Statistical methods for biostatistics and related fields

Biostatistics is one of the scientific fields for which the recent developments have been extremely important. It is also strongly related to other scientific disciplines involving statistical methodology. The aim of this book is to cover a wide scope of recent statistical methods used by scientists in biostatistics as well as in other related fields such as chemometrics, environmetrics and geophysics.

The contributed papers, coming from internationally recognized researchers, present various statistical methodologies together with a selected scope of their main mathematical properties and their applications in real case studies, making this book of interest to a wide audience among researchers and students in statistics.

Each method is accompanied with interactive and automatic Xplore routines, available on-line, allowing people to reproduce the proposed examples or to apply the methods to their own real datasets. Thus this book will also be of special interest to practitioners.

Avner Bar-Hen and Jean-Jacques DaudinJorg Breitung and Remy Slama and Axel WerwatzAli Gannoun and Beno Liquetit and Jerome Saracco and Wolfgang UrferIvana Horova and Jiri ZelinkaWolfgang Hardle and Hua LiangMasahiro KurodaQihua WangJavier Roca-Pardinas and Carmen Cadarso-Suarez and Wenceslao Gonzalez-ManteigaCarmela Cappelli and Heping ZhangSaracco Jerome and Gannoun Ali and Guinot Christiane and Liquet BenoitMakoto TomitaHerve Cardot and Christophe Crambes and Pascal SardaYuichi Mori and Masaya Iizuka and Tomoyuki Tarumi and Yutaka TanakaPavel Cizek and Wolfgang Hardle and Jurgen SymanzikMichal BenkoGraciela Estevez-Perez and Alejandro Quintela del RioFrederic Ferraty and Martin Paegelow and Pascal SardaHizir Sofyan and Muzailin Affan and Khaled Bawahidi

