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Statistical Models and Methods for Reliability and Survival Analysis

1. Aufl.

von: Vincent Couallier, Léo Gerville-Réache, Catherine Huber-Carol, Nikolaos Limnios, Mounir Mesbah
164,99 €
Verlag:	Wiley
Format:	EPUB
Veröffentl.:	11.12.2013
ISBN/EAN:	9781118826997
Sprache:	englisch
Anzahl Seiten:	432

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Titelbeschreibung

Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical Models and Methods in Survival Analysis, and Reliability and Maintenance. The book is intended for researchers interested in statistical methodology and models useful in survival analysis, system reliability and statistical testing for censored and non-censored data.

Inhaltsverzeichnis

Preface xv Biography of Mikhail Stepanovitch Nikouline xvii Vincent COUALLIER, Léo GERVILLE-RÉACHE, Catherine HUBER-CAROL, Nikolaos LIMNIOS and Mounir MESBAH Part 1. Statistical Models and Methods 1 Chapter 1. Unidimensionality, Agreement and Concordance Probability 3 Zhezhen JIN and Mounir MESBAH 1.1. Introduction 3 1.2. From reliability to unidimensionality: CAC and curve 4 1.2.1. Classical unidimensional models for measurement 4 1.2.2. Reliability of an instrument: CAC 6 1.2.3. Unidimensionality of an instrument: BRC 9 1.3. Agreement between binary outcomes: the kappa coefficient 10 1.3.1. The kappa model 10 1.3.2. The kappa coefficient 10 1.3.3. Estimation of the kappa coefficient 10 1.4. Concordance probability 11 1.4.1. Relationship with Kendall’s τ measure 12 1.4.2. Relationship with Somer’s D measure 12 1.4.3. Relationship with ROC curve 13 1.5. Estimation and inference 14 1.6. Measure of agreement 14 1.7. Extension to survival data 15 1.7.1. Harrell’s c-index 15 1.7.2. Measure of discriminatory power 16 1.8. Discussion 17 1.9. Bibliography 18 Chapter 2. A Universal Goodness-of-Fit Test Based on Regression Techniques 21 Florence GEORGE and Sneh GULATI 2.1. Introduction 21 2.2. The Brain and Shapiro procedure for the exponential distribution 22 2.3. Applications of the Brain and Shapiro test 24 2.4. Small sample null distribution of the test statistic for specific distributions 25 2.5. Power studies 28 2.6. Some real examples 28 2.7. Conclusions 31 2.8. Acknowledgment 32 2.9. Bibliography 32 Chapter 3. Entropy-type Goodness-of-Fit Tests for Heavy-Tailed Distributions 33 Andreas MAKRIDES, Alex KARAGRIGORIOU and Filia VONTA 3.1. Introduction 33 3.2. The entropy test for heavy-tailed distributions 35 3.2.1. Development and asymptotic theory 35 3.2.2. Discussion 39 3.3. Simulation study 40 3.4. Conclusions 42 3.5. Bibliography 42 Chapter 4. Penalized Likelihood Methodology and Frailty Models 45 Emmanouil ANDROULAKIS, Christos KOUKOUVINOS and Filia VONTA 4.1. Introduction 45 4.2. Penalized likelihood in frailty models for clustered data 48 4.2.1. Gamma distributed frailty 52 4.2.2. Inverse Gaussian distributed frailty 52 4.2.3. Uniform distributed frailty 54 4.3. Simulation results 55 4.4. Concluding remarks 57 4.5. Bibliography 57 Chapter 5. Interactive Investigation of Statistical Regularities in Testing Composite Hypotheses of Goodness of Fit 61 Boris LEMESHKO, Stanislav LEMESHKO and Andrey ROGOZHNIKOV 5.1. Introduction 61 5.2. Distributions of the test statistics in the case of testing composite hypotheses 63 5.3. Testing composite hypotheses in “real-time” 68 5.4. Conclusions 73 5.5. Acknowledgment 73 5.6. Bibliography 73 Chapter 6. Modeling of Categorical Data 77 Henning LÄUTER 6.1. Introduction 77 6.2. Continuous conditional distributions 78 6.2.1. Conditional normal distribution 78 6.2.1.1. Estimation of parameters 78 6.2.2. More general continuous conditional distributions 81 6.2.2.1. Conditional distribution 82 6.2.2.2. Normal copula 83 6.3. Discrete conditional distributions 84 6.3.1. Parametric conditional distributions 84 6.3.2. Estimation