Advanced Methods for Covariate Balancing: Going Beyond Propensity Score Matching and Weighting Using Optimization Techniques

Background: Propensity scores methods are perhaps the most ubiquitously-used set of statistical tools for matching and weighting to achieve covariate balance in comparative epidemiologic studies. However, they can by limited by sample size loss, unstable weights, and difficulties with estimation in small samples, among other issues. Recent advances in computing power and the science of optimization have led to the development of new optimization-based alternatives to propensity score methods: cardinality matching (CM; Zubizarreta et al., 2014) and stable balancing weights (SBW; Zubizarreta, 2015). CM and SBW have been shown to outperform propensity score methods on both balance and sample size simultaneously under a variety of conditions.

Objectives: To introduce attendees to the principles, applications, benefits, and technical implementation of CM for matching and SBW for weighting. Researchers of all experience levels who are involved in study design or statistical analysis for comparative epidemiologic studies would benefit by attending this workshop.

Description: CM and SBW are innovative new methods that use optimization to directly target covariate balance. Specifically, they allow researchers to pre-specify desired covariate balancing constraints — such as a maximum allowable standardized mean difference (SMD) for covariates between two groups — and explicitly solve an optimization problem to yield the mathematically-guaranteed largest matched sample (CM) or weights of minimum variance (SBW). Pre-specified balancing constraints may also be applied to each covariate separately to allow for tighter balance on covariates known to have greater prognostic value, and they can be applied flexibly to target balance of various moments of a distribution or even exact/perfect marginal or conditional distributional balance. CM and SBW also allow researchers to flexibly match or weight to target estimands, including the average treatment effect on the treated (ATT), controls (ATC), overall sample (ATE), or precisely-specified covariate distributions (e.g., an external control). In this workshop, we will (1) introduce the audience to the overarching optimization principles of CM and SBW; (2) discuss their applications to comparative analyses, including traditional database analyses as well as matching-adjusted indirect comparisons with or without partial individual patient data; (3) discuss their benefits and flexibilities vs. propensity score methods with empirical examples; and (4) review the steps of their technical implementation in R software. Attendees can expect to attain an advanced beginner's knowledge of CM and SMD and feel comfortable with applying these methods in future research.