A deterministic balancing score algorithm to avoid common pitfalls of propensity score matching

Propensity score matching (PSM) is the de-facto standard for estimating causal effects in observational studies. We show that PSM and its implementations are susceptible to several major drawbacks and illustrate these findings using a case study with $17,427$ patients. We derive four formal properties an optimal statistical matching algorithm should meet, and propose Deterministic Balancing Score exact Matching (DBSeM) which meets the aforementioned properties for an exact matching. Furthermore, we investigate one of the main problems of PSM, that is that common PSM results in one valid set of matched pairs or a bootstrapped PSM in a selection of possible valid sets of matched pairs. For exact matchings we provide the mathematical proof, that DBSeM, as a result, delivers the expected value of all valid sets of matched pairs for the investigated dataset.