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Survival Analysis with Interval-Censored Data: A Practical Approach with Examples in R, SAS, and BUGS [Kietas viršelis]

Kris Bogaerts (Kiostatistical Centre, Leuven, Belgium), Arnost Komarek, Emmanuel Lesaffre (Biostatistical Centre, Leuven, Belgium)

Formatas: Hardback, 616 pages, aukštis x plotis: 234x156 mm, weight: 1060 g, 45 Tables, black and white; 82 Illustrations, black and white
Serija: Chapman & Hall/CRC Interdisciplinary Statistics
Išleidimo metai: 14-Nov-2017
Leidėjas: Chapman & Hall/CRC
ISBN-10: 1420077473
ISBN-13: 9781420077476

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Formatas: Hardback, 616 pages, aukštis x plotis: 234x156 mm, weight: 1060 g, 45 Tables, black and white; 82 Illustrations, black and white
Serija: Chapman & Hall/CRC Interdisciplinary Statistics
Išleidimo metai: 14-Nov-2017
Leidėjas: Chapman & Hall/CRC
ISBN-10: 1420077473
ISBN-13: 9781420077476

Kitos knygos pagal šią temą:

Probability & statistics - (Šiuo metu turimos knygos: 2 prekės)

Pastovi nuoroda: https://www.kriso.lt/db/9781420077476.html

Raktažodžiai:

Survival Analysis with Interval-Censored Data: A Practical Approach with Examples in R, SAS, and BUGS provides the reader with a practical introduction into the analysis of interval-censored survival times. Although many theoretical developments have appeared in the last fifty years, interval censoring is often ignored in practice. Many are unaware of the impact of inappropriately dealing with interval censoring. In addition, the necessary software is at times difficult to trace. This book fills in the gap between theory and practice.

Features:

-Provides an overview of frequentist as well as Bayesian methods.

-Include a focus on practical aspects and applications.

-Extensively illustrates the methods with examples using R, SAS, and BUGS. Full programs are available on a supplementary website.

The authors:

Kris Bogaerts is project manager at I-BioStat, KU Leuven. He received his PhD in science (statistics) at KU Leuven on the analysis of interval-censored data. He has gained expertise in a great variety of statistical topics with a focus on the design and analysis of clinical trials.

Arnot Komįrek is associate professor of statistics at Charles University, Prague. His subject area of expertise covers mainly survival analysis with the emphasis on interval-censored data and classification based on longitudinal data. He is past chair of the Statistical Modelling Society and editor of Statistical Modelling: An International Journal.

Emmanuel Lesaffre is professor of biostatistics at I-BioStat, KU Leuven. His research interests include Bayesian methods, longitudinal data analysis, statistical modelling, analysis of dental data, interval-censored data, misclassification issues, and clinical trials. He is the founding chair of the Statistical Modelling Society, past-president of the International Society for Clinical Biostatistics, and fellow of ISI and ASA.

Recenzijos

"The authors succeeded in providing a practical text focused on the application of interval-censored data using various statistical software. Lastly, the authors wrote a text, which appeals to practitioners, because the text anticipates their needs and the foundational concepts and software to execute it." ~ Stephanie A. Besser

"All chapters spend a significant amount of time walking through examples with associated R code and results and do a very nice job explaining the initial CSE framework. Examples expand in complexity as the book progresses. As a biostatistician working in an academic setting, I am quite familiar with simulations used to construct new trials. However, the concept of CSE framework was brand new to me, and I think the strategies outlined in this book could definitely improve my approach to designing trial and analysis plans! This would also facilitate discussions with the clinical study team on how to proceed given our results. I would recommend this book to any clinical trial statistician who is interested in exploring simulations to better understand the implications of selected design and analysis strategies within their trials." ~Emily Dressler, Wake Forest School of Medicine

"To the best of my knowledge, this is the first book to provide a comprehensive treatment of the analysis of interval-censored data using common software such as SAS, R, and BUGS. I expect that applied statisticians and public health researchers with interest in statistical analysis of interval-censored data will find the book very useful. In addition, it seems well suited to be a reference book for a graduate-level survival analysis course. Overall, I enjoyed the presentation of the main idea of the methodology and the discussion of the strengths and limitations of approaches. If I had an opportunity to teach statistical methods for interval-censored data, I would select this book as a required text." ~ Minggen Lu, The American Statistician

