Applications of regression models in epidemiology

• Main Author: Suárez Pérez, Erick L.
• Format: eBook Book
• Language: English
• Published: Hoboken, N.J Wiley 2017; John Wiley & Sons, Incorporated; Wiley-Blackwell
• Edition: 1
• Subjects: Epidemiology; Medical statistics; Public health; Regression analysis; Statistical methods

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 usu...

Table of Contents:

• 9: Generalized Linear Models -- 9.1 Introduction -- 9.2 Specific Objectives -- 9.3 Exponential Family of Probability Distributions -- 9.3.1 Binomial Distribution -- 9.3.2 Poisson Distribution -- 9.4 Exponential Family of Probability Distributions with Dispersion -- 9.5 Mean and Variance in EF and EDF -- 9.6 Definition of a Generalized Linear Model -- 9.7 Estimation Methods -- 9.8 Deviance Calculation -- 9.9 Hypothesis Evaluation -- 9.10 Analysis of Residuals -- 9.11 Model Selection -- 9.12 Bayesian Models -- 9.13 Conclusions -- References -- 10: Poisson Regression Models for Cohort Studies -- 10.1 Introduction -- 10.2 Specific Objectives -- 10.3 Incidence Measures -- 10.3.1 Incidence Density -- 10.3.2 Cumulative Incidence -- 10.4 Confounding Variable -- 10.5 Stratified Analysis -- 10.6 Poisson Regression Model -- 10.7 Definition of Adjusted Relative Risk -- 10.8 Interaction Assessment -- 10.9 Relative Risk Estimation -- 10.10 Implementation of the Poisson Regression Model -- 10.11 Conclusion -- Practice Exercise -- References -- 11: Logistic Regression in Case-Control Studies -- 11.1 Introduction -- 11.2 Specific Objectives -- 11.3 Graphical Representation -- 11.4 Definition of the Odds Ratio -- 11.5 Confounding Assessment -- 11.6 Effect Modification -- 11.7 Stratified Analysis -- 11.8 Unconditional Logistic Regression Model -- 11.9 Types of Logistic Regression Models -- 11.9.1 Binary Case -- 11.9.2 Binomial Case -- 11.10 Computing the ORcrude -- 11.11 Computing the Adjusted OR -- 11.12 Inference on OR -- 11.13 Example of the Application of ULR Model: Binomial Case -- 11.14 Conditional Logistic Regression Model -- 11.15 Conclusions -- Practice Exercise -- References -- 12: Regression Models in a Cross-Sectional Study -- 12.1 Introduction -- 12.2 Specific Objectives -- 12.3 Prevalence Estimation Using the Normal Approach
• Applications of Regression Models in Public Health -- Contents -- Preface -- Acknowledgments -- About the Authors -- 1: Basic Concepts for Statistical Modeling -- 1.1 Introduction -- 1.2 Parameter Versus Statistic -- 1.3 Probability Definition -- 1.4 Conditional Probability -- 1.5 Concepts of Prevalence and Incidence -- 1.6 Random Variables -- 1.7 Probability Distributions -- 1.8 Centrality and Dispersion Parameters of a Random Variable -- 1.9 Independence and Dependence of Random Variables -- 1.10 Special Probability Distributions -- 1.10.1 Binomial Distribution -- 1.10.2 Poisson Distribution -- 1.10.3 Normal Distribution -- 1.11 Hypothesis Testing -- 1.12 Confidence Intervals -- 1.13 Clinical Significance Versus Statistical Significance -- 1.14 Data Management -- 1.14.1 Study Design -- 1.14.2 Data Collection -- 1.14.3 Data Entry -- 1.14.4 Data Screening -- 1.14.5 What to Do When Detecting a Data Issue -- 1.14.6 Impact of Data Issues and How to Proceed -- 1.15 Concept of Causality -- References -- 2: Introduction to Simple Linear Regression Models -- 2.1 Introduction -- 2.2 Specific Objectives -- 2.3 Model Definition -- 2.4 Model Assumptions -- 2.5 Graphic Representation -- 2.6 Geometry of the Simple Regression Model -- 2.7 Estimation of Parameters -- 2.8 Variance of Estimators -- 2.9 Hypothesis Testing About the Slope of the Regression Line -- 2.9.1 Using the Student's t-Distribution -- 2.9.2 Using ANOVA -- 2.10 Coefficient of Determination R2 -- 2.11 Pearson Correlation Coefficient -- 2.12 Estimation of Regression Line Values and Prediction -- 2.12.1 Confidence Interval for the Regression Line -- 2.12.2 Prediction Interval of Actual Values of the Response -- 2.13 Example -- 2.14 Predictions -- 2.14.1 Predictions with the Database Used by the Model -- 2.14.2 Predictions with Data Not Used to Create the Model -- 2.14.3 Residual Analysis
