标题： 贝叶斯化的目标最大似然估计在因果效应估计中不确定性量化中的应用 显示英文标题

标题： Bayesian implementation of Targeted Maximum Likelihood Estimation for uncertainty quantification in causal effect estimation

摘要： 稳健的决策制定涉及在不确定性存在的情况下做出决策，通常用于医疗保健、供应链和金融等关键领域。 因果关系在决策制定中起着至关重要的作用，因为它预测了由于处理（也称为干预）导致的结果（通常是关键绩效指标）的变化。 为了利用因果关系进行稳健的决策制定，本文提出了三种流行的靶向最大似然估计（TMLE）算法的贝叶斯方法，这是一种灵活的半参数双重稳健估计器，用于二元处理以及二元和连续结果的因果效应不确定性的概率量化。 在前两种方法中，三个TMLE模型（结果、处理和波动）是按顺序训练的。 由于处理和结果的贝叶斯实现产生概率预测，第一种方法使用平均预测，而第二种方法使用预测的平均值和标准差来训练波动模型（目标步骤）。 第三种方法通过贝叶斯网络（本文中称为BN-TMLE）同时训练所有三个模型。 所提出的几种方法在两个具有二元和连续结果的例子中进行了演示，并与经典实现进行了验证。 本文还研究了数据规模和模型误设对使用BN-TMLE方法进行因果效应估计的影响。 结果表明，在小数据情况下，所提出的BN-TMLE优于经典实现，在大数据情况下表现相似。 显示英文摘要

摘要： Robust decision making involves making decisions in the presence of uncertainty and is often used in critical domains such as healthcare, supply chains, and finance. Causality plays a crucial role in decision-making as it predicts the change in an outcome (usually a key performance indicator) due to a treatment (also called an intervention). To facilitate robust decision making using causality, this paper proposes three Bayesian approaches of the popular Targeted Maximum Likelihood Estimation (TMLE) algorithm, a flexible semi-parametric double robust estimator, for a probabilistic quantification of uncertainty in causal effects with binary treatment, and binary and continuous outcomes. In the first two approaches, the three TMLE models (outcome, treatment, and fluctuation) are trained sequentially. Since Bayesian implementation of treatment and outcome yields probabilistic predictions, the first approach uses mean predictions, while the second approach uses both the mean and standard deviation of predictions for training the fluctuation model (targeting step). The third approach trains all three models simultaneously through a Bayesian network (called BN-TMLE in this paper). The proposed approaches were demonstrated for two examples with binary and continuous outcomes and validated against classical implementations. This paper also investigated the effect of data sizes and model misspecifications on causal effect estimation using the BN-TMLE approach. Results showed that the proposed BN-TMLE outperformed classical implementations in small data regimes and performed similarly in large data regimes.