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Applications of Regression Models in Public Health.

By: Contributor(s): Publisher: New York : John Wiley & Sons, Incorporated, 2017Copyright date: ©2017Description: 1 online resource (273 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781119212492
Subject(s): Genre/Form: Additional physical formats: Print version:: Applications of Regression Models in Public HealthDDC classification:
  • 610.2/1
LOC classification:
  • RA407.A67 2017
Online resources:
Contents:
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.
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.
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.
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.
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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.

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.

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.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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