I Biostatistics	p. 1
1 Discriminant Analysis Based on Continuous and Discrete Variables	p. 3
1.1 Introduction	p. 3
1.2 Generalisation of the Mahalanobis Distance	p. 4
1.2.1 Introduction	p. 4
1.2.2 Kullback-Leibler Divergence	p. 5
1.2.3 Asymptotic Distribution of Matusita Distance	p. 10
1.2.4 Simulations	p. 12
1.3 Methods and Stopping Rules for Selecting Variables	p. 13
1.4 Reject Option	p. 15
1.4.1 Distributional Result	p. 15
1.4.2 Derivation of the Preliminary Test	p. 18
1.5 Example	p. 22
1.5.1 Location Model	p. 22
1.5.2 Comparison with the Linear Discriminant Analysis	p. 24
1.5.3 Conclusion	p. 24
Bibliography	p. 25
2 Longitudinal Data Analysis with Linear Regression	p. 29
2.1 Introduction	p. 29
2.2 Theoretical Aspects	p. 32
2.2.1 The Fixed-effect Model	p. 32
2.2.2 The Random Effects Model	p. 36
2.3 Computing Fixed and Random-effect Models	p. 37
2.3.1 Data Preparation	p. 37
2.3.2 Fixed and Random-effect Linear Regression	p. 38
2.3.3 Options for panfix	p. 38
2.3.4 Options for panrand	p. 39
2.4 Application	p. 40
2.4.1 Results	p. 41
Bibliography	p. 43
3 A Kernel Method Used for the Analysis of Replicated Micro-array Experiments	p. 45
3.1 Introduction	p. 45
3.2 Statistical Model and Some Existing Methods	p. 46
3.2.1 The Basic Model	p. 47
3.2.2 The T-test	p. 47
3.2.3 The Mixture Model Approach	p. 48
3.3 A Fully Nonparametric Approach	p. 49
3.3.1 Kernel Estimation of f[subscript 0] and f	p. 50
3.3.2 The Reflection Approach in Kernel Estimation	p. 50
3.3.3 Implementation of the Nonparametric Method	p. 51
3.4 Data Analysis	p. 52
3.4.1 Results Obtained with the Normal Mixture Model	p. 53
3.4.2 Results Obtained with the Nonparametric Approach	p. 53
3.4.3 A Simulation Study	p. 56
3.5 Discussion and Concluding Remarks	p. 58
Bibliography	p. 59
4 Kernel Estimates of Hazard Functions for Biomedical Data Sets	p. 63
4.1 Introduction	p. 63
4.2 Kernel Estimate of the Hazard Function and Its Derivatives	p. 64
4.3 Choosing the Shape of the Kernel	p. 68
4.4 Choosing the Bandwidth	p. 69
4.5 Description of the Procedure	p. 74
4.6 Application	p. 75
Bibliography	p. 83
5 Partially Linear Models	p. 87
5.1 Introduction	p. 87
5.2 Estimation and Nonparametric Fits	p. 89
5.2.1 Kernel Regression	p. 89
5.2.2 Local Polynomial	p. 90
5.2.3 Piecewise Polynomial	p. 93
5.2.4 Least Square Spline	p. 96
5.3 Heteroscedastic Cases	p. 97
5.3.1 Variance Is a Function of Exogenous Variables	p. 98
5.3.2 Variance Is an Unknown Function of T	p. 99
5.3.3 Variance Is a Function of the Mean	p. 99
5.4 Real Data Examples	p. 100
Bibliography	p. 102
6 Analysis of Contingency Tables	p. 105
6.1 Introduction	p. 105
6.2 Log-linear Models	p. 105
6.2.1 Log-linear Models for Two-way Contingency Tables	p. 106
6.2.2 Log-linear Models for Three-way Contingency Tables	p. 107
6.2.3 Generalized Linear Models	p. 109
6.2.4 Fitting to Log-linear Models	p. 111
6.3 Inference for Log-linear Models Using XploRe	p. 113
6.3.1 Estimation of the Parameter Vector [lambda]	p. 113
6.3.2 Computing Statistics for the Log-linear Models	p. 113
6.3.3 Model Comparison and Selection	p. 114
6.4 Numerical Analysis of Contingency Tables	p. 115
6.4.1 Testing Independence	p. 115
6.4.2 Model Comparison	p. 119
Bibliography	p. 124
7 Identifying Coexpressed Genes	p. 125
7.1 Introduction	p. 125
7.2 Methodology and Implementation	p. 127
7.2.1 Weighting Adjustment	p. 128
7.2.2 Clustering	p. 132
7.3 Concluding Remarks	p. 142
Bibliography	p. 144
8 Bootstrap Methods for Testing Interactions in GAMs	p. 147
8.1 Introduction	p. 147
8.2 Logistic GAM with Interactions	p. 149
8.2.1 Estimation: the Local Scoring Algorithm	p. 150
8.3 Bootstrap-based Testing for Interactions	p. 152
8.3.1 Likelihood Ratio-based Test	p. 153
8.3.2 Direct Test	p. 153
8.3.3 Bootstrap Approximation	p. 153
8.4 Simulation Study	p. 154
8.5 Application to Real Data Sets	p. 156
8.5.1 Neural Basis of Decision Making	p. 156
8.5.2 Risk of Post-operative Infection	p. 159
8.6 Discussion	p. 162
8.7 Appendix	p. 163
Bibliography	p. 165
9 Survival Trees	p. 167
9.1 Introduction	p. 167
9.2 Methodology	p. 170
9.2.1 Splitting Criteria	p. 170
9.2.2 Pruning	p. 173
9.3 The Quantlet stree	p. 174
9.3.1 Syntax	p. 174
9.3.2 Example	p. 175
Bibliography	p. 179
10 A Semiparametric Reference Curves Estimation	p. 181
10.1 Introduction	p. 181
10.2 Kernel Estimation of Reference Curves	p. 184
10.3 A Semiparametric Approach Via Sliced Inverse Regression	p. 187
10.3.1 Dimension Reduction Context	p. 187
10.3.2 Estimation Procedure	p. 191
10.3.3 Asymptotic Property	p. 192
10.3.4 A Simulated Example	p. 193
