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El. knyga: Statistical Thinking in Epidemiology

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  • Formatas: 231 pages
  • Išleidimo metai: 19-Apr-2016
  • Leidėjas: Chapman & Hall/CRC
  • Kalba: eng
  • ISBN-13: 9781420099928
Kitos knygos pagal šią temą:
Statistical Thinking in EpidemiologyDidesnis paveikslėlis
  • Formatas: 231 pages
  • Išleidimo metai: 19-Apr-2016
  • Leidėjas: Chapman & Hall/CRC
  • Kalba: eng
  • ISBN-13: 9781420099928
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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.

Recenzijos

"... this book is enjoyable ... it encourages readers to conceptualize statistical thinking in a graphically entertaining way. ... one of the impressive works of the book lies in visualization of statistically important concepts... I would recommend this book to diverse audiences. ... the book provides novel insight on how one can develop the core concepts from scratch via graphical concepts, which will definitely be beneficial. Bearing in mind the geometrical concepts from this book, statistical thinking of more complicated models is readily welcomed." -Journal of Agricultural, Biological, and Environmental Statistics, Volume 20, Number 2, 2015 "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, Universite Paris-Dauphine, CHANCE, 25.4

Preface xi
1 Introduction 1(6)
1.1 Uses of Statistics in Medicine and Epidemiology
1(1)
1.2 Structure and Objectives of This Book
2(3)
1.3 Nomenclature in This Book
5(1)
1.4 Glossary
5(2)
2 Vector Geometry of Linear Models for Epidemiologists 7(10)
2.1 Introduction
7(1)
2.2 Basic Concepts of Vector Geometry in Statistics
7(2)
2.3 Correlation and Simple Regression in Vector Geometry
9(2)
2.4 Linear Multiple Regression in Vector Geometry
11(1)
2.5 Significance Testing of Correlation and Simple Regression in Vector Geometry
12(2)
2.6 Significance Testing of Multiple Regression in Vector Geometry
14(1)
2.7 Summary
15(2)
3 Path Diagrams and Directed Acyclic Graphs 17(10)
3.1 Introduction
17(1)
3.1 Path Diagrams
17(4)
3.1.1 The Path Diagram for Simple Linear Regression
18(2)
3.1.1.1 Regression Weights, Path Coefficients and Factor Loadings
19(1)
3.1.1.2 Exogenous and Endogenous Variables
19(1)
3.1.2 The Path Diagram for Multiple Linear Regression
20(1)
3.2 Directed Acyclic Graphs
21(4)
3.2.1 Identification of Confounders
22(1)
3.2.2 Backdoor Paths and Colliders
23(1)
3.2.3 Example of a Complex DAG
24(1)
3.3 Direct and Indirect Effects
25(1)
3.4 Summary
26(1)
4 Mathematical Coupling and Regression to the Mean in the Relation between Change and Initial Value 27(24)
4.1 Introduction
27(2)
4.2 Historical Background
29(1)
4.3 Why Should Change Not Be Regressed on Initial Value? A Review of the Problem
29(1)
4.4 Proposed Solutions in the Literature
30(7)
4.4.1 Blomqvist's Formula
30(1)
4.4.2 Oldham's Method: Testing Change and Average
30(2)
4.4.3 Geometrical Presentation of Oldham's Method
32(1)
4.4.4 Variance Ratio Test
32(2)
4.4.5 Structural Regression
34(1)
4.4.6 Multilevel Modelling
35(1)
4.4.7 Latent Growth Curve Modelling
36(1)
4.5 Comparison between Oldham's Method and Blomqvist's Formula
37(1)
4.6 Oldham's Method and Blomqvist's Formula Answer Two Different Questions
38(1)
4.7 What Is Galton's Regression to the Mean?
39(1)
4.8 Testing the Correct Null Hypothesis
40(5)
4.8.1 The Distribution of the Correlation Coefficient between Change and Initial Value
41(2)
4.8.2 Null Hypothesis for the Baseline Effect on Treatment
43(1)
4.8.3 Fisher's Z-Transformation
43(1)
4.8.4 A Numerical Example
44(1)
4.8.5 Comparison with Alternative Methods
44(1)
4.9 Evaluation of the Categorisation Approach
45(2)
4.10 Testing the Relation between Changes and Initial Values When There Are More than Two Occasions
47(1)
4.11 Discussion
48(3)
5 Analysis of Change in Pre-/Post-Test Studies 51(22)
5.1 Introduction
51(1)
5.2 Analysis of Change in Randomised Controlled Trials
51(2)
5.3 Comparison of Six Methods
53(7)
5.3.1 Univariate Methods
54(1)
5.3.1.1 Test the Post-Treatment Scores Only
54(1)
5.3.1.2 Test the Change Scores
54(1)
5.3.1.3 Test the Percentage Change Scores
54(1)
5.3.1.4 Analysis of Covariance
54(1)
5.3.2 Multivariate Statistical Methods
55(4)
5.3.2.1 Random Effects Model
55(1)
5.3.2.2 Multivariate Analysis of Variance
56(3)
5.5.3 Simulation Results
59(1)
5.6 Analysis of Change in Non-Experimental Studies: Lord's Paradox
60(5)
5.6.1 Controversy around Lord's Paradox
62(2)
5.6.1.1 Imprecise Statement of Null Hypothesis
62(1)
5.6.1.2 Causal Inference in Non-Experimental Study Design
