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Mathematical Methods in Survival Analysis, Reliability and Quality of Life

, Band 13 1. Aufl.

von: Catherine Huber, Nikolaos Limnios, Mounir Mesbah, Mikhail S. Nikulin
207,99 €
Verlag:	Wiley
Format:	PDF
Veröffentl.:	05.01.2010
ISBN/EAN:	9780470393567
Sprache:	englisch
Anzahl Seiten:	420

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Beschreibungen

Titelbeschreibung

Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity of the involved mathematical theory. This title aims to redress this situation: it includes 21 chapters divided into four parts: Survival analysis, Reliability, Quality of life, and Related topics. Many of these chapters were presented at the European Seminar on Mathematical Methods for Survival Analysis, Reliability and Quality of Life in 2006.

Inhaltsverzeichnis

Preface 13 PART I 15 Chapter 1. Model Selection for Additive Regression in the Presence of Right-Censoring 17 Elodie BRUNEL and Fabienne COMTE 1.1. Introduction 17 1.2. Assumptions on the model and the collection of approximation spaces 18 1.2.1. Non-parametric regression model with censored data 18 1.2.2. Description of the approximation spaces in the univariate case 19 1.2.3. The particular multivariate setting of additive models 20 1.3. The estimation method 20 1.3.1. Transformation of the data 20 1.3.2. The mean-square contrast 21 1.4. Main result for the adaptive mean-square estimator 22 1.5. Practical implementation 23 1.5.1. The algorithm 23 1.5.2. Univariate examples 24 1.5.3. Bivariate examples 27 1.5.4. A trivariate example 28 1.6. Bibliography 30 Chapter 2. Non-parametric Estimation of Conditional Probabilities, Means and Quantiles under Bias Sampling 33 Odile PONS 2.1. Introduction 33 2.2. Non-parametric estimation of p 34 2.3. Bias depending on the value of Y 35 2.4. Bias due to truncation on X 37 2.5. Truncation of a response variable in a non-parametric regression model 37 2.6. Double censoring of a response variable in a non-parametric model 42 2.7. Other truncation and censoring of Y in a non-parametric model 44 2.8. Observation by interval 47 2.9. Bibliography 48 Chapter 3. Inference in Transformation Models for Arbitrarily Censored and Truncated Data 49 Filia VONTA and Catherine HUBER 3.1. Introduction 49 3.2. Non-parametric estimation of the survival function S 50 3.3. Semi-parametric estimation of the survival function S 51 3.4. Simulations 54 3.5. Bibliography 59 Chapter 4. Introduction of Within-area Risk Factor Distribution in Ecological Poisson Models 61 Lea FORTUNATO, Chantal GUIHENNEUC-JOUYAUX, Dominique LAURIER,Margot TIRMARCHE, Jacqueline CLAVEL and Denis HEMON 4.1. Introduction 61 4.2. Modeling framework 62 4.2.1. Aggregated model 62 4.2.2. Prior distributions 65 4.3. Simulation framework 65 4.4. Results 66 4.4.1. Strong association between relative risk and risk factor, correlated within-area means and variances (mean-dependent case) 67 4.4.2. Sensitivity to within-area distribution of the risk factor 68 4.4.3. Application: leukemia and indoor radon exposure 69 4.5. Discussion 71 4.6. Bibliography 72 Chapter 5. Semi-Markov Processes and Usefulness in Medicine 75 Eve MATHIEU-DUPAS, Claudine GRAS-AYGON and Jean-Pierre DAURES 5.1. Introduction 75 5.2. Methods 76 5.2.1. Model description and notation 76 5.2.2. Construction of health indicators 79 5.3. An application to HIV control 82 5.3.1. Context 82 5.3.2. Estimation method 82 5.3.3. Results: new indicators of health state 84 5.4. An application to breast cancer 86 5.4.1. Context 86 5.4.2. Age and stage-specific prevalence 87 5.4.3. Estimation method 88 5.4.4. Results: indicators of public health 88 5.5. Discussion 89 5.6. Bibliography 89 Chapter 6. Bivariate Cox Models 93 Michel BRONIATOWSKI, Alexandre DEPIRE and Ya’acov RITOV 6.1. Introduction 93 6.2. A dependence model for duration data 93 6.3. Some useful facts in bivariate dependence 95 6.4. Coherence 98 6.5. Covariates and estimation 102 6.6. Application: regression of Spearman’s rho on covariates 104 6.7. Bibliography 106 Chapter 7. Non-parametric Estimation of a Class of Survival Functionals 109 Belkacem ABDOUS 7.1. Introduction 109 7.2. Weighted local polynomial estimates 111 7.3. Consistency of local polynomial fitting estimators 114 7.4. Automatic selection of the smoothing parameter 116 7.5. Bibliography 119 Chapter 8. Approximate Likelihood in Survival Models 121 Henning LAUTER 8.1. Introduction 121 8.2. Likelihood in proportional hazard models 122 8.3. Likelihood in parametric models 122 8.4. Profile likelihood 