Part I. The Early Years and the Influence of William G. Cochran: 1. William G. Cochran’s contributions to the design, analysis, and evaluation of observational studies; 2. Controlling bias in observational studies: a review William G. Cochran; Part II. Univariate Matching Methods and the Dangers of Regression Adjustment: 3. Matching to remove bias in observational studies; 4. The use of matched sampling and regression adjustment to remove bias in observational studies; 5. Assignment to treatment group on the basis of a covariate; Part III. Basic Theory of Multivariate Matching: 6. Multivariate matching methods that are equal percent bias reducing, I: Some examples; 7. Multivariate matching methods that are equal percent bias reducing, II: Maximums on bias reduction for fixed sample sizes; 8. Using multivariate matched sampling and regression adjustment to control bias in observational studies; 9. Bias reduction using Mahalanobis-metric matching; Part IV. Fundamentals of Propensity Score Matching: 10. The central role of the propensity score in observational studies for causal effects Paul R. Rosenbaum; 11. Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome Paul R. Rosenbaum; 12. Reducing bias in observational studies using subclassification on the propensity score Paul R. Rosenbaum; 13. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score Paul Rosenbaum; 14. The bias due to incomplete matching Paul R. Rosenbaum; Part V: Affinely Invariant Matching Methods with Ellipsoidally Symmetric Distributions, Theory and Methodology: 15. Affinely invariant matching methods with ellipsoidal distributions Neal Thomas; 16. Characterizing the effect of matching using linear propensity score methods with normal distributions Neal Thomas; 17. Matching using estimated propensity scores: relating theory to practice Neal Thomas; 18. Combining propensity score matching with additional adjustments for prognostic covariates; Part VI. Some Applied Contributions: 19. Causal inference in retrospective studies Paul Holland; 20. The design of the New York school choice scholarships program evaluation Jennifer Hill and Neal Thomas; 21. Estimating and using propensity scores with partially missing data Ralph D’Agostino Jr.; 22. Using propensity scores to help design observational studies: application to the tobacco litigation; Part VII. Some Focused Applications: 23. Criminality, aggression and intelligence in XYY and XXY men H. A. Witkin; 24. Practical implications of modes of statistical inference for causal effects and the critical role of the assignment mechanism; 25. In utero exposure to phenobarbital and intelligence deficits in adult men June Reinisch, Stephanie Sanders, and Erik Mortensen; 26. Estimating causal effects from large data sets using propensity scores; 27. On estimating the causal effects of DNR orders Martin McIntosh.