List of Tables

xvii

List of Figures xxi

Notation

xxvii

Preface

xxix

I Introduction

(60)

1 Introduction

(32)

1.1 Survival concepts

(1)

1.2 Types of censoring

(4)

1.2.1 Right censoring

(1)

1.2.2 Interval and left censoring

(1)

1.2.3 Some special cases of interval censoring

(2)

1.2.4 Doubly interval censoring

(1)

1.2.5 Truncation

(1)

1.3 Ignoring interval censoring

(5)

1.4 Independent noninformative censoring

(2)

1.4.1 Independent noninformative right censoring

(1)

1.4.2 Independent noninformative interval censoring

(1)

1.5 Frequentist inference

(5)

1.5.1 Likelihood for interval-censored data

(2)

1.5.2 Maximum likelihood theory

(3)

1.6 Data sets and research questions

(10)

1.6.1 Homograft study

(2)

1.6.2 Breast cancer study

(1)

1.6.3 AIDS clinical trial

(1)

1.6.4 Sensory shelf life study

(2)

1.6.5 Survey on mobile phone purchases

(2)

1.6.6 Mastitis study

(1)

1.6.7 Signal Tandmobiel study

(2)

1.7 Censored data in R and SAS

(5)

1.7.1 R

(4)

1.7.2 SAS

(1)

2 Inference for right-censored data

(26)

2.1 Estimation of the survival function

(6)

2.1.1 Nonparametric maximum likelihood estimation

(3)

2.1.2 R solution

(2)

2.1.3 SAS solution

(1)

2.2 Comparison of two survival distributions

(5)

2.2.1 Review of significance tests

(3)

2.2.2 R solution

(1)

2.2.3 SAS solution

(1)

2.3 Regression models

(17)

2.3.1 Proportional hazards model

(7)

2.3.1.1 Model description and estimation

(1)

2.3.1.2 Model checking

(3)

2.3.1.3 R solution

(2)

2.3.1.4 SAS solution

(1)

2.3.2 Accelerated failure time model

(10)

2.3.2.1 Model description and estimation

(2)

2.3.2.2 Model checking

(1)

2.3.2.3 R solution

(2)

2.3.2.4 SAS solution

(3)

II Frequentist methods for interval-censored data

(220)

3 Estimating the survival distribution

(42)

3.1 Nonparametric maximum likelihood

(14)

3.1.1 Estimation

(4)

3.1.2 Asymptotic results

(1)

3.1.3 R solution

(3)

3.1.4 SAS solution

(6)

3.2 Parametric modelling

(8)

3.2.1 Estimation

(1)

3.2.2 Model selection

(1)

3.2.3 Goodness of fit

(2)

3.2.4 R solution

(2)

3.2.5 SAS solution

(3)

3.3 Smoothing methods

(19)

3.3.1 Logspline density estimation

(5)

3.3.1.1 A smooth approximation to the density

(1)

3.3.1.2 Maximum likelihood estimation

(1)

3.3.1.3 R solution

(3)

3.3.2 Classical Gaussian mixture model

(3)

3.3.3 Penalized Gaussian mixture model

(12)

3.3.3.1 R solution

(5)

3.4 Concluding remarks

104

(1)

4 Comparison of two or more survival distributions

105

(26)

4.1 Nonparametric comparison of survival curves

105

(22)

4.1.1 Weighted log-rank test: derivation

107

(2)

4.1.2 Weighted log-rank test: linear form

109

(1)

4.1.3 Weighted log-rank test: derived from the linear transformation model

109

(2)

4.1.4 Weighted log-rank test: the G ,zγ family

111

(1)

4.1.5 Weighted log-rank test: significance testing

112

(5)

4.1.6 It solution

117

(6)

4.1.7 SAS solution

123

(4)

4.2 Sample size calculation

127

(1)

4.3 Concluding remarks

128

(3)

5 The proportional hazards model

131

(48)

5.1 Parametric approaches

132

(4)

5.1.1 Maximum likelihood estimation

132

(1)

5.1.2 R solution

132

(3)

5.1.3 SAS solution

135

(1)

5.2 Towards semiparametric approaches

136

(13)

5.2.1 Piecewise exponential baseline survival model

137

(4)

5.2.1.1 Model description and estimation

137

(1)