123 8.4.1. Smoothness classes 124 8.4.2. Approximate likelihood function 125 8.5. Statistical arguments 127 8.6. Bibliography 129 PART II 131 Chapter 9.Cox Regression with Missing Values of a Covariate having a Non-proportional Effect on Risk of Failure 133 Jean-Francois DUPUY and Eve LECONTE 9.1. Introduction 133 9.2. Estimation in the Cox model with missing covariate values: a short review 136 9.3. Estimation procedure in the stratified Cox model with missing stratum indicator values 139 9.4. Asymptotic theory 141 9.5. A simulation study 145 9.6. Discussion 147 9.7. Bibliography 149 Chapter 10.Exact Bayesian Variable Sampling Plans for Exponential Distribution under Type-I Censoring 151 Chien-Tai LIN, Yen-Lung HUANG and N. BALAKRISHNAN 10.1. Introduction 151 10.2. Proposed sampling plan and Bayes risk 152 10.3. Numerical examples and comparison 156 10.4. Bibliography 161 Chapter 11. Reliability of Stochastic Dynamical Systems Applied to Fatigue Crack Growth Modeling 163 Julien CHIQUET and Nikolaos LIMNIOS 11.1. Introduction 163 11.2. Stochastic dynamical systems with jump Markov process 165 11.3. Estimation 168 11.4. Numerical application 170 11.5. Conclusion 175 11.6. Bibliography 175 Chapter 12. Statistical Analysis of a Redundant System with One Standby Unit 179 Vilijandas BAGDONAVIC¡ IUS, Inga MASIULAITYTE and Mikhail NIKULIN 12.1. Introduction 179 12.2. The models 180 12.3. The tests 181 12.4. Limit distribution of the test statistics 182 12.5. Bibliography 187 Chapter 13.A Modified Chi-squared Goodness-of-fit Test for the ThreeparameterWeibull Distribution and its Applications in Reliability 189 Vassilly VOINOV, Roza ALLOYAROVA and Natalie PYA 13.1. Introduction 189 13.2. Parameter estimation and modified chi-squared tests 191 13.3. Power estimation 194 13.4. Neyman-Pearson classes 194 13.5. Discussion 197 13.6. Conclusion 198 13.7. Appendix 198 13.8. Bibliography 201 Chapter 14.Accelerated Life Testing when the Hazard Rate Function has Cup Shape 203 Vilijandas BAGDONAVIC¡ IUS, Luc CLERJAUD and Mikhail NIKULIN 14.1. Introduction 203 14.2. Estimation in the AFT-GW model 204 14.2.1. AFT model 204 14.2.2. AFT-Weibull, AFT-lognormal and AFT-GW models 205 14.2.3. Plans of ALT experiments 205 14.2.4. Parameter estimation: AFT-GW model 206 14.3. Properties of estimators: simulation results for the AFT-GW model 207 14.4. Some remarks on the second plan of experiments 211 14.5. Conclusion 213 14.6. Appendix 213 14.7. Bibliography 215 Chapter 15. Point Processes in Software Reliability 217 James LEDOUX 15.1. Introduction 217 15.2. Basic concepts for repairable systems 219 15.3. Self-exciting point processes and black-box models 221 15.4. White-box models and Markovian arrival processes 225 15.4.1. A Markovian arrival model 226 15.4.2. Parameter estimation 228 15.4.3. Reliability growth 232 15.5. Bibliography 234 PART III 237 Chapter 16. Likelihood Inference for the Latent Markov Rasch Model 239 Francesco BARTOLUCCI, Fulvia PENNONI and Monia LUPPARELLI 16.1. Introduction 239 16.2. Latent class Rasch model 240 16.3. Latent Markov Rasch model 241 16.4. Likelihood inference for the latent Markov Rasch model 243 16.4.1. Log-likelihood maximization 244 16.4.2. Likelihood ratio testing of hypotheses on the parameters 245 16.5. An application 246 16.6. Possible extensions 247 16.6.1. Discrete response variables 248 16.6.2. Multivariate longitudinal data 248 16.7. Conclusions 251 16.8. Bibliography 252 Chapter 17. Selection of Items Fitting a Rasch Model 255 Jean-Benoit HARDOUIN and Mounir MESBAH 17.1. Introduction 255 17.2. Notations and assumptions 256 17.2.1. Notations 256 17.2.2. Fundamental assumptions of the Item Response Theory (IRT) 256 17.3. The Rasch model and the multidimensional marginally sufficient Rasch model 256 17.3.1. The Rasch model 256 17.3.2. The multidimensional marginally sufficient Rasch model 257 17.4. The Raschfit procedure 258 17.5. A fast version of Raschfit 259 17.5.1. Estimation of the parameters under the fixed effects Rasch model 259 17.5.2. Principle of Raschfit-fast 260 17.5.3. A model where the new item is explained by the same latent trait as the kernel 260 17.5.4. A model where the new item is not explained by the same latent trait as the kernel 260 17.5.5. Selection of the new item in the scale 261 17.6. A small set of simulations to compare Raschfit and Raschfit-fast 261 17.6.1. Parameters of the simulation study 261 17.6.2. Results and computing time 264 17.7. A large set of simulations to compare Raschfit-fast, MSP and HCA/CCPROX 269 17.7.1. Parameters of