Optimal Matching with Minimal Deviation from Fine Balance in a Study of Obesity and Surgical Outcomes

• Activity Number: 113
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Health Policy Statistics
• Author(s): Dan Yang*+ and Dylan Small and Paul R. Rosenbaum and Jeffrey H. Silber
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania and The Children's Hospital of Philadelphia
• Keywords: Assignment algorithm ; Fine balance ; Matching ; Network optimization ; Observational study ; Optimal matching

Abstract

In multivariate matching, fine balance constrains the marginal distributions of a nominal variable in treated and matched control groups to be identical without constraining who is matched to whom. In this way, a fine balance constraint can balance a nominal variable with many levels while focusing efforts on other more important variables when pairing individuals to minimize the total covariate distance within pairs. Fine balance is not always possible; that is, it is a constraint on an optimization problem, but the constraint is not always feasible. We propose a new problem that is always feasible and an algorithm which returns a minimum distance finely balanced match when one is feasible, and otherwise minimizes the total distance among all matched samples that minimize the deviation from fine balance. We also show how to incorporate an additional constraint. The case of knee surgery in the Obesity and Surgical Outcomes Study motivated the development of this algorithm and is used as an illustration.