Full Description
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.
Contents
Preface. Acknowledgments.
1 Introduction.
1.1 What is Robust Statistics?
1.2 Against What is Robust Statistics Robust?
1.3 Are Diagnostic Methods an Alternative to Robust Statistics?
1.4 How do Robust Statistics Compare with Other Statistical Procedures in Practice?
2 Key Measures and Results.
2.1 Introduction.
2.2 Statistical Tools for Measuring Robustness Properties.
2.3 General Approaches for Robust Estimation.
2.4 Statistical Tools for Measuring Tests Robustness.
2.5 General Approaches for Robust Testing.
3 Linear Regression.
3.1 Introduction.
3.2 Estimating the Regression Parameters.
3.3 Testing the Regression Parameters.
3.4 Checking and Selecting the Model.
3.5 CardiovascularRiskFactorsDataExample.
4 Mixed Linear Models.
4.1 Introduction.
4.2 The MLM.
4.3 Classical Estimation and Inference.
4.4 Robust Estimation.
4.5 Robust Inference.
4.6 Checking the Model.
4.7 Further Examples.
4.8 Discussion and Extensions.
5 Generalized Linear Models.
5.1 Introduction.
5.2 The GLM.
5.3 A Class of M-estimators forGLMs.
5.4 Robust Inference.
5.5 Breastfeeding Data Example.
5.6 Doctor Visits Data Example.
5.7 Discussion and Extensions.
6 Marginal Longitudinal Data Analysis.
6.1 Introduction.
6.2 The Marginal Longitudinal Data Model (MLDA) and Alternatives.
6.3 A Robust GEE-type Estimator.
6.4 Robust Inference.
6.5 LEI Data Example.
6.6 Stillbirth in Piglets Data Example.
6.7 Discussion and Extensions.
7 Survival Analysis.
7.1 Introduction.
7.2 TheCox Model.
7.3 Robust Estimation and Inference in the Cox Model.
7.4 The Veteran's Administration Lung Cancer Data.
7.5 Structural Misspecifications.
7.6 Censored Regression Quantiles.
Appendices.
A Starting Estimators for MM-estimators of Regression Parameters.
B Efficiency, LRTρ , RAIC and RCp with Biweight ρ-function for the Regression Model.
C An Algorithm Procedure for the Constrained S-estimator.
D Some Distributions of the Exponential Family.
E Computations for the Robust GLM Estimator.
E.1 Fisher Consistency Corrections.
E.2 Asymptotic Variance.
E.3 IRWLS Algorithm for Robust GLM.
F Computations for the Robust GEE Estimator.
F.1 IRWLS Algorithm for Robust GEE.
F.2 Fisher Consistency Corrections.
G Computation of the CRQ.
References.
Index.
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