Applications of Regression Models in Epidemiology

Erick Suárez, Cynthia M. Pérez, Roberto Rivera, Melissa N. Martínez

• Publisher: Wiley
• Year: 2017
• Print ISBN: 9781119212485
• eBook ISBN: 9781119212508
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

1
Basic Concepts for Statistical Modeling

Aim: Upon completing this chapter, the reader should be able to understand the basic concepts for statistical modeling in public health.

1.1 Introduction

It is assumed that the reader has taken introductory classes in biostatistics and epidemiology. Nevertheless, in this chapter we review the basic concepts of probability and statistics and their application to the public health field. The importance of data quality is also addressed and a discussion on causality in the context of epidemiological studies is provided.

Statistics is defined as the science and art of collecting, organizing, presenting, summarizing, and interpreting data. There is strong theoretical evidence backing many of the statistical procedures that will be discussed. However, in practice, statistical methods require decisions on organizing the data, constructing plots, and using rules of thumb that make statistics an art as well as a science.

Biostatistics is the branch of statistics that applies statistical methods to health sciences. The goal is typically to understand and improve the health of a population. A population, sometimes referred to as the target population, can be defined as the group of interest in our analysis. In public health, the population can be composed of healthy individuals or those at risk of disease and death. For example, study populations may include healthy people, breast cancer patients, obese subjects residing in Puerto Rico, persons exposed to high levels of asbestos, or persons with high-risk behaviors. Among the objectives of epidemiological studies are to describe the burden of disease in populations and identify the etiology of diseases, essential information for planning health services. It is convenient to frame our research questions about a population in terms of traits. A measurement made of a population is known as a parameter. Examples are: prevalence of diabetes among Hispanics, incidence of breast cancer in older women, and the average hospital stay of acute ischemic stroke patients in Puerto Rico. We cannot always obtain the parameter directly by counting or measuring from the population of interest. It might be too costly, time-consuming, the population may be too large, or unfeasible for other reasons. For example, if a health officer believes that the incidence of hepatitis C has increased in the last 5 years in a region, he or she cannot recommend a new preventive program without any data. Some information has to be collected from a sample of the population, if the resources are limited. Another example is the assessment of the effectiveness of a new breast cancer screening strategy. Since it is not practical to perform this assessment in all women at risk, an alternative is to select at least two samples of women, one that will receive the new screening strategy and another that will receive a different modality.

There are several ways to select samples from a population. We want to make the sample to be as representative of the population as possible to make appropriate inferences about that population. However, there are other aspects to consider such as convenience, cost, time, and availability of resources. The sample allows us to estimate the parameter of interest through what is known as a sample statistic, or statistic for short. Although the statistic estimates the parameter, there are key differences between the statistic and the parameter.

1.2 Parameter Versus Statistic

Let us take a look at the distinction between a parameter and a statistic. The classical concept of a parameter is a numerical value that, for our purposes, at a given period of time is constant, or fixed; for example, the mean birth weight in grams of newborns to Chinese women in 2015. On the other hand, a statistic is a numerical value that is random; for example, the mean birth weight in grams of 1000 newborns selected randomly from the women who delivered in maternity units of hospitals in China in the last 2 years. Coming from a subset of the population, the value of the statistic depends on the subjects that fall in the sample and this is what makes the statistic random. Sometimes, Greek symbols are used to denote parameters, to better distinguish between parameters and statistics. Sample statistics can provide reliable estimates of parameters as long as the population is carefully specified relative to the problem at hand and the sample is representative of that population. That the sample should be representative of the population may sound trivial but it may be easier said than done. In clinical research, participants are often volunteers, a technique known as convenience sampling. The advantage of convenience sampling is that it is less expensive and time-consuming. The disadvantage is that results from volunteers may differ from those who do not volunteer and hence the results may be biased. The process of reaching conclusions about the population based on a sample is known as statistical inference. As long as the data obtained from the sample are representative of the population, we can reach conclusions about the population by using the statistics gathered from the sample, while accounting for the uncertainty around these statistics through probab...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Preface
• Acknowledgments
• About the Authors
• Chapter 1: Basic Concepts for Statistical Modeling
• Chapter 2: Introduction to Simple Linear Regression Models
• Chapter 3: Matrix Representation of the Linear Regression Model
• Chapter 4: Evaluation of Partial Tests of Hypotheses in a MLRM
• Chapter 5: Selection of Variables in a Multiple Linear Regression Model
• Chapter 6: Correlation Analysis
• Chapter 7: Strategies for Assessing the Adequacy of the Linear Regression Model
• Chapter 8: Weighted Least-Squares Linear Regression
• Chapter 9: Generalized Linear Models
• Chapter 10: Poisson Regression Models for Cohort Studies
• Chapter 11: Logistic Regression in Case–Control Studies
• Chapter 12: Regression Models in a Cross-Sectional Study
• Chapter 13: Solutions to Practice Exercises
• Index
• End User License Agreement