of parameters 86 6.4. Goodness of fit 86 6.4.1. Distribution of ˆX2 87 6.5. Modeling of categorical data 88 6.5.1. Contingency tables 89 6.5.1.1. General tables 89 6.5.1.2. Further examples 93 6.6. Bibliography 93 Chapter 7. Within the Sample Comparison of Prediction Performance of Models and Submodels: Application to Alzheimer’s Disease 95 Catherine HUBER-CAROL, Shulamith T. GROSS and Annick ALPÉROVITCH 7.1. Introduction 95 7.2. Framework 96 7.2.1. General description of the data set and the models to be compared 96 7.2.2. Definition of the performance prediction criteria: IDI and BRI 96 7.3. Estimation of IDI and BRI 97 7.3.1. General estimating equations for IDI and BRI 98 7.3.2. Estimation of IDI and BRI in the logistic case 98 7.3.2.1. Asymptotics of IDI2/1 for logistic predictors 99 7.3.2.2. Asymptotics of BRI2/1 for logistic predictors 100 7.4. Simulation studies 102 7.4.1. First simulation 102 7.4.2. Second simulation: Gu and Pepe’s example 104 7.5. The three city study of Alzheimer’s disease 106 7.6. Conclusion 108 7.7. Bibliography 109 Chapter 8. Durbin–Knott Components and Transformations of the Cramér-von Mises Test 111 Gennady MARTYNOV 8.1. Introduction 111 8.2. Weighted Cramér-von Mises statistic 111 8.3. Examples of the Cramér-von Mises statistics 113 8.3.1. Classical Cramér-von Mises statistic 113 8.3.2. Anderson–Darling statistic 113 8.3.3. Cramér-von Mises statistic with the power weight function 114 8.4. Weighted parametric Cramér-von Mises statistic 114 8.4.1. Covariance functions of weighted parametric empirical process 114 8.4.2. Eigenvalues and eigenfunctions for weighted parametric Cramérvon Mises statistic 116 8.5. Transformations of the Cramér-von Mises statistic 117 8.5.1. Preliminary notes 117 8.5.2. Replacement of eigenvalues 118 8.5.3. Transformed statistics 119 8.6. Bibliography 122 Chapter 9. Conditional Inference in Parametric Models 125 Michel BRONIATOWSKI and Virgile CARON 9.1. Introduction and context 125 9.2. The approximate conditional density of the sample 127 9.2.1. Approximation of conditional densities 127 9.2.2. The proxy of the conditional density of the sample 129 9.2.3. Comments on implementation 131 9.3. Sufficient statistics and approximated conditional density 131 9.3.1. Keeping sufficiency under the proxy density 131 9.3.2. Rao–Blackwellization 132 9.4. Exponential models with nuisance parameters 135 9.4.1. Conditional inference in exponential families 135 9.4.2. Application of conditional sampling to MC tests 137 9.4.2.1. Context 137 9.4.2.2. Bimodal likelihood: testing the mean of a normal distribution in dimension 2 139 9.4.3. Estimation through conditional likelihood 140 9.5. Bibliography 142 Chapter 10. On Testing Stochastic Dominance by Exceedance, Precedence and Other Distribution-Free Tests, with Applications 145 Paul DEHEUVELS 10.1. Introduction 145 10.2. Results 148 10.2.1. The experimental data set 148 10.2.2. An application of the Wilcoxon–Mann–Whitney statistics 149 10.2.3. One-sided Kolmogorov-Smirnov tests 150 10.2.4. Precedence and Exceedance Tests. 152 10.3. Negative binomial limit laws 155 10.4. Conclusion 159 10.5. Bibliography 159 Chapter 11. Asymptotically Parameter-Free Tests for Ergodic Diffusion Processes 161 Yury A. KUTOYANTS and Li ZHOU 11.1. Introduction 161 11.2. Ergodic diffusion process and some limits 165 11.3. Shift parameter 168 11.4. Shift and scale parameters 172 11.5. Bibliography 175 Chapter 12. A Comparison of Homogeneity Tests for Different Alternative Hypotheses 177 Sergey POSTOVALOV and Petr PHILONENKO 12.1. Homogeneity tests 178 12.1.1. Tests for data without censoring 179 12.1.2. Tests for data with censoring 180 12.2. Alternative hypotheses 184 12.3. Power simulation 185 12.3.1. Power of tests without censoring 187 12.3.2. Power of tests with censoring 189 12.3.2.1. How does the distribution of censoring