Contents

Chemo Secrets From a Breast Cancer Survivor

Breast Cancer Survivors

Get Instant Access

Forward and Backward Recurrence Times and Length Biased Sampling: Age Specific Models

Marvin Zelen 1

1 Introduction 1

2 Motivating Problems and Preliminary Results 2

2.1 Chronic Disease Modeling 2

2.2 Early Detection Modeling 3

2.3 Preliminary Results 3

3 Development of the Chronic Disease Model 4

3.1 Forward Recurrence Time Distribution 5

3.2 Backward Recurrence Time Distribution 6

3.3 Length Biased Sampling and the Survival of Prevalent Cases 6

3.4 Chronological Time Modeling 8

4 Early Detection Disease Model 9

5 Discussion 10

References 11

Difference between Male and Female Cancer Incidence Rates: How Can It Be Explained?

Konstantin G. Arbeev, Svetlana V. Ukraintseva, Lyubov S. Arbeeva,

Anatoli I. Yashin 12

1 Introduction 12

2 Data 14

3 Three Components of the Individual Aging Process 15

4 The Incorporated Ontogenetic Model of Cancer 16

5 Application of the Ontogenetic Model to Data on Cancer Incidence Rate by Sex 17

6 Conclusion 20

References 21

Non-parametric estimation in degradation-renewal-failure models

V. Bagdonavicius, A. Bikelis, V. Kazakevicius, M. Nikulin 23

1 Introduction 23

2 Model 24

3 Decomposition of a counting process associated with Z(T) 25

4 Estimation 27

4.1 The data 27

4.2 Estimation of A 28

4.3 Large sample properties of A 30

4.4 Estimation of the probability pj(z) 35

References 36

The Impact of Dementia and Sex on the Disablement in the Elderly

P.Barberger-Gateau, V.Bagdonavicius, M.Nikulin, O.Zdorova-

Cheminade, 37

1 Introduction 37

1.1 Data 38

2 Degradation model 40

3 Estimation of the mean degradation 41

4 Application to the PAQUID data 43

4.1 The estimated mean of the disablement process in men and women 43

4.2 The estimated mean of the disablement process in demented and non-demented subjects 43

4.3 The estimated mean of the disablement process in demented and non-demented men 44

4.4 The estimated mean of the disablement process in demented and non-demented women 45

4.5 The estimated mean of the disablement process in demented men and women 46

4.6 The estimated mean of the disablement process in non-demented men and women 47

4.7 The estimated mean of the disablement process in high and low educated subjects 48

5 Joint model for degradation-failure time data 49

References 50

Nonparametric Estimation for Failure Rate Functions of Discrete Time semi-Markov Processes

Vlad Barbu, Nikolaos Limnios 53

1 Introduction 53

2 Preliminaries 54

2.1 The Discrete Time semi-Markov Model 54

2.2 Basic Results on semi-Markov Chains Estimation 58

3 Failure Rates Estimation 59

Asymptotic Confidence Intervals for Failure Rates 63

4 Proofs 63

5 Numerical Example 68

References 70

Some recent results on joint degradation and failure time modeling

Vincent Couallier 73

1 Introduction 73

2 Joint models for degradation and failure time modeling 74

2.1 Failure time as hitting times of stochastic processes 75

stochastic degradation defined as diffusion 75

A gamma process as degradation process 75

A marked point process as degradation 76

A mixed regression as degradation process : the general path model 77

2.2 Failure times with degradation-dependent hazard rate. ... 78

2.3 The joint model : a mixed regression model with traumatic censoring 79

3 Some recent results in semiparametric estimation in the general path model 80

3.1 Linear estimation 80

3.2 Nonlinear estimation 82

3.3 Estimation of the reliability functions 84

References 87

Estimation in a Markov chain regression model with missing covariates

Dorota M. Dabrowska, Robert M. Elashoff, Donald L. Morton 90

1 Introduction 90

2 The model and estimation 92

2.2 Example 96

2.3 Estimation 99

2.4 Random censoring 104

3 A data example 107

References 117

Tests of Fit based on Products of Spacings

Paul Deheuvels, Gérard Derzko 119

1 Introduction and Main Results 119

1.1 Introduction 119

1.2 Some Relations with the Kullback-Leibler Information . . . 121

2 Proofs 124

2.1 A useful Theorem 124

2.2 Appendix 133

References 135

A Survival Model With Change-Point in Both Hazard and Regression Parameters

Dupuy Jean-François 136

1 Introduction 136

2 Notations and construction of the estimators 137

2.1 Preliminaries 137

2.2 The estimators 138

3 Convergence of the estimators 139

References 143

Mortality in Varying Environment

M.S. Finkelstein 145

1 Introduction 145

2 Damage accumulation and plasticity 146

2.1 Proportional hazards 146

2.2 Accelerated life model 148

2.3 Other models 151

2.4 Damage accumulation and plasticity. Period Setting 154

3 Concluding remarks 157

References 157

Goodness of Fit of a joint model for event time and nonignorable missing Longitudinal Quality of Life data