10.4 Case Study on Biophysical Properties of the Skin	p. 195
10.4.1 Overview of the Variables	p. 196
10.4.2 Methodological Procedure	p. 197
10.4.3 Results and Interpretation	p. 198
10.5 Conclusion	p. 200
Bibliography	p. 201
11 Survival Analysis	p. 207
11.1 Introduction	p. 207
11.2 Data Sets	p. 208
11.3 Data on the Period up to Sympton Recurrence	p. 208
11.3.1 Kaplan-Meier Estimate	p. 208
11.3.2 Log-rank Test	p. 210
11.4 Data for Aseptic Necrosis	p. 211
11.4.1 Kaplan-Meier Estimate	p. 214
11.4.2 Log-rank Test	p. 214
11.4.3 Cox's Regression	p. 215
Bibliography	p. 217
II Related Sciences	p. 219
12 Ozone Pollution Forecasting	p. 221
12.1 Introduction	p. 221
12.2 A Brief Analysis of the Data	p. 222
12.2.1 Description of the Data	p. 222
12.2.2 Principal Component Analysis	p. 224
12.2.3 Functional Principal Component Analysis	p. 225
12.3 Functional Linear Model	p. 226
12.3.1 Spline Estimation of [alpha]	p. 227
12.3.2 Selection of the Parameters	p. 228
12.3.3 Multiple Functional Linear Model	p. 229
12.4 Functional Linear Regression for Conditional Quantiles Estimation	p. 231
12.4.1 Spline Estimator of [Psi][subscript alpha]	p. 232
12.4.2 Multiple Conditional Quantiles	p. 234
12.5 Application to Ozone Prediction	p. 235
12.5.1 Prediction of the Conditional Mean	p. 236
12.5.2 Prediction of the Conditional Median	p. 236
12.5.3 Analysis of the Results	p. 238
Bibliography	p. 242
13 Nonparametric Functional Chemometric AnalysisFrederic Ferraty and Aldo Goia and Philippe Vieu
13.1 Introduction	p. 245
13.2 General Considerations	p. 246
13.2.1 Introduction to Spectrometric Data	p. 246
13.2.2 Introduction to Nonparametric Statistics for Curves	p. 248
13.2.3 Notion of Proximity Between Curves	p. 249
13.2.4 XploRe Quantlets for Proximity Between Curves	p. 251
13.3 Functional Nonparametric Regression	p. 252
13.3.1 The Statistical Problem	p. 252
13.3.2 The Nonparametric Functional Estimate	p. 253
13.3.3 Prediction of Fat Percentage from Continuous Spectrum	p. 254
13.3.4 The XploRe Quantlet	p. 255
13.3.5 Comments on Bandwidth Choice	p. 256
13.4 Nonparametric Curves Discrimination	p. 257
13.4.1 The Statistical Problem	p. 257
13.4.2 A Nonparametric Curves Discrimination Method	p. 258
13.4.3 Discrimination of Spectrometric Curves	p. 260
13.4.4 The XploRe Quantlet	p. 261
13.5 Concluding Comments	p. 262
Bibliography	p. 263
14 Variable Selection in Principal Component Analysis	p. 265
14.1 Introduction	p. 265
14.2 Variable Selection in PCA	p. 267
14.3 Modified PCA	p. 268
14.4 Selection Procedures	p. 269
14.5 Quantlet	p. 272
14.6 Examples	p. 273
14.6.1 Artificial Data	p. 273
14.6.2 Application Data	p. 279
Bibliography	p. 282
15 Spatial Statistics	p. 285
15.1 Introduction	p. 285
15.2 Analysis of Geostatistical Data	p. 287
15.2.1 Trend Surfaces	p. 288
15.2.2 Kriging	p. 290
15.2.3 Correlogram and Variogram	p. 292
15.3 Spatial Point Process Analysis	p. 297
15.4 Discussion	p. 303
15.5 Acknowledgements	p. 303
Bibliography	p. 303
16 Functional Data Analysis	p. 305
16.1 Introduction	p. 305
16.2 Functional Basis Expansion	p. 307
16.2.1 Fourier Basis	p. 308
16.2.2 Polynomial Basis	p. 309
16.2.3 B-Spline Basis	p. 309
16.2.4 Data Set as Basis	p. 309
16.3 Approximation and Coefficient Estimation	p. 310
16.3.1 Software Implementation	p. 312
16.3.2 Temperature Example	p. 313
16.4 Functional Principal Components	p. 314
16.4.1 Implementation	p. 317
16.4.2 Data Set as Basis	p. 319
16.5 Smoothed Principal Components Analysis	p. 321
16.5.1 Implementation Using Basis Expansion	p. 323
16.5.2 Temperature Example	p. 323
Bibliography	p. 326
17 Analysis of Failure Time with Microearthquakes Applications	p. 329
17.1 Introduction	p. 329
17.2 Kernel Estimation of Hazard Function	p. 330
17.3 An Application to Real Data	p. 336
17.3.1 The Occurrence Process of Earthquakes	p. 336
17.3.2 Galicia Earthquakes Data	p. 337
17.4 Conclusions	p. 342
Bibliography	p. 343
18 Landcover Prediction	p. 347
18.1 Introduction	p. 347
18.2 Presentation of the Data	p. 348
18.2.1 The Area: the Garrotxes	p. 348
18.2.2 The Data Set	p. 348
18.3 The Multilogit Regression Model	p. 349
18.4 Penalized Log-likelihood Estimation	p. 351
18.5 Polychotomous Regression in Action	p. 352
18.6 Results and Interpretation	p. 353
Bibliography	p. 356
19 The Application of Fuzzy Clustering to Satellite Images Data	p. 357
19.1 Introduction	p. 357
19.2 Remote Sensing	p. 358
19.3 Fuzzy C-means Method	p. 359
19.3.1 Data and Methods	p. 361
19.4 Results and Discussions	p. 362
Bibliography	p. 366
Index	p. 367

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