Robust Methods in Biostatistics

Robust Methods in Biostatistics......Page 3
Contents......Page 9
Preface......Page 15
Acknowledgments......Page 17
What is Robust Statistics?......Page 19
Against What is Robust Statistics Robust?......Page 21
Are Diagnostic Methods an Alternative to Robust Statistics? .......Page 25
How do Robust Statistics Compare with Other Statistical Procedures in Practice?......Page 29
Introduction......Page 33
Statistical Tools for Measuring Robustness Properties......Page 34
The Influence Function......Page 35
Geometrical Interpretation......Page 38
General Approaches for Robust Estimation......Page 39
The General Class of M-estimators......Page 41
Properties of M-estimators......Page 45
The Class of S-estimators......Page 48
Statistical Tools for Measuring Tests Robustness......Page 50
Local Stability of a Test: the Univariate Case......Page 52
Global Reliability of a Test: the Breakdown Functions......Page 55
General Approaches for Robust Testing......Page 56
Wald Test, Score Test and LRT......Page 57
General  -type Classes of Tests......Page 58
Asymptotic Distributions......Page 60
Robustness Properties......Page 61
Introduction......Page 63
The Regression Model......Page 65
Robustness Properties of  the LS and MLE Estimators......Page 66
Glomerular Filtration Rate (GFR) Data Example......Page 67
Robust Estimators......Page 68
GFR Data Example (continued)......Page 72
Significance Testing......Page 73
Diabetes Data Example......Page 76
Multiple Hypothesis Testing......Page 77
Diabetes Data Example (continued)......Page 79
GFR Data Example (continued)......Page 80
Diabetes Data Example (continued)......Page 83
Coefficient of Determination......Page 84
Global Criteria for Model Comparison......Page 87
Diabetes Data Example (continued)......Page 93
Cardiovascular Risk Factors Data Example......Page 96
Introduction......Page 101
The MLM Formulation......Page 102
Skin Resistance Data......Page 106
Semantic Priming Data......Page 107
Orthodontic Growth Data......Page 108
Marginal and REML Estimation......Page 109
Classical Inference......Page 112
Lack of Robustness of Classical Procedures......Page 114
Bounded Influence Estimators......Page 115
S-estimators......Page 116
MM-estimators......Page 118
Choosing the Tuning Constants......Page 120
Skin Resistance Data  (continued)......Page 121
Testing Contrasts......Page 122
Multiple Hypothesis Testing of the Main Effects......Page 124
Semantic Priming Data Example (continued)......Page 125
Detecting Outlying and Influential Observations......Page 128
Prediction and Residual Analysis......Page 130
Metallic Oxide Data......Page 134
Orthodontic Growth Data (continued)......Page 136
Discussion and Extensions......Page 140
Introduction......Page 143
Model Building......Page 144
Classical Estimation and Inference for GLM......Page 147
Hospital Costs Data Example......Page 150
Residual Analysis......Page 151
A Class of M-estimators for GLMs......Page 154
Choice of ψ and w(x)......Page 155
Fisher Consistency Correction......Page 156
Nuisance Parameters Estimation......Page 157
Hospital Costs Example (continued)......Page 158
Significance Testing and CIs......Page 159
General Parametric Hypothesis Testing and Variable Selection......Page 160
Hospital Costs Data Example (continued)......Page 162
Robust Estimation of  the Full Model......Page 164
Variable Selection......Page 166
Robust Estimation of the Full Model......Page 169
Variable Selection......Page 172
Robust Hurdle Models for Counts......Page 176
General Cp Criterion for GLMs......Page 177
Prediction with Robust Models......Page 178
Introduction......Page 179
The Marginal Longitudinal Data Model (MLDA) and Alternatives......Page 181
Classical Estimation and Inference in MLDA......Page 182
Estimators for τ and α......Page 184
GUIDE Data Example......Page 187
Residual Analysis......Page 189
Linear Predictor Parameters......Page 190
Nuisance Parameters......Page 192
IF and Asymptotic Properties......Page 194
GUIDE Data Example (continued)......Page 195
Significance Testing and CIs......Page 196
Variable Selection......Page 197
GUIDE Data Example (continued)......Page 198
LEI Data Example......Page 200
Stillbirth in Piglets Data Example......Page 204
Discussion and Extensions......Page 207
Introduction......Page 209
The Partial Likelihood Approach......Page 211
Empirical Influence Function for the PLE......Page 214
Myeloma Data Example......Page 215
A Sandwich Formula for the Asymptotic Variance......Page 216
A Robust Alternative to the PLE......Page 218
Asymptotic Normality......Page 220
Handling of Ties......Page 222
Myeloma Data Example (continued)......Page 223
Robust Inference and its Current Limitations......Page 224
Robust Estimation......Page 227
Interpretation of the Weights......Page 228
Validation......Page 230
Performance of the ARE......Page 232
Performance of the robust Wald test......Page 234
Regression Quantiles......Page 235
Extension to the Censored Case......Page 237
Asymptotic Properties and Robustness......Page 238
Comparison with the Cox Proportional Hazard Model......Page 239
Lung Cancer Data Example (continued)......Page 240
Limitations and Extensions......Page 242
Appendices......Page 245
A Starting Estimators for MM-estimators of Regression Parameters......Page 247
B Efficiency, LRT. , RAIC and RCp with Biweight .-function for the Regression Model......Page 249
C An Algorithm Procedure for the Constrained S-estimator......Page 253
D Some Distributions of the Exponential Family......Page 255
Fisher Consistency Corrections......Page 257
Asymptotic Variance......Page 258
IRWLS Algorithm for Robust GLM......Page 260
IRWLS Algorithm for Robust GEE......Page 263
Fisher Consistency Corrections......Page 264
G Computation of the CRQ......Page 265
References......Page 267
Index......Page 283