.4.4 Cubic Spline Functions............................. 23
2.4.5 Restricted Cubic Splines .......................... 24
2.4.6 Choosing Number and Position of Knots.............. 26
2.4.7 Nonparametric Regression........................... 28
2.4.8 Advantages of Regression Splines over
Other Methods.................................... 30
XV
( mtents
xvi
2.5
2.6
2.7
2.8
2.9
Recursive Partitioning: Tree-Based Models. . .....
Multiple Degree of Freedom Tests of Association .
Assessment of Model Fit ..........................
2.7.1 Regression Assumptions................/
2.7.2 Modeling and Testing Complex Interactions
2.7.3 Fitting Ordinal Predictors................
2.7.4 Distributional Assumptions................
Further Reading...................................
Problems.............................*............
30
31
33
33
30
38
39
40
42
3 Missing Data.....................................................
3.1 Types of Missing Data.....................................
3.2 Prelude to Modeling............................... *......
3.3 Missing Values for Different Types of Response Variables . . .
3.4 Problems with Simple Alternatives to Imputation ..........
3.5 Strategies for Developing an Imputation Model.............
3.6 Single Conditional Mean Imputation........................
3.7 Predictive Mean Matching..................................
3.8 Multiple Imputation.......................................
3.8.1 The areglmpute and Other Chained Equations
Approaches...........................................
3.9 Diagnostics................................................ 56
3.10 Summary and Rough Guidelines............................... 50
3.11 Further Reading............................................ 58
3.12 Problems................................................... 59
4 Multivariable Modeling Strategies................................ (53
4.1 Prespecification of Predictor Complexity Without
Later Simplification........................................ 04
4.2 Checking Assumptions of Multiple Predictors
Simultaneously.............................................. 07
4.3 Variable Selection.......................................... 07
4.4 Sample Size, Overfitting, and Limits on Number
of Predictors............................................. 72
4.5 Shrinkage ................................................ 75
4.6 Collinearity................................................ 7^
4.7 Data Reduction.............................................. 79
4.7.1 Redundancy Analysis................................ ¿*0
4.7.2 Variable Clustering................................. gl
4.7.3 Transformation and Scaling Variables Without
Using Y........................................... H1
4.7.4 Simultaneous Transformation and Imputation........ 83
4.7.5 Simple Scoring of Variable Clusters................ 85
4.7.6 Simplifying Cluster Scores........................ K7
4.7.7 How Much Data Reduction Is Necessary?.............. 87
Contents
xvii
4.8 Other Approaches to Predictive Modeling.................. 89
4.9 Overly Influential Observations.......................... 90
4.10 Comparing Two Models..................................... 92
4.11 Improving the Practice of Multivariable Prediction....... 94
4.12 Summary: Possible Modeling Strategies.................... 94
4.12.1 Developing Predictive Models...................... 95
4.12.2 Developing Models for Effect Estimation........... 98
4.12.3 Developing Models for Hypothesis Testing.......... 99
4.13 Further Reading..........................................100
4.14 Problems.................................................102
5 Describing, Resampling, Validating, and Simplifying
the Model......................................................103
5.1 Describing the Fitted Model..............................103
5.1.1 Interpreting Effects.............................103
5.1.2 Indexes of Model Performance......................104
5.2 The Bootstrap............................................106
5.3 Model Validation.........................................109
5.3.1 Introduction................................. 109
5.3.2 Which Quantities Should Be Used in Validation? ... 110
5.3.3 Data-Splitting....................................Ill
5.3.4 Improvements on Data-Splitting: Resampling ...... 112
5.3.5 Validation Using the Bootstrap ...................114
5.4 Bootstrapping Ranks of Predictors........................117
5.5 Simplifying the Final Model by Approximating It..........118
5.5.1 Difficulties Using Full Models.................. 118
5.5.2 Approximating the Full Model......................119
5.6 Further Reading........................................ 121
5.7 Problem................................................ 124
6 R Software.....................................................127
6.1 The R Modeling Language..................................128
6.2 User-Contributed Functions...............................129
6.3 The rms Package..........................................130
6.4 Other Functions..........................................141
6.5 Further Reading..........................................142
7 Modeling Longitudinal Responses using Generalized
Least Squares...................................................M3
7.1 Notation and Data Setup..................................143
7.2 Model Specification for Effects on E(Y)..................144
7.3 Modeling Within-Subject Dependence.......................144
7.4 Parameter Estimation Procedure....................... 147
7.5 Common Correlation Structures......................... 147
7.6 Checking Model Fit.......................................148
xvili
Contents
7.7 Sample Size Considerations........................... . . 149
7.8 R Softwaie.......*............ . . 149
7.9 .. 150
7.9.1 Graphical .bxpioranon or ................. .. 151
7.9.2 Using Generalized JLeast squares.............. . . 158
7.10 .. 161
Case btuay in uata ............................