time affect the power of the test? 189 12.3.2.2. How does the censoring rate affect the power of the test? 191 12.4. Statistical inference 191 12.5. Acknowledgment 192 12.6. Bibliography 193 Chapter 13. Some Asymptotic Results for Exchangeably Weighted Bootstraps of the Empirical Estimator of a Semi-Markov Kernel with Applications 195 Salim BOUZEBDA and Nikolaos LIMNIOS 13.1. Introduction 195 13.2. Semi-Markov setting 197 13.3. Main results 201 13.4. Bootstrap for a multidimensional empirical estimator of a continuous-time semi-Markov kernel 205 13.5. Confidence intervals 208 13.6. Bibliography 210 Chapter 14. On Chi-Squared Goodness-of-Fit Test for Normality 213 Mikhail NIKULIN, Léo GERVILLE-RÉACHE and Xuan Quang TRAN 14.1. Chi–squared test for normality 213 14.2. Simulation study 221 14.3. Bibliography 226 Part 2. Statistical Models and Methods in Survival Analysis 229 Chapter 15. Estimation/Imputation Strategies for Missing Data in Survival Analysis 231 Elodie BRUNEL, Fabienne COMTE and Agathe GUILLOUX 15.1. Introduction 231 15.2. Model and strategies 233 15.2.1. Model assumptions 233 15.2.2. Strategy involving knowledge of ζ 234 15.2.3. Strategy involving knowledge of π 235 15.2.4. Estimation of ζ or π: logit or non-parametric regression 236 15.2.5. Computing the hazard estimators 236 15.2.6. Theoretical results 239 15.3. Imputation-based strategy 241 15.4. Numerical comparison 242 15.5. Proofs 244 15.6. Bibliography 251 Chapter 16. Non-Parametric Estimation of Linear Functionals of a Multivariate Distribution Under Multivariate Censoring with Applications 253 Olivier LOPEZ and Philippe SAINT-PIERRE 16.1. Introduction 253 16.2. Non-parametric estimation of the distribution 255 16.3. Asymptotic properties 257 16.4. Statistical applications of functionals 260 16.4.1. Dependence measures 260 16.4.2. Bootstrap 261 16.4.3. Linear regression 262 16.5. Illustration 263 16.6. Conclusion 264 16.7. Acknowledgment 264 16.8. Bibliography 264 Chapter 17. Kernel Estimation of Density from Indirect Observation 267 Valentin SOLEV 17.1. Introduction 267 17.1.1. Random partition 267 17.1.2. Indirect observation 268 17.1.3. Kernel density estimator 269 17.2. Density of random vector Λ(X) 271 17.3. Pseudo-kernel density estimator 273 17.3.1. Pointwise density estimation based on indirect data 273 17.3.2. Bias of the kernel estimator 274 17.3.3. Estimate of variance 276 17.4. Bibliography 279 Chapter 18. A Comparative Analysis of Some Chi-Square Goodness-of-Fit Tests for Censored Data 281 Ekaterina CHIMITOVA and Boris LEMESHKO 18.1. Introduction 281 18.2. Chi-square goodness-of-fit tests for censored data 283 18.2.1. NRR χ2 test 283 18.2.2. GPF χ2 test 284 18.3. The choice of grouping intervals 285 18.3.1. Equifrequent grouping (EFG) 289 18.3.2. Intervals with equal expected numbers of failures (EENFG) 289 18.3.3. Optimal grouping (OptG) 289 18.4. Empirical power study 290 18.5. Conclusions 293 18.6. Acknowledgment 294 18.7. Bibliography 294 Chapter 19. A Non-parametric Test for Comparing Treatments with Missing Data and Dependent Censoring 297 Amel MEZAOUER, Kamal BOUKHETALA and Jean-François DUPUY 19.1. Introduction 297 19.2. The proposed test statistic 299 19.3. Asymptotic distribution of the proposed test statistic 301 19.4. Acknowledgment 305 19.5. Appendix 306 19.6. Bibliography 309 Chapter 20. Group Sequential Tests for Treatment Effect with Covariates Adjustment through Simple Cross-Effect Models 311 Isaac Wu HONG-DAR 20.1. Introduction 311 20.2. Notations and models 313 20.3. Group sequential test 316 20.4. Discussion 318 20.5. Acknowledgment 318 20.6. Bibliography 318 Part 3. Reliability and Maintenance 321 Chapter 21. Optimal Maintenance in Degradation Processes 323 Waltraud KAHLE 21.1. Introduction 323 21.2. The degradation model 324 21.3. Optimal replacement after an inspection 326 21.4. The simulation of