Statistical models and methods for lifetime data / Jerald F. Lawless.

Format:

Book

Author/Creator:

Lawless, Jerald F., 1944-

Contributor:

Wiley InterScience (Online service)

Frances Houston Medical Book Fund.

Series:

Wiley series in probability and statistics

Language:

English

Subjects (All):

Failure time data analysis.

Survival analysis (Biometry).

Physical Description:

1 online resource (xx, 630 pages) : illustrations.

Edition:

Second edition.

Place of Publication:

Hoboken, N.J. : Wiley-Interscience, [2003]

System Details:

text file

Summary:

methodology

Contents:

1.2 Lifetime Distributions 8

1.2.1 Continuous Models 8

1.2.2 Discrete Models 10

1.2.3 A General Formulation 11

1.2.4 Some Remarks on the Hazard Function 14

1.3 Some Important Models 16

1.3.1 The Exponential Distribution 17

1.3.2 The Weibull Distribution 18

1.3.3 The Log-Normal Distribution 21

1.3.4 The Log-Logistic Distribution 23

1.3.5 The Gamma Distribution 25

1.3.6 Log-Location-Scale Models 26

1.3.7 The Inverse Gaussian Distribution 30

1.3.8 Models with Piecewise Constant or Polynomial Hazard Functions 30

1.3.9 Some Other Models 33

1.3.10 Mixture Models 33

1.4 Regression Models 34

1.5 Multiple Lifetimes and Multiple Modes of Failure 36

1.6 Some Comments on Model Selection and Statistical Analysis 37

2. Observation Schemes, Censoring, and Likelihood 49

2.2 Right Censoring and Maximum Likelihood 52

2.2.1 Some Types of Right Censoring 52

2.2.2 A General Formulation of Right Censoring 58

2.2.3 Likelihood Inference with Censored Data 61

2.3 Other Types of Incomplete Data 63

2.3.1 Intermittent Observation and Interval Censoring 63

2.3.2 Double Censoring 66

2.3.3 Remarks on Missing Data 66

2.4 Truncation and Selection Effects 67

2.4.1 Delayed Entry and Left Truncation 67

2.4.2 Retrospective Observation and Selection Effects 70

2.5 Information and Design Issues 71

3. Some Nonparametric and Graphical Procedures 79

3.2 Nonparametric Estimation of a Survivor Function and Quantiles 80

3.2.1 The Product-Limit Estimate 80

3.2.2 The Nelson-Aalen Estimate 85

3.2.3 Interval Estimation of Survival Probabilities or Quantiles 87

3.2.4 Asymptotic Properties of Estimators 95

3.3 Descriptive and Diagnostic Plots 98

3.3.1 Plots Involving Survivor or Cumulative Hazard Functions 98

3.3.2 Classic Probability Plots 108

3.4 Estimation of Hazard or Density Functions 109

3.5 Methods for Truncated and INterval Censored Data 115

3.5.1 Left-Truncated Data 116

3.5.2 Right-Truncated Data 120

3.5.3 Interval-Censored Data 124

3.6 Life Tables 128

3.6.1 Standard Life Table Methods 128

3.6.2 Theory for Life Table Methodology 132

4. Inference Procedures for Parametric Models 147

4.1 Inference Procedures for Exponential Distributions 147

4.1.1 Methods Based on Large-Sample Theory 148

4.1.2 Exact Methods for Certain Life Tests 152

4.1.3 Comparison of Distributions 154

4.1.4 Planning Experiments or Life Tests 157

4.2 Inference Procedures for Some Other Models 164

4.2.1 The Gamma Distribution 164

4.2.2 The Inverse Gaussian Distribution 170

4.2.3 Models with Polynomial-Based Hazard Functions 172

4.3 Grouped, Interval Censored, or Truncated Data 174

4.3.1 Grouped Lifetimes 174

4.3.2 Interval-Censored Data 176

4.3.3 Truncated Data 177

4.4 Mixture Models 181

4.5 Threshold Parameters 185

4.5.1 General Remarks 186

4.5.2 The Three-Parameter Weibull Distribution 187

4.5.3 The Two-Parameter Exponential Distribution 190

