One-shot variable-ratio matching with fine balance

Variable-ratio matching provides a flexible alternative to conventional 1-to-k matching for the design of observational studies. Fine balance, which ensures identical marginal distributions of selected covariates between treated and matched control groups, is often a desirable design feature. Existing variable-ratio matching approaches achieve conditional fine balance, whereby targeted covariates are balanced within matched sets of the same size (e.g., pairs or triplets), but not necessarily in the pooled matched sample. Such approaches typically proceed in two steps: units are first partitioned into strata based on estimated entire numbers, followed by 1-to-k matching with fine balance enforced within each stratum. Here, we propose a novel one-shot variable-ratio matching algorithm that achieves marginal fine balance—that is, balance on selected covariates in the pooled matched sample as a whole. This design mimics a randomized controlled trial in which units are grouped into sets of varying sizes, with one unit per set assigned to treatment. We discuss settings in which marginal fine balance is preferred and evaluate the proposed method through simulations and an application to the relationship between right heart catheterization and mortality among critically ill patients. The algorithm is implemented in the R package match2C.