5.2.1.2 Ft solution

138

(2)

5.2.1.3 SAS solution

140

(1)

5.2.2 SemiNonParametric approach

141

(3)

5.2.2.1 Model description and estimation

141

(1)

5.2.2.2 SAS solution

142

(2)

5.2.3 Spline-based smoothing approaches

144

(5)

5.2.3.1 Two spline-based smoothing approaches

144

(2)

5.2.3.2 R solution

146

(1)

5.2.3.3 SAS solution

147

(2)

5.3 Semiparametric approaches

149

(14)

5.3.1 Finkelstein's approach

149

(1)

5.3.2 Farrington's approach

150

(3)

5.3.3 Iterative convex minorant algorithm

153

(1)

5.3.4 Grouped proportional hazards model

153

(1)

5.3.5 Practical applications

154

(9)

5.3.5.1 Two examples

154

(1)

5.3.5.2 R solution

155

(3)

5.3.5.3 SAS solution

158

(5)

5.4 Multiple imputation approach

163

(7)

5.4.1 Data augmentation algorithm

163

(2)

5.4.2 Multiple imputation for interval-censored survival times

165

(5)

5.4.2.1 R solution

167

(1)

5.4.2.2 SAS solution

168

(2)

5.5 Model checking

170

(5)

5.5.1 Checking the PH model

170

(2)

5.5.2 R solution

172

(1)

5.5.3 SAS solution

173

(2)

5.6 Sample size calculation

175

(1)

5.7 Concluding remarks

175

(4)

6 The accelerated failure time model

179

(42)

6.1 Parametric model

180

(15)

6.1.1 Maximum likelihood estimation

181

(6)

6.1.2 R solution

187

(6)

6.1.3 SAS solution

193

(2)

6.2 Penalized Gaussian mixture model

195

(20)

6.2.1 Penalized maximum likelihood estimation

196

(8)

6.2.2 R solution

204

(11)

6.3 SemiNonParametric approach

215

(1)

6.3.1 SAS solution

216

(1)

6.4 Model checking

216

(1)

6.5 Sample size calculation

216

(3)

6.5.1 Computational approach

216

(2)

6.5.2 SAS solution

218

(1)

6.6 Concluding remarks

219

(2)

7 Bivariate survival times

221

(32)

7.1 Nonparametric estimation of the bivariate survival function

222

(7)

7.1.1 The NPMLE of a bivariate survival function

222

(3)

7.1.2 R solution

225

(3)

7.1.3 SAS solution

228

(1)

7.2 Parametric models

229

(3)

7.2.1 Model description and estimation

229

(1)

7.2.2 R solution

230

(1)

7.2.3 SAS solution

231

(1)

7.3 Copula models

232

(8)

7.3.1 Background

232

(4)

7.3.2 Estimation procedures

236

(3)

7.3.3 R solution

239

(1)

7.4 Flexible survival models

240

(3)

7.4.1 The penalized Gaussian mixture model

240

(2)

7.4.2 SAS solution

242

(1)

7.5 Estimation of the association parameter

243

(7)

7.5.1 Measures of association

244

(1)

7.5.2 Estimating measures of association

245

(3)

7.5.3 R solution

248

(2)

7.5.4 SAS solution

250

(1)

7.6 Concluding remarks

250

(3)

8 Additional topics

253

(28)

8.1 Doubly interval-censored data

254

(8)

8.1.1 Background

254

(6)

8.1.2 R solution

260

(2)

8.2 Regression models for clustered data

262

(12)

8.2.1 Frailty models

263

(7)

8.2.1.1 R solution

265

(3)

8.2.1.2 SAS solution

268

(2)

8.2.2 A marginal approach to correlated survival times

270

(4)

8.2.2.1 Independence working model

270

(1)

8.2.2.2 SAS solution

271

(3)

8.3 A biplot for interval-censored data

274

(5)

8.3.1 Classical biplot

274

(1)

8.3.2 Extension to interval-censored observations

275

(3)

8.3.3 R solution

278

(1)

8.4 Concluding remarks

279

(2)

III Bayesian methods for interval-censored data

281

(186)

9 Bayesian concepts

283

(42)

9.1 Bayesian inference

284

(11)

9.1.1 Parametric versus nonparametric Bayesian approaches

285

(1)