Sneh Gulati, Mounir Mesbah 159

1 Introduction and Preliminaries 159

2 The Dropout Process 161

3 The Model of Dupuy and Mesbah (2002) 162

4 The Test of Goodness of Fit 164

5 Conclusion 166

6 References 166

Three approaches for estimating prevalence of cancer with reversibility. Application to colorectal cancer

1 Introduction 169

2 Definitions 170

3 Three approaches for estimating prevalences 171

3.1 Transition Rate Method 171

Method 171

Model specifications 174

Mortality rates 174

Incidence rates 174

Transition rates from the disease 174

Age-specific non recovery prevalence estimates 175

3.2 A parametric model [CD97] 175

Method 176

Model specifications 177

3.3 Counting Method estimates 177

4 Results 178

5 Discussion 180

References 184

On statistics of inverse gamma process as a model of wear

B.P. Harlamov 187

1 Introduction 187

2 Inverse process with independent positive increments 188

Initial definitions 188

Moments of the first exit time distributions 189

Inverse gamma process 190

One-dimensional distribution 191

Example 1 193

Example 2 193

Multi-dimensional distribution 196

3 Estimation of parameters 197

The direct way of data gathering 197

Approximate maximum likelihood estimates 198

Inverse way of data gathering 199

Inverse way of data gathering when dealing with a continuous wear curve 199

Soft ware 201

References 201

Operating Characteristics of Partial Least Squares in Right-Censored Data Analysis and Its Application in Predicting the Change of HIV-I RNA

Jie Huang, David Harrington 202

1 Introduction 203

2 Analysis Methods 204

3 Simulation studies 209

4 A Description of the Data 213

5 The Data Analysis 215

6 Summary and Discussion 224

References 227

Inference for a general semi-Markov model and a sub-model for independent competing risks

Catherine Huber-Carol, Odile Pons, Natacha Heutte 231

1 Introduction 231

2 Framework 232

3 Independent Competing Risks Model 234

4 General Model 235

5 Case of a bounded number of transitions 238

6 A Test of the Hypothesis of Independent Competing Risks 239

7 Proofs 241

References 244

Estimation Of Density For Arbitrarily Censored And Truncated Data

Catherine Huber, Valentin Solev, Filia Vonta 246

1 Introduction 246

2 Partitioning the total observation time 247

2.1 Random covering 247

2.2 Short-cut covering 248

2.3 The mechanism of truncation and censoring 249

3 The distribution associated with random covering 250

4 The distribution of random vector (L(x), R(x), L(z), R(z)) 253

5 The distribution of random vector (L(X), R(X),L(Z), R(Z)) 255

6 Maximum likelihood estimators 256

6.1 The bracketing Hellinger e—entropy 257

6.2 Hellinger and Kullback-Leibler distances 259

6.3 Estimation in the presence of a nuisance parameter 262

References 265

Statistical Analysis of Some Parametric Degradation Models

Waltraud Kahle, Heide Wendt 266

1 Introduction 266

2 A Degradation Model 267

2.1 The distribution of (Tn) 268

2.2 Marking the sequence (Tn) 270

3 Maximum Likelihood Estimates 271

4 Moment Estimates 274

5 Comparison of Maximum Likelihood and Moment Estimates 276

6 Conclusion 277

References 278

Use of statistical modelling methods in clinical practice Klyuzhev V.M., Ardashev V.N., Mamchich N.G., Barsov M.I,Glukhova S.I. 280

1 Introduction 280

2 Methods of statistical modelling 280

3 Results 281

References 284

Degradation-Threshold-Shock Models

Axel Lehmann 286

1 Introduction 286

2 Degradation-Threshold-Shock-Models 288

2.1 Degradation-Threshold-Models 292

2.2 Degradation-Shock-Models 293

3 Maximum Likelihood Estimation 294

4 Concluding remarks 296

References 297

Comparisons of Test Statistics Arising from Marginal Analyses of Multivariate Survival Data