Q 1 .. 161
O.i
8.2 How Many Parameters Can Be Estimated?............. . . 164
o o .. 164
8.3 rledunaancy Analysis.....*..................
o A .. 166
0.4 vanaoie wiusvernig .......................... . . 167
8.5 Transformation and Single Imputation Using transcan... . . 170
8.6 Data Reduction Using Principal Components ........... .. 175
8.7 8.6.1 Sparse Principal Components.................. .. 176
Q ft Transformation Using Nonparametric Smoothers........ .. 177
0.0
8.9 .. 178
9 Overview of Maximum Likelihood Estimation......................181
9.1 General Notions—Simple Cases..............................181
9.2 Hypothesis Tests..........................................185
9.2.1 Likelihood Ratio Test..............................185
9.2.2 Wald Test..........................................186
9.2.3 Score Test.........................................186
9.2.4 Normal Distribution—One Sample ....................187
9.3 General Case..............................................188
9.3.1 Global Test Statistics.............................189
9.3.2 Testing a Subset of the Parameters.................190
9.3.3 Tests Based on Contrasts...........................192
9.3.4 Which Test Statistics to Use When..................193
9.3.5 Example: Binomial—Comparing Two
Proportions...................................... 194
9.4 Iterative ML Estimation................................. 195
9.5 Robust Estimation of the Covariance Matrix................196
9.6 Wald, Score, and Likelihood-Based Confidence Intervals .... 198
9.6.1 Simultaneous Wald Confidence Regions...............199
9.7 Bootstrap Confidence Regions..............................199
9.8 Further Use of the Log Likelihood....................... 203
9.8.1 Rating Two Models, Penalizing for Complexity.....203
9.8.2 Testing Whether One Model Is Better
than Another.......................................204
9.8.3 Unitless Index of Predictive Ability...............205
9.8.4 Unitless Index of Adequacy of a Subset
of Predictors......................................207
9.9 Weighted Maximum Likelihood Estimation....................208
9.10 Penalized Maximum Likelihood Estimation.................. 209
Contents xix
9.11 Further Reading.................................... 213
9.12 Problems....................................... . /____ t 216
10 Binary Logistic Regression........................ 219
10.1 Model.......................................... //,.,.. t 219
10.1.1 Model Assumptions and Interpretation
of Parameters................................. 221
10.1.2 Odds Ratio, Risk Ratio, and Risk Difference ....... 224
10.1.3 Detailed Example................................ 225
10.1.4 Design Formulations............................ 230
10.2 Estimation.............................................. 231
10.2.1 Maximum Likelihood Estimates.................... 231
10.2.2 Estimation of Odds Ratios and Probabilities......232
10.2.3 Minimum Sample Size Requirement ________......... 233
10.3 Test Statistics......................................... 234
10.4 Residuals................................................ 235
10.5 Assessment of Model Fit............................... 236
10.6 Collinearity............................................ 255
10.7 Overly Influential Observations.......................... 255
10.8 Quantifying Predictive Ability........................... 256
