Statistical Models and Methods for Biomedical and Technical Systems

✍ Scribed by Filia Vonta, M.S. Nikulin, Nikolaos Limnios, Catherine Huber-Carol

• Publisher: Birkhäuser Boston
• Year: 2008
• Tongue: English
• Leaves: 561
• Series: Statistics for Industry and Technology
• Edition: 1
• Category: Library

✦ Synopsis

This book deals with the mathematical aspects of survival analysis and reliability as well as other topics, reflecting recent developments in the following areas: applications in epidemiology; probabilistic and statistical models and methods in reliability; models and methods in survival analysis, longevity, aging, and degradation; accelerated life models; quality of life; new statistical challenges in genomics.

The work will be useful to a broad interdisciplinary readership of researchers and practitioners in applied probability and statistics, industrial statistics, biomedicine, biostatistics, and engineering.

✦ Table of Contents

Contents......Page 6
Preface......Page 19
Contributors......Page 21
List of Tables......Page 28
List of Figures......Page 31
PART I: COX MODELS, ANALYSES, AND EXTENSIONS......Page 35
1.1 Cox Model and Extensions......Page 36
1.2 General Censoring and Truncations......Page 39
1.3 Discrete Time: Logistic Regression Models for the Retro-Hazard......Page 41
1.4 Accelerated Failure Time Models (AFT)......Page 42
1.5 Correlated Survivals......Page 48
References......Page 51
2. Corrected Score Estimation in the Cox Regression Model with Misclassified Discrete Covariates......Page 55
2.1 Introduction......Page 56
2.2 Review of the Corrected Score Technique......Page 57
2.3 Application to the Cox Survival Model......Page 58
2.4 Example......Page 61
References......Page 63
3.1 Introduction......Page 65
3.2 Illustration of the Piecewise-Constant Model......Page 67
3.3 Estimation Under the Piecewise-Constant Setting......Page 68
3.4 The Tests......Page 69
3.5 Data Analysis......Page 71
3.6 Discussion......Page 73
References......Page 74
4.1 Introduction......Page 75
4.2 Closure Properties of the Individual Frailty Distribution......Page 76
4.3 Diagnostic Plots......Page 79
4.4 Application......Page 80
4.5 Shared Frailty......Page 81
References......Page 85
5.1 Introduction......Page 86
5.2 Definition of the Models......Page 87
5.3 Some Usual Bivariate Models......Page 90
5.4 NPML Estimation......Page 93
References......Page 95
PART II: RELIABLITY THEORY—DEGRATION MODELS......Page 97
6.1 Introduction......Page 98
6.2 The Black Box Virtual Age......Page 100
6.3 Information-Based Virtual Age......Page 102
6.4 Virtual Age in a Series System......Page 106
References......Page 109
7.1 Introduction......Page 111
7.2 The Degradation Failure—Estimation of F[sub(A)] and F[sub(T0)]......Page 112
7.3 A Joint Model with Both Degradation and Traumatic Failure Times......Page 115
7.4 A Joint Model with Two Failure Modes......Page 118
7.5 Conclusion......Page 119
References......Page 120
8.1 Introduction and Motivation......Page 122
8.2 Generalized B&D Process. Preliminary......Page 123
8.3 Steady-State Distribution......Page 125
8.4 Conditional Distribution Given Lifetime......Page 126
8.5 An Example......Page 130
References......Page 133
9.1 Introduction......Page 135
9.2 The Model......Page 136
9.3 Expected Total Cost......Page 142
9.4 Numerical Results and Comments......Page 146
9.5 Conclusion......Page 149
Appendix......Page 150
References......Page 151
10.1 Introduction......Page 152
10.2 Kijima-Type Repairs......Page 153
10.3 Parameter Estimation......Page 154
10.4 Optimal Maintenance as Time Scale Transformation......Page 156
References......Page 160
11.1 Introduction......Page 161
11.2 Connections Between NHPP and GOS Models......Page 164
11.3 Some Aspects of Inference......Page 166
11.4 Simulation Results......Page 167
