A Characterization of Optimal Designs for Observational Studies

SUMMARY An empirical investigation of the effects of a treatment is an observational study if it involves the comparison of treated and control groups that were not formed by randomization. In such studies, treated and control groups may differ systematically with respect to pretreatment measures or covariates, and addressing these pre- treatment differences is a central concern. Matching and subclassification are two standard methods of adjusting for observed pretreatment differences; they may be used alone (e.g. Cochran (1968)) or in conjunction with analytical or model-based adjustments (e.g. Rubin (1973, 1979), Holford (1978), Rosenbaum and Rubin (1984), section 3.3, and Rosenbaum (1987, 1988a)). In particular, Rubin's simulation studies suggest that model-based adjustments applied to matched or subclassified samples are more robust than model-based adjustments applied to unmatched samples. The purpose of this paper is to identify the structure of an optimal subclassification, i.e. one in which the treated and control subjects in the same subclass are, on average, as similar as possible with respect to observed covariates. It turns out that this structure is simple and intuitive. While adjustments may control imbalances in observed covariates, they cannot

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