the simulations 269 17.7.2. Discussion 270 17.8. The Stata module “Raschfit” 270 17.9. Conclusion 271 17.10.Bibliography 273 Chapter 18. Analysis of Longitudinal HrQoL using Latent Regression in the Context of Rasch Modeling 275 Silvia BACCI 18.1. Introduction 275 18.2. Global models for longitudinal data analysis 276 18.3. A latent regression Rasch model for longitudinal data analysis 278 18.3.1. Model structure 278 18.3.2. Correlation structure 280 18.3.3. Estimation 281 18.3.4. Implementation with SAS 281 18.4. Case study: longitudinal HrQoL of terminal cancer patients 283 18.5. Concluding remarks 287 18.6. Bibliography 289 Chapter 19. Empirical Internal Validation and Analysis of a Quality of Life Instrument in French Diabetic Patients during an Educational Intervention 291 Judith CHWALOW, Keith MEADOWS, Mounir MESBAH, Vincent COLICHE and Etienne MOLLET 19.1. Introduction 291 19.2. Material and methods 292 19.2.1. Health care providers and patients 292 19.2.2. Psychometric validation of the DHP 293 19.2.3. Psychometric methods 293 19.2.4. Comparative analysis of quality of life by treatment group 294 19.3. Results 295 19.3.1. Internal validation of the DHP 295 19.3.2. Comparative analysis of quality of life by treatment group 303 19.4. Discussion 304 19.5. Conclusion 305 19.6. Bibliography 306 19.7. Appendices 309 PART IV 315 Chapter 20. Deterministic Modeling of the Size of the HIV/AIDS Epidemic in Cuba 317 Rachid LOUNES, Hector DE ARAZOZA, Y.H. HSIEH and Jose JOANES 20.1. Introduction 317 20.2. The models 319 20.2.1. The k2X model 322 20.2.2. The k2Y model 322 20.2.3. The k2XY model 323 20.2.4. The k2 XYX+Y model 324 20.3. The underreporting rate 324 20.4. Fitting the models to Cuban data 325 20.5. Discussion and concluding remarks 326 20.6. Bibliography 330 Chapter 21.Some Probabilistic Models Useful in Sport Sciences 333 Leo GERVILLE-REACHE, Mikhail NIKULIN, Sebastien ORAZIO, Nicolas PARIS and Virginie ROSA 21.1. Introduction 333 21.2. Sport jury analysis: the Gauss-Markov approach 334 21.2.1. Gauss-Markov model 334 21.2.2. Test for non-objectivity of a variable 334 21.2.3. Test of difference between skaters 335 21.2.4. Test for the less precise judge 336 21.3. Sport performance analysis: the fatigue and fitness approach 337 21.3.1. Model characteristics 337 21.3.2. Monte Carlo simulation 338 21.3.3. Results 339 21.4. Sport equipment analysis: the fuzzy subset approach 339 21.4.1. Statistical model used 340 21.4.2. Sensorial analysis step 341 21.4.3. Results 342 21.5. Sport duel issue analysis: the logistic simulation approach 343 21.5.1. Modeling by logistic regression 344 21.5.2. Numerical simulations 345 21.5.3. Results 345 21.6. Sport epidemiology analysis: the accelerated degradation approach 347 21.6.1. Principle of degradation in reliability analysis 347 21.6.2. Accelerated degradation model 348 21.7. Conclusion 350 21.8. Bibliography 350 Appendices 353 A. European Seminar: Some Figures 353 A.1. Former international speakers invited to the European Seminar 353 A.2. Former meetings supported by the European Seminar 353 A.3. Books edited by the organizers of the European Seminar 354 A.4. Institutions supporting the European Seminar (names of colleagues) 355 B. Contributors 357 Index 367

Autorenportrait

Catherine Huber is an Emeritus professor at Université de Paris René Descartes. Her research activity concerns nonparametric and semi-parametric theory of statistics and their applications in biology and medicine. She has several publications in particular in the field of survival analysis. She is the co-author and co-editor of several books in the above fields. Nikolaos Limnios is a professor at the University of Technology of Compiègne. His research and teaching activities concern stochastic processes, statistical inference and their applications in particular in reliability and survival analysis. He is the co-author and co-editor of several books in the above fields. Mounir Mesbah is a professor at the Université Pierre et Marie Curie, Paris 6. His research and teaching activities concern statistics and its applications in health science and medicine (biostatistics). He is the co-author of several articles and co-editor of several books in the above fields. Mikhail Nikulin is a professor at the Université Victor Segalen, and a member of the Institute of Mathematics at Bordeaux. His research and teaching activities concern mathematical statistics and its applications in reliability and survival analysis. He is the co-author and co-editor of several books in the above fields.