Bagged one-to-one matching for efficient and robust treatment effect estimation

Observational studies present challenges due to bias from imbalance in baseline confounders. One-to-one matching (OOM), a popular cohort-construction technique for observational studies, reduces bias and provides a compelling basis for inference but generally leads to at least some loss of efficiency due to the exclusion of potentially informative subjects. We introduce the bagged one-to-one matching (BOOM) estimator, which combines the bias-reducing properties of OOM with the variance-reducing properties of bootstrap aggregation (bagging). We describe the BOOM algorithm in detail, provide R code for its implementation, and investigate its performance in simulation studies and a case study. In the simulation studies, under different types of model misspecification, we compare the BOOM estimator's performance in terms of mean squared error, bias, variance, accuracy of standard error estimation, and coverage of nominal 95% confidence intervals to that of OOM and to that of ordinary least squares estimation, inverse probability weighting, and targeted maximum likelihood estimation, all on the full unmatched cohort. In our simulations, the BOOM estimator achieves as much bias reduction as the estimator based on OOM, while having much lower variance. In all of the settings examined in the simulations, the BOOM's mean squared error is comparable to or better than that of the comparison methods. In the case study, BOOM yields estimates similar to those from the established methods, with narrower 95% confidence intervals.