In longitudinal observational studies with time-to-event outcomes, a common objective in causal analysis is to estimate the causal survival curve under hypothetical intervention scenarios. The g-formula is a useful tool for this analysis. To enhance the traditional parametric g-formula, we developed an alternative g-formula estimator, which incorporates the Bayesian Additive Regression Trees (BART) into the modeling of the time-evolving generative components, aiming to mitigate the bias due to model misspecification. We focus on binary time-varying treatments and introduce a general class of g-formulas for discrete survival data that can incorporate the longitudinal balancing scores. The minimum sufficient formulation of these longitudinal balancing scores is linked to the nature of treatment strategies, i.e., static or dynamic. For each type of treatment strategy, we provide posterior sampling algorithms. We conducted simulations to illustrate the empirical performance of the proposed method and demonstrate its practical utility using data from the Yale New Haven Health System's electronic health records.

翻译：在具有时间-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在假设干预情景下的因果生存曲线。g公式是进行此类分析的有用工具。为了增强传统的参数化g公式，我们开发了一种替代的g公式估计量，它将贝叶斯加性回归树（BART）纳入时变生成成分的建模中，旨在减轻因模型设定错误导致的偏倚。我们关注二元时变处理，并引入了一类适用于离散生存数据的通用g公式，该类公式能够纳入纵向平衡得分。这些纵向平衡得分的最小充分形式与处理策略的性质（即静态或动态）相关联。针对每种处理策略类型，我们提供了后验抽样算法。我们通过模拟研究说明了所提方法的实证性能，并利用耶鲁纽黑文卫生系统电子健康记录的数据展示了其实用价值。