Robust Methods in Biostatistics

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.