Applied Logistic Regression

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.

“In conclusion, the index was mercifully complete, and all items searched for were found (nice cross-referencing too)  In summary:  Highly recommended.”  (Scientific Computing, 1 May 2013)

• Preface to the Third Edition xiii1 Introduction to the Logistic Regression Model 11.1 Introduction 11.2 Fitting the Logistic Regression Model 81.3 Testing for the Significance of the Coefficients 101.4 Confidence Interval Estimation 151.5 Other Estimation Methods 201.6 Data Sets Used in Examples and Exercises 221.6.1 The ICU Study 221.6.2 The Low Birth Weight Study 241.6.3 The Global Longitudinal Study of Osteoporosis in Women 241.6.4 The Adolescent Placement Study 261.6.5 The Burn Injury Study 271.6.6 The Myopia Study 291.6.7 The NHANES Study 311.6.8 The Polypharmacy Study 31Exercises 322 The Multiple Logistic Regression Model 352.1 Introduction 352.2 The Multiple Logistic Regression Model 352.3 Fitting the Multiple Logistic Regression Model 372.4 Testing for the Significance of the Model 392.5 Confidence Interval Estimation 422.6 Other Estimation Methods 45Exercises 463 Interpretation of the Fitted Logistic Regression Model 493.1 Introduction 493.2 Dichotomous Independent Variable 503.3 Polychotomous Independent Variable 563.4 Continuous Independent Variable 623.5 Multivariable Models 643.6 Presentation and Interpretation of the Fitted Values 773.7 A Comparison of Logistic Regression and Stratified Analysis for 2 × 2 Tables 82Exercises 874 Model-Building Strategies and Methods for Logistic Regression 894.1 Introduction 894.2 Purposeful Selection of Covariates 894.2.1 Methods to Examine the Scale of a Continuous Covariate in the Logit 944.2.2 Examples of Purposeful Selection 1074.3 Other Methods for Selecting Covariates 1244.3.1 Stepwise Selection of Covariates 1254.3.2 Best Subsets Logistic Regression 1334.3.3 Selecting Covariates and Checking their Scale Using Multivariable Fractional Polynomials 1394.4 Numerical Problems 145Exercises 1505 Assessing the Fit of the Model 1535.1 Introduction 1535.2 Summary Measures of Goodness of Fit 1545.2.1 Pearson Chi-Square Statistic, Deviance, and Sum-of-Squares 1555.2.2 The Hosmer–Lemeshow Tests 1575.2.3 Classification Tables 1695.2.4 Area Under the Receiver Operating Characteristic Curve 1735.2.5 Other Summary Measures 1825.3 Logistic Regression Diagnostics 1865.4 Assessment of Fit via External Validation 2025.5 Interpretation and Presentation of the Results from a Fitted Logistic Regression Model 212Exercises 2236 Application of Logistic Regression with Different Sampling Models 2276.1 Introduction 2276.2 Cohort Studies 2276.3 Case-Control Studies 2296.4 Fitting Logistic Regression Models to Data from Complex Sample Surveys 233Exercises 2427 Logistic Regression for Matched Case-Control Studies 2437.1 Introduction 2437.2 Methods For Assessment of Fit in a 1–M Matched Study 2487.3 An Example Using the Logistic Regression Model in a 1–1 Matched Study 2517.4 An Example Using the Logistic Regression Model in a 1–M Matched Study 260Exercises 2678 Logistic Regression Models for Multinomial and Ordinal Outcomes 2698.1 The Multinomial Logistic Regression Model 2698.1.1 Introduction to the Model and Estimation of Model Parameters 2698.1.2 Interpreting and Assessing the Significance of the Estimated Coefficients 2728.1.3 Model-Building Strategies for Multinomial Logistic Regression 2788.1.4 Assessment of Fit and Diagnostic Statistics for the Multinomial Logistic Regression Model 2838.2 Ordinal Logistic Regression Models 2898.2.1 Introduction to the Models, Methods for Fitting, and Interpretation of Model Parameters 2898.2.2 Model Building Strategies for Ordinal Logistic Regression Models 305Exercises 3109 Logistic Regression Models for the Analysis of Correlated Data 3139.1 Introduction 3139.2 Logistic Regression Models for the Analysis of Correlated Data 3159.3 Estimation Methods for Correlated Data Logistic Regression Models 3189.4 Interpretation of Coefficients from Logistic Regression Models for the Analysis of Correlated Data 3239.4.1 Population Average Model 3249.4.2 Cluster-Specific Model 3269.4.3 Alternative Estimation Methods for the Cluster-Specific Model 3339.4.4 Comparison of Population Average and Cluster-Specific Model 3349.5 An Example of Logistic Regression Modeling with Correlated Data 3379.5.1 Choice of Model for Correlated Data Analysis 3389.5.2 Population Average Model 3399.5.3 Cluster-Specific Model 3449.5.4 Additional Points to Consider when Fitting Logistic Regression Models to Correlated Data 3519.6 Assessment of Model Fit 3549.6.1 Assessment of Population Average Model Fit 3549.6.2 Assessment of Cluster-Specific Model Fit 3659.6.3 Conclusions 374Exercises 37510 Special Topics 37710.1 Introduction 37710.2 Application of Propensity Score Methods in Logistic Regression Modeling 37710.3 Exact Methods for Logistic Regression Models 38710.4 Missing Data 39510.5 Sample Size Issues when Fitting Logistic Regression Models 40110.6 Bayesian Methods for Logistic Regression 40810.6.1 The Bayesian Logistic Regression Model 41010.6.2 MCMC Simulation 41110.6.3 An Example of a Bayesian Analysis and Its Interpretation 41910.7 Other Link Functions for Binary Regression Models 43410.8 Mediation 44110.8.1 Distinguishing Mediators from Confounders 44110.8.2 Implications for the Interpretation of an Adjusted Logistic Regression Coefficient 44310.8.3 Why Adjust for a Mediator? 44410.8.4 Using Logistic Regression to Assess Mediation: Assumptions 44510.9 More About Statistical Interaction 44810.9.1 Additive versus Multiplicative Scale–Risk Difference versus Odds Ratios 44810.9.2 Estimating and Testing Additive Interaction 451Exercises 456References 459Index 479