4.6 Prediction Intervals 194

5. Inference Procedures for Log-Location-Scale Distributions 211

5.1 Inference for Location-Scale Distributions 211

5.1.1 Likelihood-Based Methods 212

5.1.2 Exact Procedures Under Type 2 Censoring 217

5.2 Weibull and Extreme-Value Distributions 218

5.2.1 Likelihood-Based Inference Procedures 218

5.2.2 Exact Confidence Intervals Under Type 2 Censoring 223

5.3 Log-Normal and Log-Logistic Distributions 230

5.3.1 Inferences for Log-Normal and Normal Models 230

5.3.2 Inferences for Log-Logistic and Logistic Models 231

5.4 Comparison of Distributions 235

5.4.1 General Methods for Comparing (Log-) Location-Scale Distributions 236

5.4.2 Comparison of Weibull or Extreme Value Distributions 238

5.4.3 Comparison of Log-Normal or Log-Logistic Distributions 242

5.5 Models with Additional Shape Parameters 243

5.5.2 The Generalized Log-Burr Distribution 244

5.5.3 The Generalized Log-Gamma Distribution 247

5.6 Planning Experiments or Life Tests 252

5.6.1 Information Calculations Under Type 1 or Type 2 Censoring 252

5.6.2 Formal Tests and Acceptance Procedures 253

5.6.3 An Example 255

6. Parametric Regression Models 269

6.1.1 Log-Location-Scale (Accelerated Failure Time) Regression Models 270

6.1.2 Proportional Hazards Regression Models 271

6.1.3 Other Regression Models 273

6.2 Graphical Methods and Model Assessment 274

6.2.1 Looking for Models 274

6.2.2 Assessment of Fitted Models 283

6.3 Inference for Log-Location-Scale (Accelerated Failure Time) Models 292

6.3.1 Likelihood Methods 292

6.3.2 Weibull and Extreme Value Regression Models 296

6.3.3 Normal-Log-Normal and Logistic-Log-Logistic Regression Models 303

6.3.4 Some Comments on Least Squares, Robustness, and Efficiency 306

6.3.5 Experimental Design 308

6.4 Extensions of Log-Location-Scale Models 311

6.4.1 Families of Error Distributions 311

6.4.2 Variable Scale Parameters 317

6.4.3 Time-Varying Covariates 320

6.5 Some Other Models 321

6.5.1 Hazard-Based Models 322

6.5.2 Mechanistic Models 325

6.5.3 Transformations and Some Other Models 327

7. Semiparametric Multiplicative Hazards Regression Models 341

7.1 Methods for Continuous Multiplicative Hazards Models 341

7.1.1 Estimation and Tests for [beta] 342

7.1.2 Comparison of Two or More Lifetime Distributions 344

7.1.3 Justification and Properties of the Likelihood Function L([beta]) 348

7.1.4 Adjustments for Tied Lifetimes 351

7.1.5 Estimation of H[subscript 0](t) or S[subscript 0](t) 352

7.1.6 Stratification 354

7.1.7 Left Truncation and Delayed Entry 355

7.1.8 Time-Varying Covariates 355

7.1.9 Model Checking 358

7.3 Methods for Grouped or Discrete Lifetimes 370

7.3.1 Regression Analysis of Grouped Lifetimes 370

7.3.2 Testing the Equality of Distributions with Grouped Data 376

7.3.3 Discrete-Time Hazard-Based Models 382

7.4 Semiparametric Maximum Likelihood 384

7.4.1 Estimation from Continuous Observation 384

7.4.2 Estimation from Incomplete Data 387

8. Rank-Type and Other Semiparametric Procedures for Log-Location-Scale Models 401

8.1 Rank Tests for Comparing Distributions 402

8.1.1 Linear Rank Tests for the m-Sample Problem 402

8.1.2 The Exponential Ordered Scores (Log Rank) Test with Censored Data 409

8.1.3 The Generalized Wilcoxon Test with Censored Data 411

8.1.4 Counting Process Formulation of m-Sample Tests 413

8.1.5 Discussion and Examples 416

8.2 Estimation for Semiparametric AFT Models 420

8.2.1 Rank-Based Procedures with Fixed Covariates 420