10.9 Validating the Fitted Model.............................. 259
10.10 Describing the Fitted Model....................... 264
10.11 R Functions........................................... 269
10.12 Further Reading.......................— ................. 271
10.13 Problems............................................. 273
11 Binary Logistic Regression Case Study 1 ...................... 275
11.1 Overview.............................................. 275
11.2 Background................................. ......... — 275
11.3 Data Transformations and Single Imputation ..............276
11.4 Regression on Original Variables, Principal Components
and Pretransformations................................. • 277
11.5 Description of Fitted Model............................. 278
11.6 Backwards Step-Down.................................... 280
11.7 Model Approximation...................... * --. • *----• • 287
12 Logistic Model Case Study 2: Survival of Titanic
Passengers.............................*............... 291
12.1 Descriptive Statistics............................... 291
12.2 Exploring Trends with Nonparametric Regression......------294
12.3 Binary Logistic Model With Casewise Deletion
of Missing Values...................................... 296
12.4 Examining Missing Data Patterns......................... 302
12.5 Multiple Imputation...................................* • •
12.6 Summarizing the Fitted Model............................ 307
(’omenta
xx
13
Ordinal Logistic Regression
13.1 Background............................................
13.2 Ordinality Assumption....................................
13.3 Proportional Odds Model..................................
13.3.1 Model ......................... -.................
13.3.2 Assumptions and Interpretation of l araine et*
13.3.3 Estimation........................................
13.3.4 Residuals.........................................
13.3.5 Assessment of Model Fit...........................
13.3.6 Quantifying Predictive Ability....................
13.3.7 Describing the Fitted Model.......................
13.3.8 Validating the Fitted Model.......................
13.3.9 R Functions.......................................
13.4 Continuation Ratio Model.................................
13.4.1 Model ............................................
13.4.2 Assumptions and Interpretation of Parameters......
13.4.3 Estimation........................................
13.4.4 Residuals.........................................
13.4.5 Assessment of Model Fit...........................
13.4.6 Extended CR. Model................................
13.4.7 Role of Penalization in Extended CR Model.........
13.4.8 Validating the Fitted Model.......................
13.4.9 R Functions.......................................
13.5 Further Reading..........................................
13.6 Problems.................................................
311
311
312
313
313
313
314
314
315
318
318
318
319
319
319
320
320
321
321
321
322
322
323
324
324
14 Case Study in Ordinal Regression, Data Reduction,
and Penalization...........................................
14.1 Response Variable.................................
14.2 Variable Clustering...............................
14.3 Developing Cluster Summary Scores.................
14.4 Assessing Ordinality of for each X, and Unadjusted
Checking of PO and CR Assumptions.................
