Longitudinal settings involving outcome, competing risks and censoring events occurring and recurring in continuous time are common in medical research, but are often analyzed with methods that do not allow for taking post-baseline information into account. In this work, we define statistical and causal target parameters via the g-computation formula by carrying out interventions directly on the product integral representing the observed data distribution in a continuous-time counting process model framework. In recurrent events settings our target parameter identifies the expected number of recurrent events also in settings where the censoring mechanism or post-baseline treatment decisions depend on past information of post-baseline covariates such as the recurrent event process. We propose a flexible estimation procedure based on targeted maximum likelihood estimation coupled with highly adaptive lasso estimation to provide a novel approach for double robust and nonparametric inference for the considered target parameter. We illustrate the methods in a simulation study.

翻译：纵向研究常涉及结局事件、竞争风险事件及删失事件在连续时间内的发生与复发，这类场景在医学研究中十分普遍，但现有分析方法往往无法利用基线后信息。本研究基于连续时间计数过程模型框架，通过对表征观测数据分布的产品积分直接施加干预，利用g-计算公式定义统计与因果目标参数。在复发事件情境下，即使删失机制或基线后治疗决策依赖于复发事件过程等基线后协变量的历史信息，我们所提出的目标参数仍可识别复发事件的期望数量。我们提出一种基于目标最大似然估计与高度自适应LASSO估计相结合的灵活推断流程，为所关注的目标参数提供双稳健且非参数推断的新方法。通过模拟研究验证了该方法的有效性。