Main description:

A one-stop guide for public health students and practitioners learning the applications of classical regression models in epidemiology This book is written for public health professionals and students interested in applying regression models in the field of epidemiology. The academic material is usually covered in public health courses including (i) Applied Regression Analysis, (ii) Advanced Epidemiology, and (iii) Statistical Computing. The book is composed of 13 chapters, including an introduction chapter that covers basic concepts of statistics and probability. Among the topics covered are linear regression model, polynomial regression model, weighted least squares, methods for selecting the best regression equation, and generalized linear models and their applications to different epidemiological study designs. An example is provided in each chapter that applies the theoretical aspects presented in that chapter. In addition, exercises are included and the final chapter is devoted to the solutions of these academic exercises with answers in all of the major statistical software packages, including STATA, SAS, SPSS, and R.
It is assumed that readers of this book have a basic course in biostatistics, epidemiology, and introductory calculus. The book will be of interest to anyone looking to understand the statistical fundamentals to support quantitative research in public health. In addition, this book: Is based on the authors course notes from 20 years teaching regression modeling in public health courses Provides exercises at the end of each chapter Contains a solutions chapter with answers in STATA, SAS, SPSS, and R Provides real-world public health applications of the theoretical aspects contained in the chapters Applications of Regression Models in Epidemiology is a reference for graduate students in public health and public health practitioners. ERICK SUAREZ is a Professor of the Department of Biostatistics and Epidemiology at the University of Puerto Rico School of Public Health. He received a Ph.D. degree in Medical Statistics from the London School of Hygiene and Tropical Medicine. He has 29 years of experience teaching biostatistics. CYNTHIA M. PEREZ is a Professor of the Department of Biostatistics and Epidemiology at the University of Puerto Rico School of Public Health. She received an M.S.
degree in Statistics and a Ph.D. degree in Epidemiology from Purdue University. She has 22 years of experience teaching epidemiology and biostatistics. ROBERTO RIVERA is an Associate Professor at the College of Business at the University of Puerto Rico at Mayaguez. He received a Ph.D. degree in Statistics from the University of California in Santa Barbara. He has more than five years of experience teaching statistics courses at the undergraduate and graduate levels. MELISSA N. MARTINEZ is an Account Supervisor at Havas Media International. She holds an MPH in Biostatistics from the University of Puerto Rico and an MSBA from the National University in San Diego, California. For the past seven years, she has been performing analyses for the biomedical research and media advertising fields.

Contents:

