Heritier / Cantoni / Copt Robust Methods in Biostatistics

1. Auflage 2009
ISBN: 978-0-470-74054-5
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 292 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

Robust statistics is an extension of classical statistics thatspecifically takes into account the concept that the underlyingmodels used to describe data are only approximate. Its basicphilosophy is to produce statistical procedures which are stablewhen the data do not exactly match the postulated models as it isthe case for example with outliers.
Robust Methods in Biostatistics proposes robustalternatives to common methods used in statistics in general and inbiostatistics in particular and illustrates their use on manybiomedical datasets. The methods introduced include robustestimation, 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 appliedlevel within the framework of each general class of models, with aparticular emphasis put on practical data analysis. This book is ofparticular use for research students,applied statisticians andpractitioners in the health field interested in more stablestatistical techniques. An accompanying website provides R code forcomputing all of the methods described, as well as for analyzingall the datasets used in the book.

Autoren/Hrsg.

Heritier, Stephane

Cantoni, Eva

Copt, Samuel

Victoria-Feser, Maria-Pia

Inhaltsverzeichnis

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 RobustStatistics?
1.4 How do Robust Statistics Compare with Other StatisticalProcedures 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) andAlternatives.
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-estimatorsof Regression Parameters.
B Efficiency, LRTrho , RAIC andRCp with Biweightrho-function for the Regression Model.
C An Algorithm Procedure for the ConstrainedS-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.