11.5 Discussion......Page 173
References......Page 174
12.1 Introduction......Page 177
12.2 Model Description......Page 178
12.3 Numerical Example......Page 181
12.4 Conclusions......Page 190
References......Page 191
PART III: INFERENTAL ANALYSIS......Page 193
13.1 Introduction and Results......Page 194
13.2 An Example of Application......Page 200
13.3 Proofs......Page 205
References......Page 208
14.1 Introduction......Page 210
14.2 Transportation Metric......Page 211
14.3 Entropy, Duality of Metric Entropy......Page 212
14.4 Expectation of κ ......Page 214
14.5 Minimum Distance Estimator......Page 216
14.6 Empirical Process, Concentration Inequality......Page 218
14.7 The Main Result......Page 219
References......Page 221
15.1 Introduction and Notation......Page 222
15.2 Definitions and Characteristics of Nested Plans......Page 223
15.3 Multivariate Normal Distributions and Optimal Nested Plans......Page 224
15.4 Nested Plans for One-Parameter Exponential Distributions......Page 227
15.5 Numerical Examples and Comparisons......Page 229
References......Page 234
16.1 Introduction......Page 235
16.2 Sampling in the Lexis Diagram......Page 237
16.3 Inference for the Distribution of the r.v. X......Page 240
16.4 Inference for the Weight Function ω......Page 241
16.5 Simulation Study......Page 242
References......Page 245
17.1 Introduction......Page 247
17.2 The Parametric ALT Model......Page 248
17.3 The ALT Model with Nonparametric Baseline Distribution......Page 251
17.4 The ALT Model with Parametric Baseline Distribution and Nonparametric Acceleration Function......Page 253
17.5 The Nonparametric ALT Model......Page 258
References......Page 260
18.1 Introduction......Page 262
18.2 A Contemporary Status of the Theory of Modified Chi-Squared Tests......Page 265
18.3 Some Recent Results......Page 269
18.4 Conclusion......Page 273
Appendix......Page 274
References......Page 276
19.1 Introduction......Page 280
19.3 Test for the Type I Pareto Distribution......Page 283
19.4 Power Study......Page 285
19.5 Type II Pareto Distribution......Page 286
19.6 Null Distribution of the Proposed Procedure and Power Study......Page 289
19.7 Power of the Proposed Procedure......Page 290
19.8 Examples......Page 292
References......Page 293
20.1 Introduction......Page 296
20.2 Definition and Solution of Inverse Problem......Page 298
20.3 Estimation on Incomplete Follow-Up......Page 301
20.4 Estimation of HIV Infection Rate on the Dynamics of AIDS Cases......Page 303
20.5 Estimation of Survival in the Wild......Page 306
References......Page 309
PART IV: ANALYSIS OF CENSORED DATA......Page 313
21.1 Introduction......Page 314
21.2 Johnson's Bayesian Chi-Squared Statistic......Page 315
21.3 Sampling-Based Chi-Squared Test for Interval-Censored Data......Page 317
21.4 Simulation Study......Page 322
21.5 Discussion......Page 323
References......Page 324
22. Semiparametric Regression Models for Interval-Censored Survival Data, With and Without Frailty Effects......Page 326
22.1 Introduction......Page 327
22.3 Nonparametric Models......Page 328
22.4 Proportional Hazards Models......Page 330
22.5 Conditional Proportional Hazards (Frailty Model)......Page 331
22.6 Extensions......Page 332
References......Page 335
23.1 Introduction......Page 337
23.2 Results for Type-I Progressive Hybrid Censoring......Page 338
23.3 Results for Type-II Progressive Hybrid Censoring......Page 344
23.4 Examples......Page 346
References......Page 348
PART V: QUALITY OF LIFE......Page 349
24. Sequential Analysis of Quality-of-Life Measurements Using Mixed Rasch Models......Page 350
24.1 Introduction......Page 351
24.2 IRT Models......Page 352
24.3 Sequential Analysis......Page 353
24.4 Simulations......Page 356
24.5 Discussion—Conclusion......Page 359
References......Page 362