63(1)
5.6.2 Variable Geometry of Lord's Paradox
64(1)
5.6.3 Illustration of the Difference between ANCOVA and Change Scores in RCTs Using Variable Space Geometry
65(1)
5.7 ANCOVA and t-Test for Change Scores Have Different Assumptions
65(6)
5.7.1 Scenario One: Analysis of Change for Randomised Controlled Trials
67(2)
5.7.2 Scenario Two: The Analysis of Change for Observational Studies
69(2)
5.8 Conclusion
71(2)
6 Collinearity and Multicollinearity 73(24)
6.1 Introduction: Problems of Collinearity in Linear Regression
73(3)
6.2 Collinearity
76(1)
6.3 Multicollinearity
77(2)
6.4 Mathematical Coupling and Collinearity
79(1)
6.5 Vector Geometry of Collinearity
79(5)
6.5.1 Reversed Relation between the Outcome and Covariate due to Collinearity
80(1)
6.5.2 Unstable Regression Models due to Collinearity
81(1)
6.5.3 The Relation between the Outcome–Explanatory Variable's Correlations and Collinearity
82(2)
6.6 Geometrical Illustration of Principal Components Analysis as a Solution to Multicollinearity
84(1)
6.7 Example: Mineral Loss in Patients Receiving Parenteral Nutrition
85(4)
6.8 Solutions to Collinearity
89(5)
6.8.1 Removal of Redundant Explanatory Variables
89(1)
6.8.2 Centring
89(1)
6.8.3 Principal Component Analysis
90(3)
6.8.4 Ridge Regression
93(1)
6.9 Conclusion
94(3)
7 Is 'Reversal Paradox' a Paradox? 97(22)
7.1 A Plethora of Paradoxes: The Reversal Paradox
97(1)
7.2 Background: The Foetal Origins of Adult Disease Hypothesis (Barker's Hypothesis)
98(11)
7.2.1 Epidemiological Evidence on the Foetal Origins Hypothesis
99(1)
7.2.2 Criticisms of the Foetal Origins Hypothesis
100(2)
7.2.3 Reversal Paradox and Suppression in Epidemiological Studies on the Foetal Origins Hypothesis
102(2)
7.2.4 Catch-Up Growth and the Foetal Origins Hypothesis
104(3)
7.2.5 Residual Current Body Weight: A Proposed Alternative Approach
107(1)
7.2.6 Numerical Example
108(1)
7.3 Vector Geometry of the Foetal Origins Hypothesis
109(2)
7.4 Reversal Paradox and Adjustment for Current Body Size: Empirical Evidence from Meta-Analysis
111(1)
7.5 Discussion
112(5)
7.5.1 The Reversal Paradox and the Foetal Origins Hypothesis
112(3)
7.5.2 Multiple Adjustments for Current Body Sizes
115(1)
7.5.3 Catch-Up Growth and the Foetal Origins Hypothesis
116(1)
7.6 Conclusion
117(2)
8 Testing Statistical Interaction 119(20)
8.1 Introduction: Testing Interactions in Epidemiological Research
119(2)
8.1 Testing Statistical Interaction between Categorical Variables
121(3)
8.2 Testing Statistical Interaction between Continuous Variables
124(4)
8.3 Partial Regression Coefficient for Product Term in Regression Models
128(2)
8.4 Categorization of Continuous Explanatory Variables
130(1)
8.5 The Four-Model Principle in the Foetal Origins Hypothesis
131(1)
8.6 Categorization of Continuous Covariates and Testing Interaction
132(2)
8.6.1 Simulations
132(1)
8.6.2 Numerical Example
133(1)
8.7 Discussion
134(3)
8.8 Conclusion
137(2)
9 Finding Growth Trajectories in Lifecourse Research 139(26)
9.1 Introduction
139(7)
9.1.1 Example: Catch-Up Growth and Impaired Glucose Tolerance
140(1)
9.1.2 Galton and Regression to the Mean
141(3)
9.1.3 Revisiting the Growth Trajectory of Men with Impaired Glucose Tolerance
144(2)
9.2 Current Approaches to Identifying Postnatal Growth Trajectories in Lifecourse Research
146(16)
9.2.1 The Lifecourse Plot
147(3)
9.2.2 Regression with Changes Scores
150(1)
9.2.3 Latent Growth Curve Models
151(8)
9.2.4 Growth Mixture Models
159(3)
9.3 Discussion
162(3)
10 Partial Least Squares Regression for Lifecourse Research 165(22)
10.1 Introduction
165(1)
10.2 Data
166(1)
10.3 OLS Regression
166(1)
10.4 PLS Regression
167(15)
10.4.1 History of PLS
167(3)
10.4.2 PCA Regression
170(1)
10.4.3 PLS Regression
171(1)
10.4.4 PLS and Perfect Collinearity
172(1)
10.4.5 Singular Value Decomposition, PCA and PLS Regression
173(3)
10.4.6 Selection of PLS Component
176(1)
10.4.7 PLS Regression for Lifecourse Data Using Weight z-Scores at Birth, Changes in z-Scores, and Current Weight z-Scores
177(1)
10.4.8 The Relationship between OLS Regression and PLS Regression Coefficients
178(3)
10.4.9 PLS Regression for Lifecourse Data Using Weight z-Scores Measured at Six Different Ages
181(1)
10.4.10 PLS Regression for Lifecourse Data Using Weight z-Scores Measured at Six Different Ages and Five Changes in z-Scores
182(1)
10.5 Discussion
182(2)
10.6 Conclusion
184(3)
11 Concluding Remarks 187(2)
References 189(14)
Index 203
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
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