Robust Methods in Biostatistics

, by Heritier, Stephane; Cantoni, Eva; Copt, Samuel; Victoria-Feser, Maria-Pia

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780470027264 | 0470027266
Cover: Hardcover
Copyright: 5/26/2009

Buy New

Print on Demand: 2-4 Weeks. This item cannot be cancelled or returned.

$124.99

Robust statistics is an extension of classical statistics that specifically takes into account the concept that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable when the data do not exactly match the postulated models as it is the case for example with outliers.

Preface	p. xiii
Acknowledgments	p. xv
Introduction	p. 1
What is Robust Statistics?	p. 1
Against What is Robust Statistics Robust?	p. 3
Are Diagnostic Methods an Alternative to Robust Statistics?	p. 7
How do Robust Statistics Compare with Other Statistical Procedures in Practice?	p. 11
Key Measures and Results	p. 15
Introduction	p. 15
Statistical Tools for Measuring Robustness Properties	p. 16
The Influence Function	p. 17
The Breakdown Point	p. 20
Geometrical Interpretation	p. 20
The Rejection Point	p. 21
General Approaches for Robust Estimation	p. 21
The General Class of M-estimators	p. 23
Properties of M-estimators	p. 27
The Class of S-estimators	p. 30
Statistical Tools for Measuring Tests Robustness	p. 32
Sensitivity of the Two-sample t-test	p. 34
Local Stability of a Test: the Univariate Case	p. 34
Global Reliability of a Test: the Breakdown Functions	p. 37
General Approaches for Robust Testing	p. 38
Wald Test, Score Test and LRT	p. 39
Geometrical Interpretation	p. 40
General ¿-type Classes of Tests	p. 40
Asymptotic Distributions	p. 42
Robustness Properties	p. 43
Linear Regression	p. 45
Introduction	p. 45
Estimating the Regression Parameters	p. 47
The Regression Model	p. 47
Robustness Properties of the LS and MLE Estimators	p. 48
Glomerular Filtration Rate (GFR) Data Example	p. 49
Robust Estimators	p. 50
GFR Data Example (continued)	p. 54
Testing the Regression Parameters	p. 55
Significance Testing	p. 55
Diabetes Data Example	p. 58
Multiple Hypothesis Testing	p. 59
Diabetes Data Example (continued)	p. 61
Checking and Selecting the Model	p. 62
Residual Analysis	p. 62
GFR Data Example (continued)	p. 62
Diabetes Data Example (continued)	p. 65
Coefficient of Determination	p. 66
Global Criteria for Model Comparison	p. 69
Diabetes Data Example (continued)	p. 75
Cardiovascular Risk Factors Data Example	p. 78
Mixed Linear Models	p. 83
Introduction	p. 83
The MLM	p. 84
The MLM Formulation	p. 84
Skin Resistance Data	p. 88
Semantic Priming Data	p. 89
Orthodontic Growth Data	p. 90
Classical Estimation and Inference	p. 91
Marginal and REML Estimation	p. 91
Classical Inference	p. 94
Lack of Robustness of Classical Procedures	p. 96
Robust Estimation	p. 97
Bounded Influence Estimators	p. 97
S-estimators	p. 98
MM-estimators	p. 100
Choosing the Tuning Constants	p. 102
Skin Resistance Data (continued)	p. 103
Robust Inference	p. 104
Testing Contrasts	p. 104
Multiple Hypothesis Testing of the Main Effects	p. 106
Skin Resistance Data Example (continued)	p. 107
Semantic Priming Data Example (continued)	p. 107
Testing the Variance Components	p. 110
Checking the Model	p. 110
Detecting Outlying and Influential Observations	p. 110
Prediction and Residual Analysis	p. 112
Further Examples	p. 116
Metallic Oxide Data	p. 116
Orthodontic Growth Data (continued)	p. 118
Discussion and Extensions	p. 122
Generalized Linear Models	p. 125
