Statistical Methods for Biostatistics and Related Fields

By: Wolfgang HÃ¤rdle (Editor), Yuichi Mori (Editor), Philippe Vieu (Editor)

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Hardcover | 16 October 2006

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392 Pages

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23.39 x 15.6 x 2.24

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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.

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Biostatistics	p. 1
Discriminant Analysis Based on Continuous and Discrete Variables	p. 3
Introduction	p. 3
Generalisation of the Mahalanobis Distance	p. 4
Introduction	p. 4
Kullback-Leibler Divergence	p. 5
Asymptotic Distribution of Matusita Distance	p. 10
Simulations	p. 12
Methods and Stopping Rules for Selecting Variables	p. 13
Reject Option	p. 15
Distributional Result	p. 15
Derivation of the Preliminary Test	p. 18
Example	p. 22
Location Model	p. 22
Comparison with the Linear Discriminant Analysis	p. 24
Conclusion	p. 24
Bibliography	p. 25
Longitudinal Data Analysis with Linear Regression	p. 29
Introduction	p. 29
Theoretical Aspects	p. 32
The Fixed-effect Model	p. 32
The Random Effects Model	p. 36
Computing Fixed and Random-effect Models	p. 37
Data Preparation	p. 37
Fixed and Random-effect Linear Regression	p. 38
Options for panfix	p. 38
Options for panrand	p. 39
Application	p. 40
Results	p. 41
Bibliography	p. 43
A Kernel Method Used for the Analysis of Replicated Micro-array Experiments	p. 45
Introduction	p. 45
Statistical Model and Some Existing Methods	p. 46
The Basic Model	p. 47
The T-test	p. 47
The Mixture Model Approach	p. 48
A Fully Nonparametric Approach	p. 49
Kernel Estimation of f[subscript 0] and f	p. 50
The Reflection Approach in Kernel Estimation	p. 50
Implementation of the Nonparametric Method	p. 51
Data Analysis	p. 52
Results Obtained with the Normal Mixture Model	p. 53
Results Obtained with the Nonparametric Approach	p. 53
A Simulation Study	p. 56
Discussion and Concluding Remarks	p. 58
Bibliography	p. 59
Kernel Estimates of Hazard Functions for Biomedical Data Sets	p. 63
Introduction	p. 63
Kernel Estimate of the Hazard Function and Its Derivatives	p. 64
Choosing the Shape of the Kernel	p. 68
Choosing the Bandwidth	p. 69
Description of the Procedure	p. 74
Application	p. 75
Bibliography	p. 83
Partially Linear Models	p. 87
Introduction	p. 87
Estimation and Nonparametric Fits	p. 89
Kernel Regression	p. 89
Local Polynomial	p. 90
Piecewise Polynomial	p. 93
Least Square Spline	p. 96
Heteroscedastic Cases	p. 97
Variance Is a Function of Exogenous Variables	p. 98
Variance Is an Unknown Function of T	p. 99
Variance Is a Function of the Mean	p. 99
Real Data Examples	p. 100
Bibliography	p. 102
Analysis of Contingency Tables	p. 105
Introduction	p. 105
Log-linear Models	p. 105
Log-linear Models for Two-way Contingency Tables	p. 106
Log-linear Models for Three-way Contingency Tables	p. 107
Generalized Linear Models	p. 109
Fitting to Log-linear Models	p. 111
Inference for Log-linear Models Using XploRe	p. 113
Estimation of the Parameter Vector [lambda]	p. 113
Computing Statistics for the Log-linear Models	p. 113
Model Comparison and Selection	p. 114
Numerical Analysis of Contingency Tables	p. 115
Testing Independence	p. 115
Model Comparison	p. 119
Bibliography	p. 124
Identifying Coexpressed Genes	p. 125
Introduction	p. 125
Methodology and Implementation	p. 127
Weighting Adjustment	p. 128
Clustering	p. 132
Concluding Remarks	p. 142
Bibliography	p. 144
Bootstrap Methods for Testing Interactions in GAMs	p. 147
Introduction	p. 147
Logistic GAM with Interactions	p. 149
Estimation: the Local Scoring Algorithm	p. 150
Bootstrap-based Testing for Interactions	p. 152
Likelihood Ratio-based Test	p. 153
Direct Test	p. 153
Bootstrap Approximation	p. 153
Simulation Study	p. 154
Application to Real Data Sets	p. 156
Neural Basis of Decision Making	p. 156
Risk of Post-operative Infection	p. 159
Discussion	p. 162
Appendix	p. 163
Bibliography	p. 165
Survival Trees	p. 167
Introduction	p. 167
Methodology	p. 170
Splitting Criteria	p. 170
Pruning	p. 173
The Quantlet stree	p. 174
Syntax	p. 174
Example	p. 175
Bibliography	p. 179
A Semiparametric Reference Curves Estimation	p. 181
Introduction	p. 181
