Applications of regression models in epidemiology / Erick Suarez [and three others].

Format:

Book

Author/Creator:

Suarez Perez, Erick L., 1953- author.

Series:

THEi Wiley ebooks.

THEi Wiley ebooks

Language:

English

Subjects (All):

Epidemiology--Statistical methods.

Epidemiology.

Medical statistics.

Regression analysis.

Public health.

Physical Description:

1 online resource (212 pages) : illustrations, tables

Edition:

1st ed.

Place of Publication:

Hoboken, New Jersey : Wiley, 2017.

System Details:

Access using campus network via VPN at home (THEi Users Only).

Summary:

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 SUÁREZ 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. PÉREZ 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. MARTÍNEZ 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:

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

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

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

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

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

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

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

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

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

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

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

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.

Notes:

Description based on print version record.

Includes bibliographical references at the end of each chapters and index.

ISBN:

9781119212508

1119212502

9781119212515

1119212510

OCLC:

972641699