8.2.2 Rank-Type Procedures with Time-Varying Covariates 424

9. Multiple Modes of Failure 433

9.1.1 Basic Characteristics and Model Specification 433

9.1.2 Likelihood Function Formulation 435

9.2 Nonparametric Methods 437

9.3 Parametric Methods 444

9.3.1 Grouped or Discrete Data 448

9.4 Semiparametric Methods for Multiplicative Hazards Models 449

9.4.1 Estimation of Cumulative Incidence Functions 452

10. Goodness-of-Fit Tests 465

10.2 Some General Methods of Testing Fit 467

10.2.1 Tests Based on Comparing Empirical and Hypothesized Distributions 467

10.2.2 Model Expansion and Smooth Tests 469

10.2.3 Tests Based on Grouped Data 471

10.3 Tests of Fit for Specific Distributions 476

10.3.1 Tests of Fit for the Exponential Distribution 476

10.3.2 Tests of Fit for the Weibull and Extreme Value Distributions 478

10.3.3 Tests of Fit for the Normal and Log-Normal Distributions 480

10.3.4 Additional Remarks 481

10.4 Tests of Fit with Regression Models 482

10.4.2 Location-Scale Regression Models 483

10.4.3 Multiplicative Hazards Models 484

11. Beyond Univariate Survival Analysis 491

11.2 Multivariate Lifetime Distributions and Clustered Lifetimes 493

11.2.1 Multivariate Lifetime Distributions 494

11.2.2 Maximum Likelihood and Pseudolikelihood Methods 500

11.3 Sequences of Lifetimes 507

11.3.1 Some Models and Methods 507

11.3.2 An Example 509

11.4 General Event History Processes 512

11.5 Failure and Related Processes 518

11.5.1 Some Context and Objectives 518

11.5.2 Some Approaches to Modeling and Analysis 520

B. Asymptotic Variance Formulas, Gamma Functions, and Order Statistics 539

B.1 Asymptotic Variance Formulas 539

B.2 Gamma Functions 541

B.3 Order Statistics 542

C. Large-Sample Theory for Likelihood and Estimating Function Methods 545

C.1 Maximum Likelihood Large-Sample Theory 545

C.1.1 Asymptotic Results and Large-Sample Methods 545

C.1.2 Marginal, Conditional, and Partial Likelihoods 551

C.2 Estimating Function Asymptotics 552

D. Computational Methods and Simulation 555

D.1 Optimization Methods for Maximum Likelihood 555

D.2 Simulation and Bootstrap Methods 557

D.2.1 Parametric Bootstrap 558

D.2.2 Nonparametric Bootstrap 559

D.2.3 Additional Remarks 560

E. Inference in Location-Scale Parameter Models 561

E.1 Equivariant Statistics 561

E.2 Pivotals and Ancillaries 562

E.3 Confidence Intervals 564

E.4 Regression Models 565

F. Martingales and Counting Processes 567

F.1 Martingales 567

F.2 Counting Processes and Survival Models 568

G. Data Sets 571

G.1 Transfusion-Related AIDS Data 571

G.2 Times to First Pulmonary Exacerbation 571

G.3 Breaking Strengths of Carbon Fibers 573

G.4 Lifetimes of Steel Specimens 573

G.5 VA Lung Cancer Survival Data 574

G.6 Survival Times for Persons with Lupus Nephritis 574

G.7 Primary Biliary Cirrhosis (PBC) Data 575

G.8 Diabetic Retinopathy Study Data 575

G.9 Stanford Heart Transplant Data 575

G.10 Colon Cancer Recurrence and Survival Data 575.

Notes:

Description based on print version record.

Includes bibliographical references (pages 577-610) and indexes.

Electronic reproduction. Hoboken, N.J. Available via World Wide Web.

Local Notes:

Acquired for the Penn Libraries with assistance from the Frances Houston Medical Book Fund.

Other Format:

Print version: Statistical models and methods for lifetime data.

ISBN:

1118031253

9781118031254

Publisher Number:

99950203227

Access Restriction:

Restricted for use by site license.