A Characterization of Optimal Designs for Observational Studies

SUMMARY Subclassification and matching are often used to adjust for covariates in observational studies. Here, the form of an ‘optimal’ subclassification is determined, i.e. a subclassification which makes the treated and control subjects in the same subclass as similar as possible. This optimal form is simple, intuitive and quite practical, though it is rarely used. The optimal form has several consequences. First, it suggests that theoretical investigations may assume that observational studies have this form, for if they do not they may be changed to this form without a loss, and often with a gain. Second, in searching for an optimal subclassification, the search may be confined to subclassifications of this form, for one is sure to be optimal. Finally, it is shown that finding an optimal subclassification of this form may often be reduced to finding the minimum cost flow in a certain network, i.e. to a standard combinatorial optimization problem for which good algorithms exist.