Applied Logistic Regression

A new edition of the definitive guide to logistic regression modeling for health science and other applications

This thoroughly expanded Third Edition provides an easily accessible introduction to the logistic regression (LR) model and highlights the power of this model by examining the relationship between a dichotomous outcome and a set of covariables.

Applied Logistic Regression, Third Edition emphasizes applications in the health sciences and handpicks topics that best suit the use of modern statistical software. The book provides readers with state-of-the-art techniques for building, interpreting, and assessing the performance of LR models. New and updated features include:

• A chapter on the analysis of correlated outcome data

• A wealth of additional material for topics ranging from Bayesian methods to assessing model fit

• Rich data sets from real-world studies that demonstrate each method under discussion

• Detailed examples and interpretation of the presented results as well as exercises throughout

Applied Logistic Regression, Third Edition is a must-have guide for professionals and researchers who need to model nominal or ordinal scaled outcome variables in public health, medicine, and the social sciences as well as a wide range of other fields and disciplines.

Auteur

DAVID W. HOSMER, Jr., PhD, is Professor Emeritus of
Biostatistics at the School of Public Health and Health Sciences at
the University of Massachusetts Amherst.

STANLEY LEMESHOW, PhD, is Professor of Biostatistics and
Founding Dean of the College of Public Health at The Ohio State
University, Columbus, Ohio.

RODNEY X. STURDIVANT, PhD, is Associate Professor and
Founding Director of the Center for Data Analysis and Statistics at
the United States Military Academy at West Point, New York.

Résumé
A new edition of the definitive guide to logistic regression modeling for health science and other applications This thoroughly expanded Third Edition provides an easily accessible introduction to the logistic regression (LR) model and highlights the power of this model by examining the relationship between a dichotomous outcome and a set of covariables.

Applied Logistic Regression, Third Edition emphasizes applications in the health sciences and handpicks topics that best suit the use of modern statistical software. The book provides readers with state-of-the-art techniques for building, interpreting, and assessing the performance of LR models. New and updated features include:

• A chapter on the analysis of correlated outcome data
• A wealth of additional material for topics ranging from Bayesian methods to assessing model fit
• Rich data sets from real-world studies that demonstrate each method under discussion
• Detailed examples and interpretation of the presented results as well as exercises throughout
  Applied Logistic Regression, Third Edition is a must-have guide for professionals and researchers who need to model nominal or ordinal scaled outcome variables in public health, medicine, and the social sciences as well as a wide range of other fields and disciplines.

Contenu

Preface to the Third Edition xiii

1 Introduction to the Logistic Regression Model 1

1.1 Introduction 1

1.2 Fitting the Logistic Regression Model 8

1.3 Testing for the Significance of the Coefficients 10

1.4 Confidence Interval Estimation 15

1.5 Other Estimation Methods 20

1.6 Data Sets Used in Examples and Exercises 22

1.6.1 The ICU Study 22

1.6.2 The Low Birth Weight Study 24

1.6.3 The Global Longitudinal Study of Osteoporosis in Women 24

1.6.4 The Adolescent Placement Study 26

1.6.5 The Burn Injury Study 27

1.6.6 The Myopia Study 29

1.6.7 The NHANES Study 31

1.6.8 The Polypharmacy Study 31

Exercises 32

2 The Multiple Logistic Regression Model 35

2.1 Introduction 35

2.2 The Multiple Logistic Regression Model 35

2.3 Fitting the Multiple Logistic Regression Model 37

2.4 Testing for the Significance of the Model 39

2.5 Confidence Interval Estimation 42

2.6 Other Estimation Methods 45

Exercises 46

3 Interpretation of the Fitted Logistic Regression Model 49

3.1 Introduction 49

3.2 Dichotomous Independent Variable 50

3.3 Polychotomous Independent Variable 56

3.4 Continuous Independent Variable 62

3.5 Multivariable Models 64

3.6 Presentation and Interpretation of the Fitted Values 77

3.7 A Comparison of Logistic Regression and Stratified Analysis for 2 × 2 Tables 82

Exercises 87

4 Model-Building Strategies and Methods for Logistic Regression 89

4.1 Introduction 89

4.2 Purposeful Selection of Covariates 89

4.2.1 Methods to Examine the Scale of a Continuous Covariate in the Logit 94

4.2.2 Examples of Purposeful Selection 107

4.3 Other Methods for Selecting Covariates 124

4.3.1 Stepwise Selection of Covariates 125

4.3.2 Best Subsets Logistic Regression 133

4.3.3 Selecting Covariates and Checking their Scale Using Multivariable Fractional Polynomials 139

4.4 Numerical Problems 145

Exercises 150

5 Assessing the Fit of the Model 153

5.1 Introduction 153

5.2 Summary Measures of Goodness of Fit 154

5.2.1 Pearson Chi-Square Statistic, Deviance, and Sum-of-Squares 155

5.2.2 The HosmerLemeshow Tests 157

5.2.3 Classification Tables 169

5.2.4 Area Under the Receiver Operating Characteristic Curve 173

5.2.5 Other Summary Measures 182

5.3 Logistic Regression Diagnostics 186

5.4 Assessment of Fit via External Validation 202

5.5 Interpretation and Presentation of the Results from a Fitted Logistic Regression Model 212

Exercises 223

6 Application of Logistic Regression with Different Sampling Models 227

6.1 Introduction 227

6.2 Cohort Studies 227

6.3 Case-Control Studies 229

6.4 Fitting Logistic Regression Models to Data from Complex Sample Surveys 233

Exercises 242

7 Logistic Regression for Matched Case-Control Studies 243

7.1 Introduction 243

7.2 Methods For Assessment of Fit in a 1M Matched Study 248

7.3 An Example Using the Logistic Regression Model in a 11 Matched Study 251

7.4 An Example Using the Logistic Regression Model in a 1M Matched Study 260

Exercises 267

8 Logistic Regression Models for Multinomial and Ordinal Outcomes 269

8.1 The Multinomial Logistic Regression Model 269

8.1.1 Introduction to the Model and Estimation of Model Parameters 269

8.1.2 Interpreting and Assessing the Significance of the Estimated Coefficients 272

8.1.3 Model-Building Strategies for Multinomial Logistic Regression 278

8.1.4 Assessment of Fit and Diagnostic Statistics for the Multinomial Logistic Regression Model 283 8.2 Ordinal Logistic Regr...