Abstract

Most causal inference methods consider counterfactual variables under interventions that set the exposure to a fixed value. With continuous or multi-valued treatments or exposures, such counterfactuals may be of little practical interest because no feasible intervention can be implemented that would bring them about. Longitudinal modified treatment policies (LMTPs) are a recently developed nonparametric alternative that yield effects of immediate practical relevance with an interpretation in terms of meaningful interventions such as reducing or increasing the exposure by a given amount. LMTPs also have the advantage that they can be designed to satisfy the positivity assumption required for causal inference. We present a novel sequential regression formula that identifies the LMTP causal effect, study properties of the LMTP statistical estimand such as the efficient influence function and the efficiency bound, and propose four different estimators. Two of our estimators are efficient, and one is sequentially doubly robust in the sense that it is consistent if, for each time point, either an outcome regression or a treatment mechanism is consistently estimated. We perform numerical studies of the estimators, and present the results of our motivating study on hypoxemia and mortality in intubated Intensive Care Unit (ICU) patients. Software implementing our methods is provided in the form of the open source R package lmtp freely available on GitHub (https://github.com/nt-williams/lmtp) and CRAN.

摘要

大多数因果推理方法考虑将暴露设置为固定值的干预措施下的反事实变量。通过连续或多值的治疗或暴露，这种反事实可能没有什么实际意义，因为无法实施可行的干预措施来实现它们。纵向修正治疗政策（LMTP）是最近开发的一种非参数替代方案，它产生具有直接实际相关性的效果，并根据有意义的干预措施进行解释，例如减少或增加一定量的暴露。LMTP 的另一个优点是它们可以被设计来满足因果推理所需的积极性假设。我们提出了一个新颖的序贯回归公式来识别 LMTP 因果效应，研究 LMTP 统计估计量的属性，例如有效影响函数和效率界，并提出四种不同的估计量。我们的两个估计器是有效的，并且一个是连续双稳健的，因为如果对于每个时间点，结果回归或治疗机制被一致地估计，那么它是一致的。我们对估计量进行了数值研究，并展示了我们对插管重症监护病房 (ICU) 患者低氧血症和死亡率的激励性研究结果。实现我们方法的软件以开源 R 包 lmtp 的形式提供，可在 GitHub (https://github.com/nt-williams/lmtp) 和 CRAN 上免费获取。如果对于每个时间点，结果回归或治疗机制被一致地估计，则它是一致的，因此是连续双稳健的。我们对估计量进行了数值研究，并展示了我们对插管重症监护病房 (ICU) 患者低氧血症和死亡率的激励性研究结果。实现我们方法的软件以开源 R 包 lmtp 的形式提供，可在 GitHub (https://github.com/nt-williams/lmtp) 和 CRAN 上免费获取。如果对于每个时间点，结果回归或治疗机制被一致地估计，则它是一致的，因此是连续双稳健的。我们对估计量进行了数值研究，并展示了我们对插管重症监护病房 (ICU) 患者低氧血症和死亡率的激励性研究结果。实现我们方法的软件以开源 R 包 lmtp 的形式提供，可在 GitHub (https://github.com/nt-williams/lmtp) 和 CRAN 上免费获取。