| |
| |
| |
Introduction | |
| |
| |
| |
Disease processes | |
| |
| |
| |
Statistical approaches to epidemiological data | |
| |
| |
| |
Study design | |
| |
| |
| |
Binary outcome data | |
| |
| |
| |
Causality | |
| |
| |
| |
Overview | |
| |
| |
| |
Caution: what is not covered | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Measures of Disease Occurrence | |
| |
| |
| |
Prevalence and incidence | |
| |
| |
| |
Disease rates | |
| |
| |
| |
The hazard function | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
The Role of Probability in Observational Studies | |
| |
| |
| |
Simple random samples | |
| |
| |
| |
Probability and the incidence proportion | |
| |
| |
| |
Inference based on an estimated probability | |
| |
| |
| |
Conditional probabilities | |
| |
| |
| |
Independence of two events | |
| |
| |
| |
Example of conditional probabilities--Berkson's bias | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Measures of Disease-Exposure Association | |
| |
| |
| |
Relative risk | |
| |
| |
| |
Odds ratio | |
| |
| |
| |
The odds ratio as an approximation to the relative risk | |
| |
| |
| |
Symmetry of roles of disease and exposure in the odds ratio | |
| |
| |
| |
Relative hazard | |
| |
| |
| |
Excess risk | |
| |
| |
| |
Attributable risk | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Study Designs | |
| |
| |
| |
Population-based studies | |
| |
| |
| |
Example--mother's marital status and infant birthweight | |
| |
| |
| |
Exposure-based sampling--cohort studies | |
| |
| |
| |
Disease-based sampling--case-control studies | |
| |
| |
| |
Key variants of the case-control design | |
| |
| |
| |
Risk-set sampling of controls | |
| |
| |
| |
Case-cohort studies | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Assessing Significance in a 2 x 2 Table | |
| |
| |
| |
Population-based designs | |
| |
| |
| |
Role of hypothesis tests and interpretation of p-values | |
| |
| |
| |
Cohort designs | |
| |
| |
| |
Case-control designs | |
| |
| |
| |
Comparison of the study designs | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Alternative formulations of the X[superscript 2] test statistic | |
| |
| |
| |
When is the sample size too small to do a X[superscript 2] test? | |
| |
| |
| |
Problems | |
| |
| |
| |
Estimation and Inference for Measures of Association | |
| |
| |
| |
The odds ratio | |
| |
| |
| |
Sampling distribution of the odds ratio | |
| |
| |
| |
Confidence interval for the odds ratio | |
| |
| |
| |
Example--coffee drinking and pancreatic cancer | |
| |
| |
| |
Small sample adjustments for estimators of the odds ratio | |
| |
| |
| |
The relative risk | |
| |
| |
| |
Example--coronary heart disease in the Western Collaborative Group Study | |
| |
| |
| |
The excess risk | |
| |
| |
| |
The attributable risk | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Measurement error or misclassification | |
| |
| |
| |
Problems | |
| |
| |
| |
Causal Inference and Extraneous Factors: Confounding and Interaction | |
| |
| |
| |
Causal inference | |
| |
| |
| |
Counterfactuals | |
| |
| |
| |
Confounding variables | |
| |
| |
| |
Control of confounding by stratification | |
| |
| |
| |
Causal graphs | |
| |
| |
| |
Assumptions in causal graphs | |
| |
| |
| |
Causal graph associating childhood vaccination to subsequent health condition | |
| |
| |
| |
Using causal graphs to infer the presence of confounding | |
| |
| |
| |
Controlling confounding in causal graphs | |
| |
| |
| |
Danger: controlling for colliders | |
| |
| |
| |
Simple rules for using a causal graph to choose the crucial confounders | |
| |
| |
| |
Collapsibility over strata | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Control of Extraneous Factors | |
| |
| |
| |
Summary test of association in a series of 2 X 2 tables | |
| |
| |
| |
The Cochran-Mantel-Haenszel test | |
| |
| |
| |
Sample size issues and a historical note | |
| |
| |
| |
Summary estimates and confidence intervals for the odds ratio, adjusting for confounding factors | |
| |
| |
| |
Woolf's method on the logarithm scale | |
| |
| |
| |
The Mantel-Haenszel method | |
| |
| |
| |
Example--the Western Collaborative Group Study: part 2 | |
| |
| |
| |
Example--coffee drinking and pancreatic cancer: part 2 | |
| |
| |
| |
Summary estimates and confidence intervals for the relative risk, adjusting for confounding factors | |
| |
| |
| |
Example--the Western Collaborative Group Study: part 3 | |
| |
| |
| |
Summary estimates and confidence intervals for the excess risk, adjusting for confounding factors | |
| |
| |
| |
Example--the Western Collaborative Group Study: part 4 | |
| |
| |
| |
Further discussion of confounding | |
| |
| |
| |
How do adjustments for confounding affect precision? | |
| |
| |
| |
An empirical approach to confounding | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Interaction | |
| |
| |
| |
Multiplicative and additive interaction | |
| |
| |
| |
Multiplicative interaction | |
| |
| |
| |
Additive interaction | |
| |
| |
| |
Interaction and counterfactuals | |
