Article,
Reducing Bias in Observational Studies Using Subclassification on the Propensity Score
Journal of the American Statistical Association, 79 (387): 516--524 (1984)
Abstract
The propensity score is the conditional probability of
assignment to a particular treatment given a vector of
observed covariates. Previous theoretical arguments have
shown that subclassification on the propensity score will
balance all observed covariates. Subclassification on an
estimated propensity score is illustrated, using
observational data on treatments for coronary artery
disease. Five subclasses defined by the estimated
propensity score are constructed that balance 74
covariates, and thereby provide estimates of treatment
effects using direct adjustment. These subclasses are
applied within subpopulations, and model-based adjustments
are then used to provide estimates of treatment effects
within these subpopulations. Two appendixes address
theoretical issues related to the application: the
effectiveness of subclassification on the propensity score
in removing bias, and balancing properties of propensity
scores with incomplete data.
