Using Randomized Rounding of Linear Programs to Obtain Unweighted Natural Strata That Balance Many Covariates

• Activity Number: 56 - Causal Inference
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Katherine Brumberg* and Dylan S. Small and Paul R Rosenbaum
• Companies: Wharton School, University of Pennsylvania and University of Pennsylvania and Wharton School, University of Pennsylvania
• Keywords: causal inference; covariate balance; linear programming; integer programming; randomized rounding; optimal strata

Abstract

Natural strata are a compromise between conventional strata and matching in a fixed ratio, say pair matching or matching two controls to each treated individual. Like matching in a fixed ratio, natural strata do not require weights and balance many covariates beyond those explicitly appearing in the strata definitions. Like stratification and unlike matching in a fixed ratio, the ratio of controls to treated individuals need not be an integer, so if the data permit a fixed ratio comparison of 2.5-to-1 or 0.75-to-1, then these ratios are possible using natural strata. Natural strata are defined by a fixed proportion of control to treated units in each stratum plus an integer program that minimizes the total imbalance in many covariates. In general, solving large integer programs is computationally very difficult, but we modify an established idea of randomized rounding of a linear programming solution. We discuss attractive properties of the method. When proportional strata are infeasible, we minimize the earthmover distance to find strata that minimally deviate from proportionality. Methodology is illustrated comparing birth outcomes for older and younger mothers in the US in 2018.