1. Two Measures of Risk: Odds Ratios and Average Rates
Odds Ratio
Properties of the Odds Ratio
Three Statistical Terms
Average Rates
Geometry of an Average Rate
Proportionate Mortality “Rates”
2. Tabular Data: The 2 × k Table and Summarizing
2 × 2 Tables
The 2 ×
k Table
Independence/Homogeneity
Independence
Homogeneity
Regression
Two-Sample: Comparison of Two Mean Values
An Example: Childhood Cancer and Prenatal X-ray Exposure
Summary of the Notation for a 2 ×
k Table
Summarizing 2 × 2 Tables: Application of a Weighted Average
Another Summary Measure: Difference in Proportions
Confounding
3. Two Especially Useful Estimation Tools
Maximum Likelihood Estimation
Four Properties of Maximum Likelihood Estimates
Likelihood Statistics
The Statistical Properties of a Function
Application 1: Poisson Distribution
Application 2: Variance of a Logarithm of a Variable
Application 3: Variance of the Logarithm of a Count
4. Linear Logistic Regression: Discrete Data
The Simplest Logistic Regression Model: The 2 × 2 Table
The Logistic Regression Model: The 2 × 2 × 2 Table
Additive Logistic Regression Model
A Note on the Statistical Power to Identify Interaction Effects
The Logistic Regression Model: The 2 × k Table
The Logistic Regression Model: Multivariable Table
Goodness-of-Fit: Multivariable Table
Logistic Regression Model: The Summary Odds Ratio
Description of the WCGS Data Set
5. Logistic Regression: Continuous Data
Four Basic Properties of Multivariable Regression Model Analysis
Additivity
Confounding Influence
The Geometry of Interaction and Confounding
The Geometry of Statistical Adjustment
Logistic Regression Analysis
6. Analysis of Count Data: Poisson Regression Model
Poisson Multivariable Regression Model: Technical Description
Illustration of the Poisson Regression Model
Poisson Regression Model: Hodgkin Disease Mortality
The Simplest Poisson Regression Model: The 2 × 2 Table
Application of the Poisson Regression Model: Categorical Data
Application of the Poisson Regression Model: Count Data
Poisson Regression Example: Adjusted Perinatal Mortality Rates
First Approach: Weight-Specific Comparisons
Second Approach: A Model-Free Summary
Third Approach: Poisson Regression Model
7. Analysis of Matched Case–Control Data
The 2 × 2 Case–Control Table
Odds Ratio for Matched Data
Confidence Interval for the Matched-Pairs Odds Ratio
Evaluating an Estimated Odds Ratio
Disregarding the Matched Design
Interaction with the Matching Variable
Matched Pairs Analysis: More than One Control
Matched Analysis: Multilevel Categorical Risk Factor
Conditional Analysis of Logistic Regression Models
Conditional Logistic Analysis: Binary Risk Factor
Multiple Controls per Case
Conditional Logistic Analysis: A Bivariate Regression Model
Conditional Logistic Analysis: Interactions with the Matching Variable
Conditional Logistic Analysis: k-Level Category Risk Variable
Conditional Logistic Analysis: Continuous Variables
Additive Logistic Regression Model
8. Spatial Data: Estimation and Analysis
Poisson Probability Distribution: An Introduction
Nearest-Neighbor Analysis
Comparison of Cumulative Probability Distribution Functions
Randomization Test
Bootstrap Estimation
Example: Bootstrap Estimation of a Percentage Decrease
Properties of the Odds Ratio and the Logarithm of an Odds Ratio
Estimation of ABO Allele Frequencies
An Important Property (Bootstrap versus Randomization)
A Last Example: Assessment of Spatial Data
9. Classification: Three Examples
Dendogram Classification
Principal Component Summaries
Genetic Classification
A Multivariate Picture
10. Three Smoothing Techniques
Smoothing: A Simple Approach
Kernel Density Estimation
Spline Estimated Curves
Data Analysis with Spline-Estimated Curves: An Example
11. Case Study: Description and Analysis
12. Longitudinal Data Analysis
Within and Between Variability
A Simple Example
Elementary Longitudinal Models: Polynomial Models
Elementary Longitudinal Models: Spline Models
Random Intercept Model
Random Intercept and Random Slope Regression Model
Mechanics of a Variance/Covariance Array
13. Analysis of Multivariate Tables
Analysis of Ordinal Data
Wilcoxon (Mann–Whitney) Rank Sum Test
Correlation Between Ordinal Variables
Log–Linear Models: Categorical Data Analysis
Independence in a Two-Way Table
Tables with Structural Zeros
Capture/Recapture Model
Categorical Variable Analysis from Matched Pairs Data
Quasi-Independence: Association in a
R ×
C Table
The Analysis of a Three-Way Table
Complete Independence
Joint Independence
Conditional Independence
Additive Measures of Association
14. Misclassification: A Detailed Description of a Simple Case
Example: Misclassification of the Disease Status
Example: Misclassification of the Risk Factor Status
A Few Illustrations of Misclassification
Agreement Between Two Methods of Classification: Categorical Data
Disagreement
A Measurement of Accuracy: Continuous Data
Parametric Approach
Nonparametric Approach
A Detailed Example of a Nonparametric ROC Curve
Area Under the ROC Curve
Application: ROC Analysis Applied to Carotid Artery Disease Data
Agreement Between Two Methods of Measurement: Continuous Data
A Statistical Model: “Two-Measurement” Model
An Alternative Approach: Bland–Altman Analysis
Another Application of Perpendicular Least-Squares Estimation
15. Advanced Topics
Confidence Intervals
An Example of a Bivariate Confidence Region
Confidence Band
Nonparametric Regression Methods
Bivariate Loess Estimation
Two-Dimensional Kernel Estimation
Statistical Tests and a Few of Their Properties
Power of a Specific Statistical Test: The Normal Distribution Case
Power of a Statistical Test: The Chi-Square Distribution Case
Three Applications
Multiple Statistical Tests: Accumulation of Type I Errors
References
Index
