Longitudinal data often contains outcomes measured at multiple visits, and scientific interest may lie in quantifying the effect of an intervention on an outcome's rate of change. For example, one may wish to study the progression (or trajectory) of a disease over time under different hypothetical interventions. We extend the longitudinal modified treatment policy (LMTP) methodology to estimate effects of complex, exposure-dependent interventions on rates of change in an outcome over time. We exploit the theoretical properties of a nonparametric efficient influence function (EIF)-based estimator to introduce a novel inference framework that can be used to construct simultaneous confidence intervals for a variety of causal effects of interest and to formally test relevant global and local hypotheses about rates of change. We demonstrate the utility of our framework in investigating whether a longitudinal shift intervention affects an outcome's counterfactual trajectory, as compared with no intervention. We present results from a simulation study to illustrate the performance of our inference framework in a longitudinal setting with time-varying confounding and a continuous exposure. We also apply our inference framework to the Columbia Brain Health DataBank (CBDB) to examine the effect of shifting blood pressure on the progression of dementia.

翻译：纵向数据常包含多个随访节点测量的结局变量，科学兴趣常在于量化干预措施对结局变化速率的影响。例如，研究者可能希望研究不同假设干预下疾病随时间进展（或轨迹）的变化。我们扩展了纵向修正治疗策略（LMTP）方法论，以估计复杂、暴露依赖性干预对结局随时间变化速率的影响。利用基于非参数有效影响函数（EIF）估计量的理论性质，我们提出了一种新型推断框架，可构建多种感兴趣因果效应的同时置信区间，并正式检验关于变化速率的全局及局部假设。通过比较无干预情境，我们展示了该框架在探究纵向偏移干预是否影响结局反事实轨迹方面的实用性。通过模拟研究，在存在时变混杂和连续暴露的纵向环境下验证了推断框架的性能。我们还将该框架应用于哥伦比亚大脑健康数据库（CBDB），以分析血压偏移对痴呆进展的影响效应。