There are limited options to estimate the treatment effects of variables which are continuous and measured at multiple time points, particularly if the true dose-response curve should be estimated as closely as possible. However, these situations may be of relevance: in pharmacology, one may be interested in how outcomes of people living with -- and treated for -- HIV, such as viral failure, would vary for time-varying interventions such as different drug concentration trajectories. A challenge for doing causal inference with continuous interventions is that the positivity assumption is typically violated. To address positivity violations, we develop projection functions, which reweigh and redefine the estimand of interest based on functions of the conditional support for the respective interventions. With these functions, we obtain the desired dose-response curve in areas of enough support, and otherwise a meaningful estimand that does not require the positivity assumption. We develop $g$-computation type plug-in estimators for this case. Those are contrasted with g-computation estimators which are applied to continuous interventions without specifically addressing positivity violations, which we propose to be presented with diagnostics. The ideas are illustrated with longitudinal data from HIV positive children treated with an efavirenz-based regimen as part of the CHAPAS-3 trial, which enrolled children $<13$ years in Zambia/Uganda. Simulations show in which situations a standard $g$-computation approach is appropriate, and in which it leads to bias and how the proposed weighted estimation approach then recovers the alternative estimand of interest.

翻译：针对在多个时间点测量的连续变量，估计其处理效应的可用方法有限，尤其是在需要尽可能精确估计真实剂量-反应曲线时。然而，这类情形可能具有实际意义：在药理学中，我们可能关注接受HIV治疗的人群（如病毒学失败等）的结局如何随随时间变化的干预（例如不同药物浓度轨迹）而改变。连续干预措施进行因果推断的一大挑战在于，正值假设通常被违反。为解决正值违背问题，我们开发了投影函数，该函数基于各自干预的条件支持函数对目标估计量进行重新加权和重新定义。借助这些函数，我们可在支持度充分的区域获得所需的剂量-反应曲线，而在其他区域则得到无需正值假设的有意义估计量。针对该情形，我们构建了g-计算类型的插件估计量，并将其与未专门处理正值违背而直接应用于连续干预的g-计算估计量进行对比——我们建议后者应附带诊断结果呈现。以赞比亚/乌干达招募的<13岁HIV阳性儿童接受依法韦仑方案治疗的CHAPAS-3试验纵向数据为例，阐述上述思想。模拟研究展示了在哪些情况下标准g-计算方法适用，哪些情况下会导致偏倚，以及本文提出的加权估计方法如何恢复替代目标估计量。