9.1.2 Bayesian data augmentation

285

(2)

9.1.3 Markov chain Monte Carlo

287

(2)

9.1.4 Credible regions and contour probabilities

289

(2)

9.1.5 Selecting and checking the model

291

(4)

9.1.6 Sensitivity analysis

295

(1)

9.2 Nonparametric Bayesian. inference

295

(7)

9.2.1 Bayesian nonparametric modelling of the hazard function

297

(2)

9.2.2 Bayesian nonparametric modelling of the distribution function

299

(3)

9.3 Bayesian software

302

(4)

9.3.1 WinBUGS and OpenBUGS

302

(1)

9.3.2 JAGS

303

(3)

9.3.3 R software

306

(1)

9.3.4 SAS procedures

306

(1)

9.3.5 Stan software

306

(1)

9.4 Applications for right-censored data

306

(17)

9.4.1 Parametric models

307

(9)

9.4.1.1 BUGS solution

308

(7)

9.4.1.2 SAS solution

315

(1)

9.4.2 Nonparametric Bayesian estimation of a survival curve

316

(2)

9.4.2.1 R solution

317

(1)

9.4.3 Semiparametric Bayesian survival analysis

318

(7)

9.4.3.1 BUGS solution

321

(2)

9.5 Concluding remarks

323

(2)

10 Bayesian estimation of the survival distribution for interval-censored observations

325

(30)

10.1 Bayesian parametric modelling

325

(10)

10.1.1 JAGS solution

326

(5)

10.1.2 SAS solution

331

(4)

10.2 Bayesian smoothing methods

335

(8)

10.2.1 Classical Gaussian mixture

335

(8)

10.2.1.1 R solution

339

(4)

10.2.2 Penalized Gaussian mixture

343

(1)

10.3 Nonparametric Bayesian estimation

343

(10)

10.3.1 The Dirichlet Process prior approach

343

(4)

10.3.1.1 R solution

345

(2)

10.3.2 The Dirichlet Process Mixture approach

347

(8)

10.3.2.1 R solution

348

(5)

10.4 Concluding remarks

353

(2)

11 The Bayesian proportional hazards model

355

(26)

11.1 Parametric PH model

355

(13)

11.1.1 JAGS solution

356

(9)

11.1.2 SAS solution

365

(3)

11.2 PH model with flexible baseline hazard

368

(12)

11.2.1 Bayesian PH model with a smooth baseline hazard

368

(4)

11.2.1.1 R solution

369

(3)

11.2.2 PH model with piecewise constant baseline hazard

372

(9)

11.2.2.1 R solution

376

(4)

11.3 Semiparametric PH model

380

(1)

11.4 Concluding remarks

380

(1)

12 The Bayesian accelerated failure time model

381

(42)

12.1 Bayesian parametric AFT model

381

(8)

12.1.1 JAGS solution

384

(3)

12.1.2 SAS solution

387

(2)

12.2 AFT model with a classical Gaussian mixture as an error distribution

389

(14)

12.2.1 R solution

395

(8)

12.3 AFT model with a penalized Gaussian mixture as an error distribution

403

(9)

12.3.1 R solution

408

(4)

12.4 Bayesian semiparametric AFT model

412

(9)

12.4.1 R solution

418

(3)

12.5 Concluding remarks

421

(2)

13 Additional topics

423

(44)

13.1 Hierarchical models

424

(16)

13.1.1 Parametric shared frailty models

424

(6)

13.1.1.1 JAGS solution

426

(3)

13.1.1.2 SAS solution

429

(1)

13.1.2 Flexible shared frailty models

430

(10)

13.1.2.1 R solution

436

(4)

13.1.3 Semiparametric shared frailty models

440

(1)

13.2 Multivariate models

440

(17)

13.2.1 Parametric bivariate models

440

(4)

13.2.1.1 JAGS solution

441

(2)

13.2.1.2 SAS solution

443

(1)

13.2.2 Bivariate copula models

444

(1)

13.2.3 Flexible bivariate models

445

(6)

13.2.3.1 R solution

448

(3)

13.2.4 Semiparametric bivariate models

451

(4)

13.2.4.1 R solution

451

(4)

13.2.5 Multivariate case

455

(2)

13.3 Doubly interval censoring

457

(9)