Kernel Estimation of Reference Curves	p. 184
A Semiparametric Approach Via Sliced Inverse Regression	p. 187
Dimension Reduction Context	p. 187
Estimation Procedure	p. 191
Asymptotic Property	p. 192
A Simulated Example	p. 193
Case Study on Biophysical Properties of the Skin	p. 195
Overview of the Variables	p. 196
Methodological Procedure	p. 197
Results and Interpretation	p. 198
Conclusion	p. 200
Bibliography	p. 201
Survival Analysis	p. 207
Introduction	p. 207
Data Sets	p. 208
Data on the Period up to Sympton Recurrence	p. 208
Kaplan-Meier Estimate	p. 208
Log-rank Test	p. 210
Data for Aseptic Necrosis	p. 211
Kaplan-Meier Estimate	p. 214
Log-rank Test	p. 214
Cox's Regression	p. 215
Bibliography	p. 217
Related Sciences	p. 219
Ozone Pollution Forecasting	p. 221
Introduction	p. 221
A Brief Analysis of the Data	p. 222
Description of the Data	p. 222
Principal Component Analysis	p. 224
Functional Principal Component Analysis	p. 225
Functional Linear Model	p. 226
Spline Estimation of [alpha]	p. 227
Selection of the Parameters	p. 228
Multiple Functional Linear Model	p. 229
Functional Linear Regression for Conditional Quantiles Estimation	p. 231
Spline Estimator of [Psi][subscript alpha]	p. 232
Multiple Conditional Quantiles	p. 234
Application to Ozone Prediction	p. 235
Prediction of the Conditional Mean	p. 236
Prediction of the Conditional Median	p. 236
Analysis of the Results	p. 238
Bibliography	p. 242
Nonparametric Functional Chemometric Analysis
Introduction	p. 245
General Considerations	p. 246
Introduction to Spectrometric Data	p. 246
Introduction to Nonparametric Statistics for Curves	p. 248
Notion of Proximity Between Curves	p. 249
XploRe Quantlets for Proximity Between Curves	p. 251
Functional Nonparametric Regression	p. 252
The Statistical Problem	p. 252
The Nonparametric Functional Estimate	p. 253
Prediction of Fat Percentage from Continuous Spectrum	p. 254
The XploRe Quantlet	p. 255
Comments on Bandwidth Choice	p. 256
Nonparametric Curves Discrimination	p. 257
The Statistical Problem	p. 257
A Nonparametric Curves Discrimination Method	p. 258
Discrimination of Spectrometric Curves	p. 260
The XploRe Quantlet	p. 261
Concluding Comments	p. 262
Bibliography	p. 263
Variable Selection in Principal Component Analysis	p. 265
Introduction	p. 265
Variable Selection in PCA	p. 267
Modified PCA	p. 268
Selection Procedures	p. 269
Quantlet	p. 272
Examples	p. 273
Artificial Data	p. 273
Application Data	p. 279
Bibliography	p. 282
Spatial Statistics	p. 285
Introduction	p. 285
Analysis of Geostatistical Data	p. 287
Trend Surfaces	p. 288
Kriging	p. 290
Correlogram and Variogram	p. 292
Spatial Point Process Analysis	p. 297
Discussion	p. 303
Acknowledgements	p. 303
Bibliography	p. 303
Functional Data Analysis	p. 305
Introduction	p. 305
Functional Basis Expansion	p. 307
Fourier Basis	p. 308
Polynomial Basis	p. 309
B-Spline Basis	p. 309
Data Set as Basis	p. 309
Approximation and Coefficient Estimation	p. 310
Software Implementation	p. 312
Temperature Example	p. 313
Functional Principal Components	p. 314
Implementation	p. 317
Data Set as Basis	p. 319
Smoothed Principal Components Analysis	p. 321
Implementation Using Basis Expansion	p. 323
Temperature Example	p. 323
Bibliography	p. 326
Analysis of Failure Time with Microearthquakes Applications	p. 329
Introduction	p. 329
Kernel Estimation of Hazard Function	p. 330
An Application to Real Data	p. 336
The Occurrence Process of Earthquakes	p. 336
Galicia Earthquakes Data	p. 337
Conclusions	p. 342
Bibliography	p. 343
Landcover Prediction	p. 347
Introduction	p. 347
Presentation of the Data	p. 348
The Area: the Garrotxes	p. 348
The Data Set	p. 348
The Multilogit Regression Model	p. 349
Penalized Log-likelihood Estimation	p. 351
Polychotomous Regression in Action	p. 352
Results and Interpretation	p. 353
Bibliography	p. 356
The Application of Fuzzy Clustering to Satellite Images Data	p. 357
Introduction	p. 357
Remote Sensing	p. 358
Fuzzy C-means Method	p. 359
Data and Methods	p. 361
Results and Discussions	p. 362
Bibliography	p. 366
Index	p. 367
Table of Contents provided by Ingram. All Rights Reserved.

Statistical Methods for Biostatistics and Related Fields

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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