STATISTICAL MATCHING AND SUBCLASSIFICATION WITH A CONTINUOUS DOSE: CHARACTERIZATION, ALGORITHM, AND APPLICATION TO A HEALTH OUTCOMES STUDY

Subclassification and matching are often used in empirical studies to adjust for observed covariates; however, they are largely restricted to rela-tively simple study designs with a binary treatment and less developed for designs with a continuous exposure. Matching with exposure doses is partic-ularly useful in instrumental variable designs and in understanding the dose -response relationships. In this article we propose two criteria for optimal sub-classification based on subclass homogeneity, in the context of having a con-tinuous exposure dose, and propose an efficient polynomial-time algorithm that is guaranteed to find an optimal subclassification with respect to one criterion and serves as a 2-approximation algorithm for the other criterion. We discuss how to incorporate dose and use appropriate penalties to control the number of subclasses in the design. Via extensive simulations, we sys-tematically compare our proposed design to optimal nonbipartite pair match-ing and demonstrate that combining our proposed subclassification scheme with regression adjustment helps to reduce model dependence for paramet-ric causal inference with a continuous dose. We apply the new design and associated randomization-based inferential procedure to study the effect of transesophageal echocardiography (TEE) monitoring during coronary artery bypass graft (CABG) surgery on patients' postsurgery clinical outcomes, us-ing Medicare and Medicaid claims data, and find evidence that TEE monitor-ing lowers patients' all-cause 30-day mortality rate.