Multivariate Methods in Epidemiology

Contents......Page 12
Part I: Concepts and Definitions......Page 20
1. Associations between Exposure and Disease......Page 22
Strategies for Studying Disease in a Population......Page 23
Rationale for Multivariate Methods......Page 28
Statistical Approaches to Data Analysis......Page 29
How to Use This Book......Page 30
Models for the Disease Process......Page 34
Models for the Effect of Factors......Page 41
Summary......Page 53
Part II: Non-Regression Methods......Page 56
Studies That Yield Proportion Responses......Page 58
A Single Binary Risk Factor......Page 62
Likelihood-Based Inference......Page 66
Interval Estimates of the Odds Ratio......Page 73
More Than Two Levels of Exposure......Page 77
Stratified Analysis......Page 82
Summary......Page 93
Exercises......Page 94
4. Analysis of Rates......Page 100
Rates as an Outcome......Page 101
Comparing Nominal Groups......Page 107
Score Test for Trend......Page 113
Stratification......Page 114
Summary Rates......Page 116
Summary......Page 122
Exercises......Page 123
Estimating Survival Curves......Page 128
Graphical Displays......Page 138
Tests for Comparing Hazards......Page 145
Types of Incomplete Data......Page 152
Summary......Page 154
Exercises......Page 155
Part III: Regression Methods......Page 158
6. Regression Models for Proportions......Page 160
Generalized Linear Model for Proportions......Page 161
Fitting Binary Response Models......Page 166
Summary......Page 178
Exercises......Page 179
Categorical Variables......Page 182
Testing Linear Hypotheses......Page 205
Power Transformations of Continuous Regressor Variables......Page 214
Summary......Page 219
Exercises......Page 221
8. Parametric Models for Hazard Functions......Page 224
Constant Hazard Model......Page 225
Weibull Hazard Model......Page 237
Other Parametric Models......Page 239
Extra Poisson Variation......Page 242
Summary......Page 243
Exercises......Page 244
9. Proportional Hazards Regression......Page 246
Piecewise Constant Hazards Model......Page 247
Nonparametric Proportional Hazards......Page 254
Evaluating the Fit of a Proportional Hazards Model......Page 258
Time-Dependent Covariates......Page 259
Summary......Page 266
Exercises......Page 268
Part IV: Study Desisn and New Directions......Page 270
10. Analysis of Matched Studies......Page 272
Designing Matched Studies......Page 273
Case-Control Studies with Matched Pairs......Page 277
Case-Control Studies with More Than One Control per Case......Page 287
Cohort Studies with Matched Pairs......Page 291
Summary......Page 295
Exercises......Page 296
Estimation......Page 300
Two-Group Hypothesis Tests......Page 305
General Hypothesis Tests......Page 314
Simulation......Page 328
Summary......Page 329
Exercises......Page 330
12. Extending Regression Models......Page 334
Classification and Regression Trees (CART)......Page 335
Splines......Page 345
Missing Observations......Page 349
Variance Components......Page 351
Errors in Variables......Page 352
Collinearity......Page 354
Summary......Page 358
Appendix 1. Theory on Models for Disease......Page 362
Constant Rates in Time......Page 364
Idealized Model for Rates Changing over Time......Page 365
Relationship between Models for Rates and Proportions......Page 366
Likelihood for the Linear Logistic Model......Page 370
Wald Statistic for a 2×2 Table......Page 372
Likelihood Ratio Statistic for a 2×2 Table......Page 373
Score Statistics for an I×2 Table......Page 374
Score Statistics for Combining I×2 Tables......Page 376
Time to Failure Models......Page 380
Counts of Failures......Page 381
Estimation......Page 382
Score Test for Nominal Categories......Page 383
Score Test Controlling for Strata......Page 385
Actuarial Estimate......Page 388
Two-Sample Score Test for Piecewise Constant Hazards......Page 391
Log-Rank Test......Page 393
Distribution for Binary Responses......Page 396
Functions of the Linear Predictor......Page 398
Using Results to Conduct Inference......Page 399
Poisson Regression......Page 404
Weibull Hazards......Page 406
Alternatives to Log-Linear Hazard Models......Page 409
Appendix 7. Theory on Proportional Hazards Regression......Page 412
Conditional Likelihood for Case-Control Study......Page 416
Matched Pairs for Case-Control Studies......Page 417
Conditional Likelihood for Cohort Studies......Page 418
C......Page 422
F......Page 423
L......Page 424
P......Page 425
S......Page 426
Z......Page 427