Estimating causal effects from large experimental and observational data has become increasingly prevalent in both industry and research. The bootstrap is an intuitive and powerful technique used to construct standard errors and confidence intervals of estimators. Its application however can be prohibitively demanding in settings involving large data. In addition, modern causal inference estimators based on machine learning and optimization techniques exacerbate the computational burden of the bootstrap. The bag of little bootstraps has been proposed in non-causal settings for large data but has not yet been applied to evaluate the properties of estimators of causal effects. In this paper, we introduce a new bootstrap algorithm called causal bag of little bootstraps for causal inference with large data. The new algorithm significantly improves the computational efficiency of the traditional bootstrap while providing consistent estimates and desirable confidence interval coverage. We describe its properties, provide practical considerations, and evaluate the performance of the proposed algorithm in terms of bias, coverage of the true 95% confidence intervals, and computational time in a simulation study. We apply it in the evaluation of the effect of hormone therapy on the average time to coronary heart disease using a large observational data set from the Women's Health Initiative.

翻译：从大规模实验和观测数据中估计因果效应在工业界和学术界日益普遍。Bootstrap是一种直观且强大的技术，用于构建估计量的标准误差和置信区间。然而，在处理大规模数据时，其应用可能面临巨大的计算负担。此外，基于机器学习和优化技术的现代因果推断估计器进一步加剧了Bootstrap的计算复杂性。非因果场景下已有针对大规模数据提出的“小Bootstrap袋”方法，但尚未应用于评估因果效应估计量的性质。本文提出了一种名为“因果小Bootstrap袋”的新型Bootstrap算法，用于大规模数据的因果推断。新算法在显著提升传统Bootstrap计算效率的同时，提供了相合估计和理想的置信区间覆盖。我们描述了其性质，给出了实际应用建议，并通过模拟研究评估了所提算法在偏差、真实95%置信区间覆盖率及计算时间方面的表现。此外，我们利用女性健康倡议组织的大规模观测数据集，将其应用于评估激素疗法对平均冠心病发病时间的影响。