Statistical Tools for Epidemiologic Research

Contents......Page 12
Odds Ratio......Page 20
Properties of the Odds Ratio......Page 30
Three Statistical Terms......Page 33
Average Rates......Page 36
Geometry of an Average Rate......Page 40
Proportionate Mortality “Rates”......Page 42
The 2 × k Table......Page 45
Independence/Homogeneity......Page 46
Independence......Page 47
Homogeneity......Page 49
Regression......Page 50
Two-Sample: Comparison of Two Mean Values......Page 55
An Example: Childhood Cancer and Prenatal X-ray Exposure......Page 57
Summary of the Notation for a 2 × k Table......Page 60
Summarizing 2 × 2 Tables: Application of a Weighted Average......Page 61
Another Summary Measure: Difference in Proportions......Page 67
Confounding......Page 69
Maximum Likelihood Estimation......Page 71
Four Properties of Maximum Likelihood Estimates......Page 75
Likelihood Statistics......Page 76
The Statistical Properties of a Function......Page 80
Application 1: Poisson Distribution......Page 81
Application 2: Variance of a Logarithm of a Variable......Page 82
Application 3: Variance of the Logarithm of a Count......Page 83
4. Linear Logistic Regression: Discrete Data......Page 84
The Simplest Logistic Regression Model: The 2 × 2 Table......Page 86
The Logistic Regression Model: The 2 × 2 × 2 Table......Page 92
Additive Logistic Regression Model......Page 98
A Note on the Statistical Power to Identify Interaction Effects......Page 101
The Logistic Regression Model: The 2 × k Table......Page 103
The Logistic Regression Model: Multivariable Table......Page 108
Goodness-of-Fit: Multivariable Table......Page 111
Logistic Regression Model: The Summary Odds Ratio......Page 115
Description of the WCGS Data Set......Page 122
5. Logistic Regression: Continuous Data......Page 124
Additivity......Page 126
Confounding Influence......Page 128
The Geometry of Interaction and Confounding......Page 131
The Geometry of Statistical Adjustment......Page 133
Logistic Regression Analysis......Page 136
6. Analysis of Count Data: Poisson Regression Model......Page 148
Poisson Multivariable Regression Model: Technical Description......Page 149
Illustration of the Poisson Regression Model......Page 150
Poisson Regression Model: Hodgkin Disease Mortality......Page 152
The Simplest Poisson Regression Model: The 2 × 2 Table......Page 159
Application of the Poisson Regression Model: Categorical Data......Page 162
Application of the Poisson Regression Model: Count Data......Page 164
First Approach: Weight-Specific Comparisons......Page 168
Second Approach: A Model-Free Summary......Page 173
Third Approach: Poisson Regression Model......Page 176
The 2 × 2 Case–Control Table......Page 181
Odds Ratio for Matched Data......Page 186
Confidence Interval for the Matched-Pairs Odds Ratio......Page 187
Evaluating an Estimated Odds Ratio......Page 189
Disregarding the Matched Design......Page 191
Interaction with the Matching Variable......Page 192
Matched Pairs Analysis: More than One Control......Page 194
Matched Analysis: Multilevel Categorical Risk Factor......Page 198
Conditional Analysis of Logistic Regression Models......Page 202
Conditional Logistic Analysis: Binary Risk Factor......Page 203
Multiple Controls per Case......Page 204
Conditional Logistic Analysis: A Bivariate Regression Model......Page 205
Conditional Logistic Analysis: Interactions with the Matching Variable......Page 206
Conditional Logistic Analysis: k-Level Category Risk Variable......Page 208
Conditional Logistic Analysis: Continuous Variables......Page 209
Additive Logistic Regression Model......Page 212
8. Spatial Data: Estimation and Analysis......Page 214
Poisson Probability Distribution: An Introduction......Page 215
Nearest-Neighbor Analysis......Page 220
Comparison of Cumulative Probability Distribution Functions......Page 225
Randomization Test......Page 228
Bootstrap Estimation......Page 234
Example: Bootstrap Estimation of a Percentage Decrease......Page 239
Properties of the Odds Ratio and the Logarithm of an Odds Ratio......Page 242
Estimation of ABO Allele Frequencies......Page 245
An Important Property (Bootstrap versus Randomization)......Page 248
A Last Example: Assessment of Spatial Data......Page 250
9. Classification: Three Examples......Page 255
Dendogram Classification......Page 257
Principal Component Summaries......Page 261
Genetic Classification......Page 266
A Multivariate Picture......Page 271
10. Three Smoothing Techniques......Page 274
Smoothing: A Simple Approach......Page 275
Kernel Density Estimation......Page 278
Spline Estimated Curves......Page 284
Data Analysis with Spline-Estimated Curves: An Example......Page 300
11. Case Study: Description and Analysis......Page 304
12. Longitudinal Data Analysis......Page 327
Within and Between Variability......Page 330
A Simple Example......Page 336
Elementary Longitudinal Models: Polynomial Models......Page 338
Elementary Longitudinal Models: Spline Models......Page 344
Random Intercept Model......Page 348
Random Intercept and Random Slope Regression Model......Page 358
Mechanics of a Variance/Covariance Array......Page 360
Analysis of Ordinal Data......Page 362
Wilcoxon (Mann-Whitney) Rank Sum Test......Page 363
Correlation Between Ordinal Variables......Page 371
Log-Linear Models: Categorical Data Analysis......Page 375
Independence in a Two-Way Table......Page 376
Tables with Structural Zeros......Page 379
Capture/Recapture Model......Page 382
Categorical Variable Analysis from Matched Pairs Data......Page 386
Quasi-Independence: Association in a R × C Table......Page 390
The Analysis of a Three-Way Table......Page 392
Complete Independence......Page 394
Joint Independence......Page 395
Conditional Independence......Page 396
Additive Measures of Association......Page 398
Example: Misclassification of the Disease Status......Page 405
Example: Misclassification of the Risk Factor Status......Page 406
A Few Illustrations of Misclassification......Page 408
Agreement Between Two Methods of Classification: Categorical Data......Page 411
Disagreement......Page 416
A Measurement of Accuracy: Continuous Data......Page 418
Parametric Approach......Page 420
Nonparametric Approach......Page 425
A Detailed Example of a Nonparametric ROC Curve......Page 429
Area Under the ROC Curve......Page 431
Application: ROC Analysis Applied to Carotid Artery Disease Data......Page 434
A Statistical Model: “Two-Measurement”Model......Page 438
An Alternative Approach: Bland-Altman Analysis......Page 446
Another Application of Perpendicular Least-Squares Estimation......Page 450
Confidence Intervals......Page 453
An Example of a Bivariate Confidence Region......Page 459
Confidence Band......Page 461
Nonparametric Regression Methods......Page 464
Bivariate Loess Estimation......Page 471
Two-Dimensional Kernel Estimation......Page 475
Statistical Tests and a Few of Their Properties......Page 479
Power of a Specific Statistical Test: The Normal Distribution Case......Page 480
Power of a Statistical Test: The Chi-Square Distribution Case......Page 484
Three Applications......Page 487
Multiple Statistical Tests: Accumulation of Type I Errors......Page 494
References......Page 502
B......Page 506
D......Page 507
L......Page 508
O......Page 509
S......Page 510
W......Page 511