Robust Methods in Biostatistics

Maybe the title is redundant -- I'm not sure how many standard-bearer texts exist on robust biostatistics exist (Huber's general treatment of robust statistics, in its revised edition, is quite good, but it does not cover some of the practicalities involved in longitudinal studies or survival analysis). This one has a full development of the relevant M-estimators and R-estimators without a ton of measure theoretic filler (sorry folks, but if measure theory was relevant to me, my committee would have forced me to take it). My copy -- actually, the University's copy -- currently resides with a physicist friend who signed on to work with me on a doubly robust model for estimating side effect risks. I didn't realize it until recently, but this book also covers some of the material underlying marginal structural models, in addition to a good treatment of standard, weighted, and robust GLM practicalities. The book contains some example code in R, but it is most certainly not an 'R book' -- do not expect a hand-holding practicum on how to use someone else's packages, because that is not what the book is about.I haven't seen a better treatment of the material. It's not McCullagh & Nelder, but it's as well written as Huber's book, and that's no small feat in itself. 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 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. Robust Methods in Biostatistics proposes robust alternatives to common methods used in statistics in general and in biostatistics in particular and illustrates their use on many biomedical datasets. The methods introduced include robust estimation, testing, model selection, model check and diagnostics. They are developed for the following general classes of models: Linear regression Generalized linear models Linear mixed models Marginal longitudinal data models Cox survival analysis model The methods are introduced both at a theoretical and applied level within the framework of each general class of models, with a particular emphasis put on practical data analysis. This book is of particular use for research students,applied statisticians and practitioners in the health field interested in more stable statistical techniques. An accompanying website provides R code for computing all of the methods described, as well as for analyzing all the datasets used in the book. 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. This Book Proposes Robust Alternatives To Common Methods Used In Statistics In General And In Biostatistics In Particular And Illustrates Their Use On Many Biomedical Datasets. The Methods Introduced Include Robust Estimation, Testing, Model Selection, Model Check And Diagnostics. The Methods Are Introduced Both At A Theoretical And Applied Level Within The Framework Of Each General Class Of Models, With A Particular Emphasis Put On Practical Data Analysis. Key Measures And Results -- Linear Regression -- Mixed Linear Models -- Generalized Linear Models -- Marginal Longitudinal Data Analysis -- Survival Analysis. Stephane Heritier ... [et Al.]. Includes Bibliographical References (p. [249]-264) And Index. Regulatory bodies and medical journals regularly raise their standards in terms of the quality of statistical analyses presented, wanting to ensure statistical methods are not misused leading to wrong conclusions. Following this trend, there is a growing need for robust statistics in medical research. Robust statistics is an extension of classical statistics that specifically takes into account that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable with respect to changes in the data or model departures. Robust Methods in Biostatistics is the first book on robust methodology to be directed specifically at biostatistics, which would benefit both fields greatly. It allows students, biostatisticians and researchers of all levels easy access by introducing each chapter's topic with the classical approach before explaining the robust alternatives Regulatory bodies and medical journals regularly raise their standards in terms of the quality of statistical analyses presented, wanting to ensure statistical methods are not misused leading to wrong conclusions. Following this trend there is a growing need for robust statistics in medical research. Robust statistics is an extension of classical statistics that specifically takes into account that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable withy respect to changes in the data or model departures.