Statistical Thinking in Epidemiology

Statistical Thinking in Epidemiology

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    • Provides an alternative and intuitive understanding of statistical modeling using vector geometry
    • Uses vector geometry extensively to explain the problems with collinearity in linear models and other complex statistical models
    • Introduces a wide range of statistical models as analytical tools: from simple regression, analysis of covariance, multilevel models, latent growth models, growth mixture models to partial least square regression
    • Examples come from real research settings and are discussed in great detail without over-simplification
    • Discusses vital but often poorly understood statistical concepts, such as mathematical coupling, regression to the mean, co-linearity, reversal paradox and statistical interaction


    While biomedical researchers may be able to follow instructions in the manuals accompanying the statistical software packages, they do not always have sufficient knowledge to choose the appropriate statistical methods and correctly interpret their results. Statistical Thinking in Epidemiology examines common methodological and statistical problems in the use of correlation and regression in medical and epidemiological research: mathematical coupling, regression to the mean, collinearity, the reversal paradox, and statistical interaction.

    Statistical Thinking in Epidemiology is about thinking statistically when looking at problems in epidemiology. The authors focus on several methods and look at them in detail: specific examples in epidemiology illustrate how different model specifications can imply different causal relationships amongst variables, and model interpretation is undertaken with appropriate consideration of the context of implicit or explicit causal relationships. This book is intended for applied statisticians and epidemiologists, but can also be very useful for clinical and applied health researchers who want to have a better understanding of statistical thinking.

    Throughout the book, statistical software packages R and Stata are used for general statistical modeling, and Amos and Mplus are used for structural equation modeling.

    Table of Contents

    Uses of Statistics in Medicine and Epidemiology
    Structure and Objectives of This Book
    Nomenclature in This Book

    Vector Geometry of Linear Models for Epidemiologists

    Basic Concepts of Vector Geometry in Statistics
    Correlation and Simple Regression in Vector Geometry
    Linear Multiple Regression in Vector Geometry
    Significance Testing of Correlation and Simple Regression in Vector Geometry
    Significance Testing of Multiple Regression in Vector Geometry

    Path Diagrams and Directed Acyclic Graphs

    Path Diagrams
    Directed Acyclic Graphs
    Direct and Indirect Effects

    Mathematical Coupling and Regression to the Mean in the Relation between Change and Initial Value
    Historical Background
    Why Should Change Not Be Regressed on Initial Value? A Review of the Problem
    Proposed Solutions in the Literature
    Comparison between Oldham’s Method and Blomqvist’s Formula
    Oldham’s Method and Blomqvist’s Formula Answer Two Different Questions
    What Is Galton’s Regression to the Mean?
    Testing the Correct Null Hypothesis
    Evaluation of the Categorisation Approach
    Testing the Relation between Changes and Initial Values When There Are More than Two Occasions

    Analysis of Change in Pre-/Post-Test Studies

    Analysis of Change in Randomised Controlled Trials
    Comparison of Six Methods
    Analysis of Change in Non-Experimental Studies: Lord’s Paradox
    ANCOVA and t-Test for Change Scores Have Different Assumptions

    Collinearity and Multicollinearity

    Introduction: Problems of Collinearity in Linear Regression
    Mathematical Coupling and Collinearity
    Vector Geometry of Collinearity
    Geometrical Illustration of Principal Components Analysis as a Solution to Multicollinearity
    Example: Mineral Loss in Patients Receiving Parenteral Nutrition
    Solutions to Collinearity

    Is ‘Reversal Paradox’ a Paradox?

    A Plethora of Paradoxes: The Reversal Paradox
    Background: The Foetal Origins of Adult Disease
    Hypothesis (Barker’s Hypothesis)
    Vector Geometry of the Foetal Origins Hypothesis
    Reversal Paradox and Adjustment for Current Body Size: Empirical Evidence from Meta-Analysis

    Testing Statistical Interaction

    Introduction: Testing Interactions in Epidemiological Research
    Testing Statistical Interaction between Categorical Variables
    Testing Statistical Interaction between Continuous Variables
    Partial Regression Coefficient for Product Term in Regression Models
    Categorization of Continuous Explanatory Variables
    The Four-Model Principle in the Foetal Origins Hypothesis
    Categorization of Continuous Covariates and Testing Interaction

    Finding Growth Trajectories in Lifecourse Research

    Current Approaches to Identifying Postnatal Growth Trajectories in Lifecourse Research

    Partial Least Squares Regression for Lifecourse Research

    OLS Regression
    PLS Regression

    Concluding Remarks



    Author Bio(s)

    Dr Yu-Kang Tu is a Senior Clinical Research Fellow in the Division of Biostatistics, School of Medicine, and in the Leeds Dental Institute, University of Leeds, Leeds, UK. He was a visiting Associate Professor to the National Taiwan University, Taipei, Taiwan. First trained as a dentist and then an epidemiologist, he has published extensively in dental, medical, epidemiological and statistical journals. He is interested in developing statistical methodologies to solve statistical and methodological problems such as mathematical coupling, regression to the mean, collinearity and the reversal paradox. His current research focuses on applying latent variables methods, e.g. structural equation modeling, latent growth curve modelling, and lifecourse epidemiology. More recently, he has been working on applying partial least squares regression to epidemiological data.

    Prof Mark S Gilthorpe is professor of Statistical Epidemiology, Division of Biostatistics, School of Medicine, University of Leeds, Leeds, UK. Having completed a single honours degree in mathematical Physics (University of Nottingham), he undertook a PhD in Mathematical Modelling (University of Aston in Birmingham), before initially embarking upon a career as self-employed Systems and Data Analyst and Computer Programmer, and eventually becoming an academic in biomedicine. Academic posts include systems and data analyst of UK regional routine hospital data in the Department of Public Health and Epidemiology, University of Birmingham; Head of Biostatistics at the Eastman Dental Institute, University College London; and founder and Head of the Division of Biostatistics, School of Medicine, University of Leeds. His research focus has persistently been that of the development and promotion of robust and sophisticated modelling methodologies for non-experimental (and sometimes large and complex) observational data within biomedicine, leading to extensive publications in dental, medical, epidemiological and statistical journals.

    Editorial Reviews

    "There are extensive references to the literature, both in statistics and in medicine. This is a demanding text, not mathematically but for the subtlety of the issues canvassed, some of which remain controversial. Should any reader come to this text thinking that the interpretation of regression results is a simple matter, they will be quickly disabused."
    International Statistical Review, 2013

    "The graphical explanations proposed are quite convincing and these tools should be more exploited in statistical classes."
    —Sophie Donnet, Université Paris-Dauphine, CHANCE, 25.4

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