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Estimating causal effects from large experimental and observational data hasbecome increasingly prevalent in both industry and research. The bootstrap isan intuitive and powerful technique used to construct standard errors andconfidence intervals of estimators. Its application however can beprohibitively demanding in settings involving large data. In addition, moderncausal inference estimators based on machine learning and optimizationtechniques exacerbate the computational burden of the bootstrap. The bag oflittle bootstraps has been proposed in non-causal settings for large data buthas not yet been applied to evaluate the properties of estimators of causaleffects. In this paper, we introduce a new bootstrap algorithm called causalbag of little bootstraps for causal inference with large data. The newalgorithm significantly improves the computational efficiency of thetraditional bootstrap while providing consistent estimates and desirableconfidence interval coverage. We describe its properties, provide practicalconsiderations, and evaluate the performance of the proposed algorithm in termsof bias, coverage of the true 95% confidence intervals, and computational timein a simulation study. We apply it in the evaluation of the effect of hormonetherapy on the average time to coronary heart disease using a largeobservational data set from the Women's Health Initiative.

A Fast Bootstrap Algorithm for Causal Inference with Large Data