Introduction	p. 125
The GLM	p. 126
Model Building	p. 126
Classical Estimation and Inference for GLM	p. 129
Hospital Costs Data Example	p. 132
Residual Analysis	p. 133
A Class of M-estimators for GLMs	p. 136
Choice of ¿ and ¿ w(x)	p. 137
Fisher Consistency Correction	p. 138
Nuisance Parameters Estimation	p. 139
IF and Asymptotic Properties	p. 140
Hospital Costs Example (continued)	p. 140
Robust Inference	p. 141
Significance Testing and CIs	p. 141
General Parametric Hypothesis Testing and Variable Selection	p. 142
Hospital Costs Data Example (continued)	p. 144
Breastfeeding Data Example	p. 146
Robust Estimation of the Full Model	p. 146
Variable Selection	p. 148
Doctor Visits Data Example	p. 151
Robust Estimation of the Full Model	p. 151
Variable Selection	p. 154
Discussion and Extensions	p. 158
Robust Hurdle Models for Counts	p. 158
Robust Akaike Criterion	p. 159
General CP Criterion for GLMs	p. 159
Prediction with Robust Models	p. 160
Marginal Longitudinal Data Analysis	p. 161
Introduction	p. 161
The Marginal Longitudinal Data Model (MLDA) and Alternatives	p. 163
Classical Estimation and Inference in MLDA	p. 164
Estimators for ¿ and ¿	p. 166
GUIDE Data Example	p. 169
Residual Analysis	p. 171
A Robust GEE-type Estimator	p. 172
Linear Predictor Parameters	p. 172
Nuisance Parameters	p. 174
IF and Asymptotic Properties	p. 176
GUIDE Data Example (continued)	p. 177
Robust Inference	p. 178
Significance Testing and CIs	p. 178
Variable Selection	p. 179
GUIDE Data Example (continued)	p. 180
LEI Data Example	p. 182
Stillbirth in Piglets Data Example	p. 186
Discussion and Extensions	p. 189
Survival Analysis	p. 191
Introduction	p. 191
The Cox Model	p. 193
The Partial Likelihood Approach	p. 193
Empirical Influence Function for the PLe	p. 196
Myeloma Data Example	p. 197
A Sandwich Formula for the Asymptotic Variance	p. 198
Robust Estimation and Inference in the Cox Model	p. 200
A Robust Alternative to the PLE	p. 200
Asymptotic Normality	p. 202
Handling of Ties	p. 204
Myeloma Data Example (continued)	p. 205
Robust Inference and its Current Limitations	p. 206
The Veteran's Administration Lung Cancer Data	p. 209
Robust Estimation	p. 209
Interpretation of the Weights	p. 210
Validation	p. 212
Structural Misspecifications	p. 214
Performance of the Are	p. 214
Performance of the robust Wald test	p. 216
Other Issues	p. 217
Censored Regression Quantiles	p. 217
Regression Quantiles	p. 217
Extension to the Censored Case	p. 219
Asymptotic Properties and Robustness	p. 220
Comparison with the Cox Proportional Hazard Model	p. 221
Lung Cancer Data Example (continued)	p. 222
Limitations and Extensions	p. 224
Appendices	p. 227
Starting Estimators for MM-estimators of Regression Parameters	p. 229
Efficiency, LRT¿, RAIC and RCp with Biweight ¿-function for the Regression Model	p. 231
An Algorithm Procedure for the Constrained S-estimator	p. 235
Some Distributions of the Exponential Family	p. 237
Computations for the Robust GLM Estimator	p. 239
Fisher Consistency Corrections	p. 239
Asymptotic Variance	p. 240
IRWLS Algorithm for Robust GLM	p. 242
Computations for the Robust GEE Estimator	p. 245
IRWLS Algorithm for Robust GEE	p. 245
Fisher Consistency Corrections	p. 246
Computation of the CRQ	p. 247
References	p. 249
Index	p. 265
Table of Contents provided by Ingram. All Rights Reserved.

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Robust Methods in Biostatistics

Summary

Author Biography

Table of Contents

Supplemental Materials