Balance Optimization Subset Selection (BOSS): An Alternative Approach for Causal Inference with Observational Data

Abstract

Scientists in all disciplines attempt to identify and document causal relationships. Those not fortunate enough to be able to design and implement randomized control trials must resort to observational studies. To make causal inferences outside the experimental realm, researchers attempt to control for bias sources by postprocessing observational data. Finding the subset of data most conducive to unbiased or least biased treatment effect estimation is a challenging, complex problem. However, the rise in computational power and algorithmic sophistication leads to an operations research solution that circumvents many of the challenges presented by methods employed over the past 30 years.

Complexity and Approximation Results for the Balance Optimization Subset Selection Model for Causal Inference in Observational Studies

“…The first step in solving such problems is to establish their computational complexity. Nikolaev et al (2013) showed that BOSS is NP-hard. This section will consider the complexity of the balanced matching problem, including special cases where certain restrictions are placed on the balancing covariates.…”

“…Specifically, as the residual imbalance measured by D increased, the quality of the estimated treatment effect decreased. As demonstrated by Nikolaev et al (2013), when the imbalance score for D is zero, it is possible to construct a bound on the remaining bias in the estimate of the treatment effect when certain assumptions are made concerning the form of the response function. However, these bounds do not apply when D is nonzero.…”

“…The BOSS model proposed by Nikolaev et al (2013) focuses primarily on covariate balance to identify a control group. Specifically, BOSS seeks a C ⊆ C that minimizes some imbalance measure T C on the (empirical) distributions of covariates in the treatment and control groups.…”

“…For the purposes of assessing balance on the joint distributions of covariates, Nikolaev et al (2013) defined a covariate cluster D ⊆ X as a subset of covariates. Then the categories, or values, for a covariate cluster…”

Identifying NCAA tournament upsets using Balance Optimization Subset Selection

“…The Balance Optimization Subset Selection (BOSS) framework (Nikolaev et al 2013) is used to do the selection. BOSS is a framework that allows the selection of a small control group from a larger control pool that is similar to a treatment group, where similarity is determined by a defined balance measure.…”