• 2.15 Conclusions -- Practice Exercise -- References -- 3: Matrix Representation of the Linear Regression Model -- 3.1 Introduction -- 3.2 Specific Objectives -- 3.3 Definition -- 3.3.1 Matrix -- 3.4 Matrix Representation of a SLRM -- 3.5 Matrix Arithmetic -- 3.5.1 Addition and Subtraction of Matrices -- 3.6 Matrix Multiplication -- 3.7 Special Matrices -- 3.8 Linear Dependence -- 3.9 Rank of a Matrix -- 3.10 Inverse Matrix [A-1] -- 3.11 Application of an Inverse Matrix in a SLRM -- 3.12 Estimation of β Parameters in a SLRM -- 3.13 Multiple Linear Regression Model (MLRM) -- 3.14 Interpretation of the Coefficients in a MLRM -- 3.15 ANOVA in a MLRM -- 3.16 Using Indicator Variables (Dummy Variables) -- 3.17 Polynomial Regression Models -- 3.18 Centering -- 3.19 Multicollinearity -- 3.20 Interaction Terms -- 3.21 Conclusion -- Practice Exercise -- References -- 4: Evaluation of Partial Tests of Hypotheses in a MLRM -- 4.1 Introduction -- 4.2 Specific Objectives -- 4.3 Definition of Partial Hypothesis -- 4.4 Evaluation Process of Partial Hypotheses -- 4.5 Special Cases -- 4.6 Examples -- 4.7 Conclusion -- Practice Exercise -- References -- 5: Selection of Variables in a Multiple Linear Regression Model -- 5.1 Introduction -- 5.2 Specific Objectives -- 5.3 Selection of Variables According to the Study Objectives -- 5.4 Criteria for Selecting the Best Regression Model -- 5.4.1 Coefficient of Determination, R2 -- 5.4.2 Adjusted Coefficient of Determination, RA2 -- 5.4.3 Mean Square Error (MSE) -- 5.4.4 Mallows's Cp -- 5.4.5 Akaike Information Criterion -- 5.4.6 Bayesian Information Criterion -- 5.4.7 All Possible Models -- 5.5 Stepwise Method in Regression -- 5.5.1 Forward Selection -- 5.5.2 Backward Elimination -- 5.5.3 Stepwise Selection -- 5.6 Limitations of Stepwise Methods -- 5.7 Conclusion -- Practice Exercise -- References -- 6: Correlation Analysis
• 12.4 Definition of the Magnitude of the Association -- 12.5 POR Estimation -- 12.5.1 Woolf's Method -- 12.5.2 Exact Method -- 12.6 Prevalence Ratio -- 12.7 Stratified Analysis -- 12.8 Logistic Regression Model -- 12.8.1 Modeling Prevalence Odds Ratio -- 12.8.2 Modeling Prevalence Ratio -- 12.9 Conclusions -- Practice Exercise -- References -- 13: Solutions to Practice Exercises -- Chapter 2 Practice Exercise -- Chapter 3 Practice Exercise -- Chapter 4 Practice Exercise -- Chapter 5 Practice Exercise -- Chapter 6 Practice Exercise -- Chapter 7 Practice Exercise -- Chapter 8 Practice Exercise -- Chapter 10 Practice Exercise -- Chapter 11 Practice Exercise -- Chapter 12 Practice Exercise -- Index -- End User License Agreement
• 6.1 Introduction -- 6.2 Specific Objectives -- 6.3 Main Correlation Coefficients Based on SLRM -- 6.3.1 Pearson Correlation Coefficient ρ -- 6.3.2 Relationship Between r and β1 -- 6.4 Major Correlation Coefficients Based on MLRM -- 6.4.1 Pearson Correlation Coefficient of Zero Order -- 6.4.2 Multiple Correlation Coefficient -- 6.5 Partial Correlation Coefficient -- 6.5.1 Partial Correlation Coefficient of the First Order -- 6.5.2 Partial Correlation Coefficient of the Second Order -- 6.5.3 Semipartial Correlation Coefficient -- 6.6 Significance Tests -- 6.7 Suggested Correlations -- 6.8 Example -- 6.9 Conclusion -- Practice Exercise -- References -- 7: Strategies for Assessing the Adequacy of the Linear Regression Model -- 7.1 Introduction -- 7.2 Specific Objectives -- 7.3 Residual Definition -- 7.4 Initial Exploration -- 7.5 Initial Considerations -- 7.6 Standardized Residual -- 7.7 Jackknife Residuals (R-Student Residuals) -- 7.8 Normality of the Errors -- 7.9 Correlation of Errors -- 7.10 Criteria for Detecting Outliers, Leverage, and Influential Points -- 7.11 Leverage Values -- 7.12 Cook's Distance -- 7.13 COV RATIO -- 7.14 DFBETAS -- 7.15 DFFITS -- 7.16 Summary of the Results -- 7.17 Multicollinearity -- 7.18 Transformation of Variables -- 7.19 Conclusion -- Practice Exercise -- References -- 8: Weighted Least-Squares Linear Regression -- 8.1 Introduction -- 8.2 Specific Objectives -- 8.3 Regression Model with Transformation into the Original Scale of Y -- 8.4 Matrix Notation of the Weighted Linear Regression Model -- 8.5 Application of the WLS Model with Unequal Number of Subjects -- 8.5.1 Design without Intercept -- 8.5.2 Model with Intercept and Weighting Factor -- 8.6 Applications of the WLS Model When Variance Increases -- 8.6.1 First Alternative -- 8.6.2 Second Alternative -- 8.7 Conclusions -- Practice Exercise -- References