14.5 A Tentative Full Proportional Odds Model .........
14.6 Residual Plots..................................
14.7 Graphical Assessment of Fit of CR Model
14.8 Extended Continuation Ratio Model.................
14.9 Penalized Estimation.......................
14.10 Using Approximations to Simplify the Model
14.11 Validating the Model ...................
14.12 Summary..................
14.13 Further Reading...............
14.14 Problems............
327
328
329
330
333
333
336
338
340
342
348
353
355
356
357
Contents xxi
15 Regression Models for Continuous Y and Case Study
in Ordinal Regression........................................359
15.1 The Linear Model.......................................359
15.2 Quantile Regression....................................360
15.3 Ordinal Regression Models for Continuous Y.............361
15.3.1 Minimum Sample Size Requirement ................363
15.4 Comparison of Assumptions of Various Models............364
15.5 Dataset and Descriptive Statistics.....................365
15.5.1 Checking Assumptions of OLS and Other Models... 368
15.6 Ordinal Regression Applied to HbAic...................370
15.6.1 Checking Fit for Various Models Using Age......370
15.6.2 Examination of BMI.............................374
15.6.3 Consideration of All Body Size Measurements.....375
16 Transform-Both-Sides Regression..............................389
16.1 Background............................................389
16.2 Generalized Additive Models...........................390
16.3 Nonparametric Estimation of V-Transformation..........390
16.4 Obtaining Estimates on the Original Scale..............391
16.5 R Functions...........................................392
16.6 Case Study.......................................... 393
17 Introduction to Survival Analysis............................399
17.1 Background............................................399
17.2 Censoring, Delayed Entry, and Truncation............ 401
17.3 Notation, Survival, and Hazard Functions..............402
17.4 Homogeneous Failure Time Distributions................407
17.5 Nonparametric Estimation of S and A ..................409
17.5.1 Kaplan-Meier Estimator.........................409
17.5.2 Altschuler-Nelson Estimator.................. 413
17.6 Analysis of Multiple Endpoints..................... 413
17.6.1 Competing Risks.............................. 414
17.6.2 Competing Dependent Risks.................... 414
17.6.3 State Transitions and Multiple Types of Nonfatal
Events...................................... 416
17.6.4 Joint Analysis of Time and Severity of an Event-417
17.6.5 Analysis of Multiple Events....................417
17.7 R Functions.......................................... 418
17.8 Further Reading...................................... 420
17.9 Problems..................................*.......... * 421
18 Parametric Survival Models...................................423
18.1 Homogeneous Models (No Predictors)....................423
18.1.1 Specific Models................................423
18.1.2 Estimation.....................................424
18.1.3 Assessment of Model Fit........................426
Contentó
xxii
18.2 Parametric Proportional Hazards Models...............
18.2.1 Model........................................
18.2.2 Model Assumptions and Interpretation
of Parameters................................
18.2.3 Hazard Ratio, Risk Ratio, and Risk Difference
18.2.4 Specific Models..............................
18.2.5 Estimation...................................
18.2.6 Assessment of Model Fit......................
18.3 Accelerated Failure Time Models......................
18.3.1 Model........................................
18.3.2 Model Assumptions and Interpretation
of Parameters..........*.....................
18.3.3 Specific Models..............................
18.3.4 Estimation...............*...................
18.3.5 Residuals....................................
18.3.6 Assessment of Model Fit......................
18.3.7 Validating the Fitted Model..................
18.4 Buckley-James Regression Model.......................
18.5 Design Formulations..................................
18.6 Test Statistics......................................
18.7 Quantifying Predictive Ability.......................
18.8 Time-Dependent Covariates............................
18.9 R Functions..........................................
18.10 Further Reading.....................................
18.11 Problems............................................
. 427
. 427
. 428
. 430
. 431
. 432
. 434
. 436
. 436
. 436
. 437
. 438
. 440
. 440
. 446
. 447
. 447
. 447
. 447
. 447
. 448
. 450
. 451
19 Case Study in Parametric Survival Modeling and Model
Approximation................................................453
19.1 Descriptive Statistics..................................453
19.2 Checking Adequacy of Log-Normal Accelerated Failure
Time Model..............................................458
19.3 Summarizing the Fitted Model............................466
19.4 Internal Validation of the Fitted Model Using
the Bootstrap...........................................466
19.5 Approximating the Full Model............................469
19.6 Problems.................................................
20 Cox Proportional Hazards Regression Model....................475
20.1 Model............................................ 475
20.1.1 Preliminaries....................................475
20.1.2 Model Definition..................................
20.1.3 Estimation of ¡3..................................
20.1.4 Model Assumptions and Interpretation
of Parameters.....................................