degradation processes 327 21.5. Shape of cost functions and optimal δ and a 329 21.6. Incomplete preventive maintenance 330 21.7. Bibliography 333 Chapter 22. Planning Accelerated Destructive Degradation Tests with Competing Risks 335 Ying SHI and William Q. MEEKER 22.1. Introduction 336 22.1.1. Background 336 22.1.2. Motivation: adhesive bond C 336 22.1.3. Related literature 337 22.1.4. Overview 338 22.2. Degradation models with competing risks 338 22.2.1. Accelerated degradation model for the primary response 338 22.2.2. Accelerated degradation model for the competing response 339 22.2.3. Degradation models for adhesive bond C 339 22.2.4. Degradation distribution and quantiles 340 22.3. Failure-time distribution with competing risks 341 22.3.1. Relationship between degradation and failure 341 22.3.2. Failure-time distribution and quantiles 342 22.4. Test planning with competing risks 342 22.4.1. ADDT planning information 342 22.4.2. Criterion for ADDT planning with competing risks 343 22.5. ADDT plans with competing risks 344 22.5.1. Initial optimum ADDT plan with competing risks 344 22.5.2. Constrained optimum ADDT plan with competing risks 348 22.5.3. General equivalence theorem 348 22.5.4. Compromise ADDT plan with competing risks 350 22.6. Monte Carlo simulation to evaluate test plans 352 22.7. Conclusions and extensions 353 22.8. Appendix: technical details 354 22.8.1. The Fisher information matrix for ADDT with competing risks 354 22.8.2. Large-sample approximate variance of ht (tp) and tp 355 22.9. Bibliography 355 Chapter 23. A New Goodness-of-Fit Test for Shape-Scale Families 357 Vilijandas BAGDONAVIČIUS 23.1. Introduction 357 23.2. The test statistic 358 23.3. The asymptotic distribution of the test statistic 359 23.4. The test 364 23.5. Weibull distribution 364 23.6. Loglogistic distribution 365 23.7. Lognormal distribution 366 23.8. Bibliography 367 Chapter 24. Time-to-Failure of Markov-Modulated Gamma Process with Application to Replacement Policies 369 Christian PAROISSIN and Landy RABEHASAINA 24.1. Introduction 369 24.2. Degradation model 370 24.2.1. Covariate process 370 24.2.2. Degradation process 371 24.3. Time-to-failure distribution 371 24.3.1. Case of a non-modulated gamma process 372 24.3.2. Case of a Markov-modulated gamma process 373 24.3.3. Stochastic comparison 374 24.4. Replacement policies 376 24.4.1. Block replacement policy 377 24.4.2. Age replacement policy 379 24.5. Conclusion 381 24.6. Acknowledgment 381 24.7. Bibliography 382 Chapter 25. Calculation of the Redundant Structure Reliability for Agingtype Elements 383 Alexandr ANTONOV, Alexandr PLYASKIN and Khizri TATAEV 25.1. Introduction 383 25.2. The operation process of the renewal and repaired products 384 25.3. The model of the geometric process 386 25.4. Task solution 387 25.5. Conclusion 389 25.6. Bibliography 390 Chapter 26. On Engineering Risks of Complex Hierarchical Systems Analysis 391 Vladimir RYKOV 26.1. Introduction 391 26.2. Risk definition and measurement 392 26.3. Engineering risk 393 26.4. Risk characteristics for general model calculation 395 26.4.1. Lifelength and appropriate loss size CDF 395 26.4.2. Probability of risk event evolution 396 26.4.3. Lifelength and loss moments 397 26.4.4. Mostly dangerous paths of risk event evolution and sensitivity analysis 399 26.5. Risk analysis for short-time risk models 400 26.6. Conclusion 402 26.7. Bibliography 402 List of Authors 405 Index 409

Autorenportrait

Vincent Couallier is Associate Professor at Bordeaux Segalen University in France Léo Gerville-Réache is Associate Professor at Bordeaux 2 University in France. Catherine Huber-Carol is Professor Emeritus at Paris René Descartes University in France. Nikolaos Limnios is Professor at Compiègne University of Technology in France. Mounir Mesbah is Professor at University Pierre and Marie Curie in Paris, France.