| |
| |
| |
Test of consistency of association across strata | |
| |
| |
| |
The Woolf method | |
| |
| |
| |
Alternative tests of homogeneity | |
| |
| |
| |
Example--the Western Collaborative Group Study: part 5 | |
| |
| |
| |
The power of the test for homogeneity | |
| |
| |
| |
Example of extreme interaction | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Exposures at Several Discrete Levels | |
| |
| |
| |
Overall test of association | |
| |
| |
| |
Example--coffee drinking and pancreatic cancer: part 3 | |
| |
| |
| |
A test for trend in risk | |
| |
| |
| |
Qualitatively ordered exposure variables | |
| |
| |
| |
Goodness of fit and nonlinear trends in risk | |
| |
| |
| |
Example--the Western Collaborative Group Study: part 6 | |
| |
| |
| |
Example--coffee drinking and pancreatic cancer: part 4 | |
| |
| |
| |
Adjustment for confounding, exact tests, and interaction | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Regression Models Relating Exposure to Disease | |
| |
| |
| |
Some introductory regression models | |
| |
| |
| |
The linear model | |
| |
| |
| |
Pros and cons of the linear model | |
| |
| |
| |
The log linear model | |
| |
| |
| |
The probit model | |
| |
| |
| |
The simple logistic regression model | |
| |
| |
| |
Interpretation of logistic regression parameters | |
| |
| |
| |
Simple examples of the models with a binary exposure | |
| |
| |
| |
Multiple logistic regression model | |
| |
| |
| |
The use of indicator variables for discrete exposures | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Estimation of Logistic Regression Model Parameters | |
| |
| |
| |
The likelihood function | |
| |
| |
| |
The likelihood function based on a logistic regression model | |
| |
| |
| |
Properties of the log likelihood function and the maximum likelihood estimate | |
| |
| |
| |
Null hypotheses that specify more than one regression coefficient | |
| |
| |
| |
Example--the Western Collaborative Group Study: part 7 | |
| |
| |
| |
Logistic regression with case-control data | |
| |
| |
| |
Example--coffee drinking and pancreatic cancer: part 5 | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Confounding and Interaction within Logistic Regression Models | |
| |
| |
| |
Assessment of confounding using logistic regression models | |
| |
| |
| |
Example--the Western Collaborative Group Study: part 8 | |
| |
| |
| |
Introducing interaction into the multiple logistic regression model | |
| |
| |
| |
Example--coffee drinking and pancreatic cancer: part 6 | |
| |
| |
| |
Example--the Western Collaborative Group Study: part 9 | |
| |
| |
| |
Collinearity and centering variables | |
| |
| |
| |
Centering independent variables | |
| |
| |
| |
Fitting quadratic models | |
| |
| |
| |
Restrictions on effective use of maximum likelihood techniques | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Measurement error | |
| |
| |
| |
Missing data | |
| |
| |
| |
Problems | |
| |
| |
| |
Goodness of Fit Tests for Logistic Regression Models and Model Building | |
| |
| |
| |
Choosing the scale of an exposure variable | |
| |
| |
| |
Using ordered categories to select exposure scale | |
| |
| |
| |
Alternative strategies | |
| |
| |
| |
Model building | |
| |
| |
| |
Goodness of fit | |
| |
| |
| |
The Hosmer-Lemeshow test | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Matched Studies | |
| |
| |
| |
Frequency matching | |
| |
| |
| |
Pair matching | |
| |
| |
| |
Mantel-Haenszel techniques applied to pair-matched data | |
| |
| |
| |
Small sample adjustment for odds ratio estimator | |
| |
| |
| |
Example--pregnancy and spontaneous abortion in relation to coronary heart disease in women | |
| |
| |
| |
Confounding and interaction effects | |
| |
| |
| |
Assessing interaction effects of matching variables | |
| |
| |
| |
Possible confounding and interactive effects due to nonmatching variables | |
| |
| |
| |
The logistic regression model for matched data | |
| |
| |
| |
Example--pregnancy and spontaneous abortion in relation to coronary heart disease in women: part 2 | |
| |
| |
| |
Example--the effect of birth order on respiratory distress syndrome in twins | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
When can we break the match? | |
| |
| |
| |
Final thoughts on matching | |
| |
| |
| |
Problems | |
| |
| |
| |
Alternatives and Extensions to the Logistic Regression Model | |
| |
| |
| |
Flexible regression model | |
| |
| |
| |
Beyond binary outcomes and independent observations | |
| |
| |
| |
Introducing general risk factors into formulation of the relative hazard--the Cox model | |
| |
| |
| |
Fitting the Cox regression model | |
| |
| |
| |
When does time at risk confound an exposure-disease relationship? | |
| |
| |
| |
Time-dependent exposures | |
| |
| |
| |
Differential loss to follow-up | |
| |
| |
| |
Comments and further reading | |
| |
| |
| |
Problems | |
| |
| |
| |
Epilogue: The Examples | |
| |
| |
References | |
| |
| |
Glossary of Common Terms and Abbreviations | |
| |
| |
Index | |