Mathematical Methods in Survival Analysis, Reliability and Quality of Life
ISTE Ltd and John Wiley & Sons Inc (Verlag)
978-1-84821-010-3 (ISBN)
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.
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.
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
| Erscheint lt. Verlag | 10.6.2008 |
|---|---|
| Verlagsort | London |
| Sprache | englisch |
| Maße | 161 x 240 mm |
| Gewicht | 703 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-10 | 1-84821-010-8 / 1848210108 |
| ISBN-13 | 978-1-84821-010-3 / 9781848210103 |
| Zustand | Neuware |
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