20.1.5 Example......................................... 470
Contents
xxiii
20. L6 Design Formulations................................ 480
20.1.7 Extending the Model by Stratification ........... 481
20.2 Estimation of Survival Probability and Secondary
Parameters.............................................. 483
20.3 Sample Size Considerations............................... 486
20.4 Test Statistics........................................ 486
20.5 Residuals................................................ 487
20.6 Assessment of Model Fit ............................... 487
20.6.1 Regression Assumptions............................487
20.6.2 Proportional Hazards Assumption ..................494
20.7 What to Do When PH Fails.................................. 501
20.8 Collinearity............................................. 503
20.9 Overly Influential Observations............................504
20.10 Quantifying Predictive Ability............................504
20.11 Validating the Fitted Model...............................506
20.11.1 Validation of Model Calibration...................506
20.11.2 Validation of Discrimination and Other Statistical
Indexes......................................* • • * 507
20.12 Describing the Fitted Model............................... 509
20.13 R Functions............................................ . 513
20.14 Further Reading....................................... 517
21 Case Study in Cox Regression.....................................521
21.1 Choosing the Number of Parameters and Fitting
the Model............................................. 521
21.2 Checking Proportional Hazards............................. 525
21.3 Testing Interactions..................................... 527
21.4 Describing Predictor Effects ....................• •......527
21.5 Validating the Model .................................... 529
21.6 Presenting the Model............................ —.....* • 530
21.7 Problems.................................................. 531
A Datasets, R Packages, and Internet Resources..................... 535
References.......................................................• * *.539
Index......................................................* * ....571
|
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| author | Harrell, Frank E. |
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| author_variant | f e h fe feh |
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| bvnumber | BV042771462 |
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| classification_tum | MAT 628f |
| ctrlnum | (OCoLC)924750688 (DE-599)BVBBV042771462 |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| edition | 2nd ed. |
| format | Book |
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| id | DE-604.BV042771462 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T11:27:47Z |
| institution | BVB |
| isbn | 9783319194240 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028201757 |
| oclc_num | 924750688 |
| open_access_boolean | |
| owner | DE-83 DE-M49 DE-BY-TUM DE-29 DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-862 DE-BY-FWS DE-898 DE-BY-UBR DE-29T DE-188 DE-20 |
| owner_facet | DE-83 DE-M49 DE-BY-TUM DE-29 DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-862 DE-BY-FWS DE-898 DE-BY-UBR DE-29T DE-188 DE-20 |
| physical | XXV, 582 S. Ill., graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spellingShingle | Harrell, Frank E. Regression modeling strategies with applications to linear models, logistic and ordinal regression, and survival analysis Regressionsmodell (DE-588)4127980-3 gnd |
| subject_GND | (DE-588)4127980-3 |
| title | Regression modeling strategies with applications to linear models, logistic and ordinal regression, and survival analysis |
| title_auth | Regression modeling strategies with applications to linear models, logistic and ordinal regression, and survival analysis |
| title_exact_search | Regression modeling strategies with applications to linear models, logistic and ordinal regression, and survival analysis |
| title_full | Regression modeling strategies with applications to linear models, logistic and ordinal regression, and survival analysis Frank E. Harrell, jr. |
| title_fullStr | Regression modeling strategies with applications to linear models, logistic and ordinal regression, and survival analysis Frank E. Harrell, jr. |
| title_full_unstemmed | Regression modeling strategies with applications to linear models, logistic and ordinal regression, and survival analysis Frank E. Harrell, jr. |
| title_short | Regression modeling strategies |
| title_sort | regression modeling strategies with applications to linear models logistic and ordinal regression and survival analysis |
| title_sub | with applications to linear models, logistic and ordinal regression, and survival analysis |
| topic | Regressionsmodell (DE-588)4127980-3 gnd |
| topic_facet | Regressionsmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028201757&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT harrellfranke regressionmodelingstrategieswithapplicationstolinearmodelslogisticandordinalregressionandsurvivalanalysis |
Inhaltsverzeichnis
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| Signatur: |
2000 SK 840 H296(2) |
|---|---|
| Exemplar 1 | nicht ausleihbar Checked out – Rückgabe bis: 31.12.2099 Vormerken |