In longitudinal observational studies with a time-to-event outcome, a common objective in causal analysis is to estimate the causal survival curve under hypothetical intervention scenarios within the study cohort. The g-formula is a particularly useful tool for this analysis. To enhance the traditional parametric g-formula approach, we developed a more adaptable Bayesian g-formula estimator. This estimator facilitates both longitudinal predictive and causal inference. It incorporates Bayesian additive regression trees in the modeling of the time-evolving generative components, aiming to mitigate bias due to model misspecification. Specifically, we introduce a more general class of g-formulas for discrete survival data. These formulas can incorporate the longitudinal balancing scores, which serve as an effective method for dimension reduction and are vital when dealing with an expanding array of time-varying confounders. The minimum sufficient formulation of these longitudinal balancing scores is linked to the nature of treatment regimes, whether static or dynamic. For each type of treatment regime, we provide posterior sampling algorithms, which are grounded in the Bayesian additive regression trees framework. We have conducted simulation studies to illustrate the empirical performance of our proposed Bayesian g-formula estimators, and to compare them with existing parametric estimators. We further demonstrate the practical utility of our methods in real-world scenarios using data from the Yale New Haven Health System's electronic health records.

翻译：在具有时间至事件结局的纵向观察性研究中，因果分析的一个常见目标是估计研究队列中假设干预情景下的因果生存曲线。g-公式是此类分析中特别有用的工具。为增强传统参数化g-公式方法，我们开发了一种更灵活的贝叶斯g-公式估计量。该估计量同时支持纵向预测和因果推断。它在时间演变的生成成分建模中整合了贝叶斯加性回归树（Bayesian additive regression trees），旨在减轻因模型误设导致的偏差。具体而言，我们针对离散生存数据引入了一类更具一般性的g-公式。这些公式能够纳入纵向平衡得分（longitudinal balancing scores），这既是一种有效的降维方法，也在处理不断增多的时变混杂变量时至关重要。这些纵向平衡得分的最小充分形式与治疗方案的静态或动态性质相关联。针对每种类型的治疗方案，我们提供了基于贝叶斯加性回归树框架的后验采样算法。我们开展了模拟研究以展示所提出的贝叶斯g-公式估计量的实证性能，并与其现有的参数化估计量进行比较。我们还利用耶鲁纽黑文健康系统（Yale New Haven Health System）电子健康记录的数据，进一步证明了我们的方法在实际场景中的实用性。