Qian H. Li, Stephen W. Lagakos 299

1 Introduction 299

2 The WLW Method and Definitions of Test Statistics 301

3 Asymptotic Properties of the Test Statistics under Contiguous Alternatives 303

4 Comparisons of Test Statistics 304

4.1 Equal 304

4.3 Special Correlation Structures 306

5 Determining Sample Size and K 307

6 Example: Recurring Opportunistic Infections in HIV/AIDS 310

7 Discussion 311

References 314

Nonparametric Estimation and Testing in Survival Models

Henning Läuter, Hannelore Liero 319

1 Stating the Problem 319

2 Nonparametric Estimators 322

2.1 Model with censoring 322

2.2 The Nelson-Aalen estimator for the cumulative hazard function 323

2.3 A kernel estimator for the hazard function 324

3 Testing the Hazard Rate 325

3.1 An asymptotic a-test 326

3.2 Application to the example 327

Conclusions 327

4 Some further remarks 328

5 About the Extension to the Model with Covariates 329

References 331

Selecting a semi-parametric estimator by the expected log-likelihood

Benoit Liquet, Daniel Commenges 332

1 Introduction 332

2 The expected log-likelihood as theoretical criterion 334

2.1 Definitions and notations 334

2.2 The expected log-likelihood 334

2.3 Case of right-censored data 335

2.4 Case of explanatory variable 336

3 Estimation of ELL 336

3.1 Likelihood cross-validation : LCV 336

3.2 Direct bootstrap method for estimating ELL (ELL6OQi and ELLi6ooi) 337

3.3 Bias corrected bootstrap estimators 338

4 Simulation 338

4.1 Kernel estimator 339

4.2 Penalized likelihood estimator 342

5 Choosing between stratified and unstratified survival models 343

5.1 Method 343

5.2 Example 345

6 Conclusion 346

References 347

Imputing responses that are not missing

Ursula U. Müller, Anton Schick, Wolfgang Wefelmeyer 350

1 Introduction 350

2 Efficient influence functions 352

3 Efficient estimators 357

Achnowledgment 362

References 362

Bivariate Decision Processes

Martin Newby 364

1 Introduction 364

2 The Structure of the Model 366

3 Inspection Policies 366

4 The Inspection Cycle 367

4.1 System Renewal 367

4.2 Arbitrary Restoration 368

5 Optimal Policies 368

5.1 Average Cost Criterion 369

5.2 Total Cost Criterion 369

5.3 Obtaining Solutions 370

6 Levy Processes as Degradation Models 370

7 Examples 371

7.1 Maximum Process 371

7.2 The Integrated Process 372

7.3 The Absolute Value 372

7.4 Bessel Processes 373

7.5 Models for Imperfect Inspection 374

8 Summary 375

References 375

Weighted Logrank Tests With Multiple Events

1 Introduction and notations 378

2 Asymptotic distribution of (LRi,LR^)' under Hq in a copula model 380

2.1 Preliminary results for the martingales under Hq 381

2.2 Asymptotic distribution of (LRi, LR2)' under Hq 384

2.3 What if the joint censoring distributions or the joint survival functions differ in groups A and B under Hq ?... 386

3 Simulations study 388

4 Application 389

5 Discussion 390

References 391

Explained Variation and Predictive Accuracy in General Parametric Statistical Models: The Role of Model Misspecification

Susanne Rosth0j, Niels Keiding 392

1 Introduction 392

2 Measures of explained variation 393

2.1 Definition of the explained variation 394

2.2 Estimation of the explained variation 395

3 Misspecification and definition of the predictive accuracy 397

4 The failure time model 399

5 Which estimation method to choose - model based or not? 401

6 Acknowledgement 402

7 Appendix 402

References 403

Optimization of Breast Cancer Screening Modalities

Yu Shen, Giovanni Parmigiani 405

1 Introduction 405

2 Model 407

2.1 Natural History of Breast Cancer 407

2.2 Survival Distributions and Mortality 410

2.3 Sensitivities of Mammography and Clinical Breast Examinations 411

2.4 Costs of Screening Programs 412

3 Optimization of Screening Strategies and Sensitivity Analyses 413

4 Discussion 415

References 416

Sequential Analysis of Quality of Life Rasch Measurements

Veronique Sebille, Mounir Mesbah 421

1 Introduction 421

2 Methods 423

2.1 IRT models 423

2.2 The Rasch Model 424

2.3 Estimation of the parameters 424

2.4 Sequential Analysis 425

Traditional Sequential Analysis 425

Sequential Analysis based on Rasch measurements 426

Estimation of parameters 427

Z and V statistics 427

2.5 The Sequential Probability Ratio Test and the Triangular Test 428

2.6 Study framework 428

3 Results 430

4 Discussion 434

5 Conclusion 435

6 References 436

7 Appendix 1 438

7.2 2. Efficient score: Z(X) statistic under H0(m = Mo = 0) ... 438

7.3 3. Fisher's information: V(X) statistic under

8 Appendix 2 439

8.1 Stopping boundaries for the one-sided SPRT and TT 439

Three Types of Hazard Functions Curves Described

Sidorovich G.I., Shamansky S.V., Pop V.P., Rukavicin O.A 440

1 Patients and method 440

2 Results 441

References 445

On the Analysis of Fuzzy Life Times and Quality of Life Data

Reinhard Viertl 446

1 Introduction 446

2 Fuzzy data 447

3 Empirical reliability functions for fuzzy life times 448

4 Generalized classical statistical inference for fuzzy data 449

5 Generalized Bayesian inference in case of fuzzy information 450

6 Conclusion 451

References 451

Statistical Inference for Two-Sample and Regression Models with Heterogeneity Effect: A Collected-Sample Perspective

Hong-Dar Isaac Wu 452

1 Introduction 452

2 Two-Sample Models 453

2.1 Two-sample location-scale model 454

2.2 Two-sample transformation model 455

3 Hazards Regression 456

4 Non-proportional Hazards Model 460

5 Extensions and Brief Discussion 462

References 463

Failure Distributions Associated With General Compound Renewal Damage Processes

S. Zacks 466

1 Introduction 466

2 The General Compound Renewal Damage Process, and The Associated Failure Distribution 467

3 Compound Poisson With Exponential Damage 469

4 Compound Poisson With Erlang Damage 473

References 474

Index 477

Was this article helpful?

0 0

Post a comment