Preface xv Acknowledgments xvii About the Authors xix 1 Basic Concepts for Statistical Modeling 1 1.1 Introduction 1 1.2 Parameter Versus Statistic 2 1.3 Probability Definition 3 1.4 Conditional Probability 3 1.5 Concepts of Prevalence and Incidence 4 1.6 Random Variables 4 1.7 Probability Distributions 4 1.8 Centrality and Dispersion Parameters of a Random Variable 6 1.9 Independence and Dependence of Random Variables 7 1.10 Special Probability Distributions 7 1.11 Hypothesis Testing 11 1.12 Confidence Intervals 14 1.13 Clinical Significance Versus Statistical Significance 14 1.14 Data Management 15 1.15 Concept of Causality 21 References 22 2 Introduction to Simple Linear Regression Models 25 2.1 Introduction 25 2.2 Specific Objectives 26 2.3 Model Definition 26 2.4 Model Assumptions 28 2.5 Graphic Representation 29 2.6 Geometry of the Simple Regression Model 29 2.7 Estimation of Parameters 30 2.8 Variance of Estimators 31 2.9 Hypothesis Testing About the Slope of the Regression Line 32 2.10 Coefficient of Determination R2 34 2.11 Pearson Correlation Coefficient 34 2.12 Estimation of Regression Line Values and Prediction 35 2.13 Example 36 2.14 Predictions 39 2.15 Conclusions 46 Practice Exercise 47 References 48 3 Matrix Representation of the Linear Regression Model 49 3.1 Introduction 49 3.2 Specific Objectives 49 3.3 Definition 50 3.3.1 Matrix 50 3.4 Matrix Representation of a SLRM 50 3.5 Matrix Arithmetic 51 3.6 Matrix Multiplication 52 3.7 Special Matrices 53 3.8 Linear Dependence 54 3.9 Rank of a Matrix 54 3.10 Inverse Matrix [A 54 3.11 Application of an Inverse Matrix in a SLRM 56 3.12 Estimation of Parameters in a SLRM 56 3.13 Multiple Linear Regression Model (MLRM) 57 3.14 Interpretation of the Coefficients in a MLRM 58 3.15 ANOVA in a MLRM 58 3.16 Using Indicator Variables (Dummy Variables) 60 3.17 Polynomial Regression Models 63 3.18 Centering 64 3.19 Multicollinearity 65 3.20 Interaction Terms 65 3.21 Conclusion 66 Practice Exercise 66 References 67 4 Evaluation of Partial Tests of Hypotheses in a MLRM 69 4.1 Introduction 69 4.2 Specific Objectives 69 4.3 Definition of Partial Hypothesis 70 4.4 Evaluation Process of Partial Hypotheses 71 4.5 Special Cases 71 4.6 Examples 72 4.7 Conclusion 75 Practice Exercise 75 References 75 5 Selection of Variables in a Multiple Linear Regression Model 77 5.1 Introduction 77 5.2 Specific Objectives 77 5.3 Selection of Variables According to the Study Objectives 77 5.4 Criteria for Selecting the Best Regression Model 78 5.5 Stepwise Method in Regression 80 5.6 Limitations of Stepwise Methods 83 5.7 Conclusion 83 Practice Exercise 84 References 85 6 Correlation Analysis 87 6.1 Introduction 87 6.2 Specific Objectives 87 6.3 Main Correlation Coefficients Based on SLRM 87 6.4 Major Correlation Coefficients Based on MLRM 89 6.5 Partial Correlation Coefficient 90 6.6 Significance Tests 92 6.7 Suggested Correlations 92 6.8 Example 92 6.9 Conclusion 94 Practice Exercise 95 References 95 7 Strategies for Assessing the Adequacy of the Linear Regression Model 97 7.1 Introduction 97 7.2 Specific Objectives 98 7.3 Residual Definition 98 7.4 Initial Exploration 98 7.5 Initial Considerations 102 7.6 Standardized Residual 102 7.7 Jackknife Residuals (R-Student Residuals) 104 7.8 Normality of the Errors 105 7.9 Correlation of Errors 106 7.10 Criteria for Detecting Outliers, Leverage, and Influential Points 107 7.11 Leverage Values 108 7.12 Cook s Distance 108 7.13 COV RATIO 109 7.14 DFBETAS 110 7.15 DFFITS 110 7.16 Summary of the Results 111 7.17 Multicollinearity 111 7.18 Transformation of Variables 114 7.19 Conclusion 114 Practice Exercise 115 References 116 8 Weighted Least-Squares Linear Regression 117 8.1 Introduction 117 8.2 Specific Objectives 117 8.3 Regression Model with Transformation into the Original Scale of Y 117 8.4 Matrix Notation of the Weighted Linear Regression Model 119 8.5 Application of the WLS Model with Unequal Number of Subjects 120 8.6 Applications of the WLS Model When Variance Increases 123 8.7 Conclusions 125 Practice Exercise 126 References 127 9 Generalized Linear Models 129 9.1 Introduction 129 9.2 Specific Objectives 129 9.3 Exponential Family of Probability Distributions 130 9.4 Exponential Family of Probability Distributions with Dispersion 131 9.5 Mean and Variance in EF and EDF 132 9.6 Definition of a Generalized Linear Model 133 9.7 Estimation Methods 134 9.8 Deviance Calculation 135 9.9 Hypothesis Evaluation 136 9.10 Analysis of Residuals 138 9.11 Model Selection 139 9.12 Bayesian Models 139 9.13 Conclusions 140 References 140 10 Poisson Regression Models for Cohort Studies 141 10.1 Introduction 141 10.2 Specific Objectives 142 10.3 Incidence Measures 142 10.4 Confounding Variable 146 10.5 Stratified Analysis 147 10.6 Poisson Regression Model 148 10.7 Definition of Adjusted Relative Risk 149 10.8 Interaction Assessment 150 10.9 Relative Risk Estimation 151 10.10 Implementation of the Poisson Regression Model 152 10.11 Conclusion 161 Practice Exercise 162 References 162 11 Logistic Regression in Case Control Studies 165 11.1 Introduction 165 11.2 Specific Objectives 166 11.3 Graphical Representation 166 11.4 Definition of the Odds Ratio 167 11.5 Confounding Assessment 168 11.6 Effect Modification 168 11.7 Stratified Analysis 169 11.8 Unconditional Logistic Regression Model 170 11.9 Types of Logistic Regression Models 171 11.10 Computing the ORcrude 173 11.11 Computing the Adjusted OR 173 11.12 Inference on OR 174 11.13 Example of the Application of ULR Model: Binomial Case 175 11.14 Conditional Logistic Regression Model 178 11.15 Conclusions 183 Practice Exercise 183 References 188 12 Regression Models in a Cross-Sectional Study 191 12.1 Introduction 191 12.2 Specific Objectives 192 12.3 Prevalence Estimation Using the Normal Approach 192 12.4 Definition of the Magnitude of the Association 198 12.5 POR Estimation 200 12.6 Prevalence Ratio 204 12.7 Stratified Analysis 204 12.8 Logistic Regression Model 207 12.9 Conclusions 210 Practice Exercise 210 References 211 13 Solutions to Practice Exercises 213 Chapter 2 Practice Exercise 213 Chapter 3 Practice Exercise 216 Chapter 4 Practice Exercise 220 Chapter 5 Practice Exercise 221 Chapter 6 Practice Exercise 223 Chapter 7 Practice Exercise 225 Chapter 8 Practice Exercise 228 Chapter 10 Practice Exercise 230 Chapter 11 Practice Exercise 233 Chapter 12 Practice Exercise 240 Index 245