13.3.1 Parametric modelling of univariate DI-censored data

457

(4)

13.3.1.1 JAGS solution

458

(3)

13.3.2 Flexible modelling of univariate DI-censored data

461

(2)

13.3.2.1 R solution

462

(1)

13.3.3 Semiparametric modelling of univariate DI-censored data

463

(2)

13.3.3.1 R solution

465

(1)

13.3.4 Modelling of multivariate DI-censored data

465

(1)

13.4 Concluding remarks

466

(1)

IV Concluding remarks

467

(14)

14 Omitted topics and outlook

469

(12)

14.1 Omitted topics

469

(9)

14.1.1 Competing risks and multistate models

470

(1)

14.1.2 Survival models with a cured subgroup

471

(1)

14.1.3 Multilevel models

472

(1)

14.1.4 Informative censoring

472

(2)

14.1.5 Interval-censored covariates

474

(1)

14.1.6 Joint longitudinal and survival models

475

(2)

14.1.7 Spatial-temporal models

477

(1)

14.1.8 Time points measured with error

477

(1)

14.1.9 Quantile regression

478

(1)

14.2 Outlook

478

(3)

V Appendices

481

(66)

A Data sets

483

(6)

A.1 Homograft study

483

(1)

A.2 AIDS clinical trial

483

(2)

A.3 Survey on mobile phone purchases

485

(1)

A.4 Mastitis study

485

(1)

A.5 Signal Tandmobiel study

486

(3)

B Distributions

489

(12)

B.1 Log-normal LAr(γ, α)

490

(1)

B.2 Log-logistic LG(γ, α)

490

(1)

B.3 Weibull W(γ, α)

491

(1)

B.4 Exponential E(α)

492

(1)

B.5 Rayleigh R(α)

492

(1)

B.6 Gamma(γ, α)

493

(1)

B.7 R solution

493

(3)

B.8 SAS solution

496

(1)

B.9 BUGS solution

496

(1)

B.10 R and BUGS parametrization

497

(4)

C Prior distributions

501

(10)

C.1 Beta prior: Beta(α1, α2)

502

(1)

C.2 Dirichlet prior: Dir(α)

503

(1)

C.3 Gamma prior: G(α, β)

504

(1)

C.4 Inverse gamma prior: IG(α, β)

505

(1)

C.5 Wishart prior: Wishart(R, k)

506

(1)

C.6 Inverse Wishart prior: Wishart(R, k)

507

(1)

C.7 Link between Beta, Dirichlet and Dirichlet Process prior

508

(3)

D Description of selected R packages

511

(14)

D.1 icensBKL package

511

(1)

D.2 Icens package

512

(1)

D.3 interval package

513

(2)

D.4 survival package

515

(1)

D.5 logspline package

516

(1)

D.6 smoothSury package

517

(1)

D.7 mixAK package

518

(1)

D.8 bayesSury package

519

(3)

D.9 DPpackage package

522

(1)

D.10 Other packages

523

(2)

E Description of selected SAS procedures

525

(10)

E.1 PROC LIFEREG

525

(2)

E.2 PROC Reliability

527

(1)

E.3 PROC ICLIFETEST

527

(3)

E.4 PROC ICPHREG

530

(5)

F Technical details

535

(12)

F.1 Iterative Convex Minorant (ICM) algorithm

535

(1)

F.2 Regions of possible support for bivariate interval-censored data

536

(3)

F.2.1 Algorithm of Gentleman and Vandal (2001)

536

(1)

F.2.2 Algorithm of Bogaerts and Lesaffre (2004)

537

(1)

F.2.3 Height map algorithm of Maathuis (2005)

538

(1)

F.3 Splines

539

(8)

F.3.1 Polynomial fitting

540

(1)

F.3.2 Polynomial splines

540

(1)

F.3.3 Natural cubic splines

541

(1)

F.3.4 Truncated power series

541

(1)

F.3.5 B-splines

541

(2)

F.3.6 M-splines and I-splines

543

(1)

F.3.7 Penalized splines (P-splines)

543

(4)

References

547

(21)

Author Index

568

(9)

Subject Index

577

Kris Bogaerts, Arnost Komarek and Emmauel Lesaffre

Survival Analysis with Interval-Censored Data: A Practical Approach with Examples in R, SAS, and BUGS [Kietas viršelis]

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