The role of covariate balance in observational studies

Jason J. Sauppe, Sheldon H. Jacobson

Research output: Contribution to journalArticlepeer-review


Observational data are prevalent in many fields of research, and it is desirable to use this data to make causal inferences. Because this data is nonrandom, additional assumptions are needed in order to construct unbiased estimators for causal effects. The standard assumption is strong ignorability, though it is often impossible to achieve the level of covariate balance that it requires. As such, researchers often settle for lesser balance levels within their datasets. However, these balance levels are generally insufficient to guarantee an unbiased estimate of the treatment effect without further assumptions. This article presents several extensions to the strong ignorability assumption that address this issue. Under these additional assumptions, specific levels of covariate balance are both necessary and sufficient for the treatment effect estimate to be unbiased. There is a trade-off, however: as balance decreases, stronger assumptions are required to guarantee estimator unbiasedness. These results unify parametric and nonparametric adjustment methods for causal inference and are actualized by the Balance Optimization Subset Selection framework, which identifies the best level of balance that can be achieved within a dataset.

Original languageEnglish (US)
Pages (from-to)323-344
Number of pages22
JournalNaval Research Logistics
Issue number4
StatePublished - Jun 2017


  • balance
  • causal inference
  • matching
  • observational data
  • optimization
  • strong ignorability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research

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