25.1 Introduction......Page 365
25.2 Material and Methods......Page 366
25.3 Results......Page 370
25.4 Discussion......Page 376
Appendix......Page 377
References......Page 383
26.1 Introduction and Overview......Page 384
26.2 The Three-Party Architecture......Page 387
26.3 The Rasch Model for P[sub(s)] Input to QoL......Page 389
26.4 The Case of Multiple Dimensions: Fusing Information......Page 391
26.5 Defining the Quality of Life......Page 393
26.6 Summary and Conclusions......Page 394
References......Page 395
PART VI: INFERENCE FOR PROCESSES......Page 397
27.1 Introduction......Page 398
27.2 Diffusion Process with Small Noise......Page 401
27.3 Ergodic Diffusion Processes......Page 403
27.4 Poisson and Self-Exciting Processes......Page 408
27.5 Simulation......Page 413
References......Page 415
28.1 Introduction......Page 417
28.2 The Semi-Markov Setting......Page 418
28.3 Integral Functionals......Page 421
28.4 Nonparametric Estimation of Moments......Page 422
28.5 Confidence Intervals for the Moments......Page 426
28.6 Numerical Application......Page 427
References......Page 428
29.1 Introduction......Page 431
29.2 Nonparametric Estimators......Page 432
29.3 Linear Autoregression......Page 437
References......Page 444
30.1 Introduction......Page 446
30.2 Base Model......Page 447
30.3 On a Class of Processes with the Complete Sufficient Statistics for the Plans of A-Type......Page 448
30.4 On Complete Sufficient Statistics for a Class of Labeled Processes with the Plans of B-Type......Page 450
30.5 On Procedures of Data Variant Generation......Page 451
30.6 Numerical Examples......Page 452
References......Page 455
PART VII: DESIGNS......Page 456
31.1 Introduction......Page 457
31.2 Decision-Theoretic Formulation......Page 460
31.3 Two-Look Optimal Decision Rules......Page 464
31.4 Modified Trial Designs with Accrual-Stopping......Page 465
References......Page 468
32.1 Introduction......Page 470
32.2 Sequence Enumeration and the Model......Page 471
32.3 Optimal Designs for Two Periods......Page 474
References......Page 478
PART VIII: MEASURES OF DIVERGENCE, MODEL SELECTION, AND SURVIVAL MODELS......Page 480
33. Discrepancy-Based Model Selection Criteria Using Cross-Validation......Page 481
33.1 Introduction......Page 482
33.2 Framework for Discrepancy-Based Selection Criteria......Page 483
33.3 The Bias-Adjustment Approach to Developing a Criterion......Page 484
33.4 The Cross-Validatory Approach to Developing a Criterion......Page 485
33.5 Examples in the Linear Regression Setting......Page 486
33.6 Linear Regression Simulations......Page 488
Appendix......Page 491
References......Page 493
34.1 Introduction: Which Covariates to Include?......Page 495
34.2 Estimators in Submodels......Page 497
34.3 Bias, Variance, and Mean Squared Error Calculations......Page 499
34.4 Estimating the Risks......Page 502
34.5 The FIC and the Weighted FIC......Page 503
34.6 Exact Risk Calculations......Page 505
34.7 Concluding Remarks......Page 508
References......Page 509
35.1 Introduction......Page 511
35.2 Classes of Measures......Page 512
35.3 Properties of Information Measures......Page 516
35.4 Information Under Censoring and Truncation......Page 518
35.5 Model Selection Criteria......Page 521
35.6 Discussion......Page 523
References......Page 524
36.1 Introduction......Page 527
36.2 The Model......Page 528
36.3 Entropy and Divergence in the Location Model......Page 530
36.4 Sampling Properties......Page 534
References......Page 540
PART IX: NEW STATISCAL CHALLAENGES......Page 543
37.1 Introduction......Page 544
37.2 Biometry to Clinical Trial Methodology......Page 545
37.3 Interim Analysis and Statistical Tests......Page 547
37.4 Genomics Impact......Page 552
References......Page 556
H......Page 559
S......Page 560
W......Page 561