|
Abstract:
|
In observational studies, estimation of treatment effects may be complicated by the presence of confounders. Statistical matching, in which each treated unit is paired with a control unit with similar covariate values, is a common way to account these confounders. Most matching methods aim to minimize the total dissimilarity between treated and matched control units. However, this may open the door for a matching with significant imbalances on certain covariates within a small proportion of units. Hence, a researcher may also desire to limit the maximum imbalance possible within a matched pair. We formulate statistical matching as a graph theory problem, where nodes are units, edges are drawn between potential matches, and each edge has a weight measuring the dissimilarity between the corresponding match. We then show that matching with a constraint on the maximum imbalance on a covariate is equivalent to finding a match within a bottleneck subgraph, in which edges in the graph are drawn if and only if their weight is less than some pre-specified threshold. We conclude by demonstrating how to implement statistical matching methods subject to this constraint.
|
