N-of-1 experiments, where a unit serves as its own control and treatment in different time windows, have been used in certain medical contexts for decades. However, due to effects that accumulate over long time windows and interventions that have complex evolution, a lack of robust inference tools has limited the widespread applicability of such N-of-1 designs. This work combines techniques from experiment design in causal inference and system identification from control theory to provide such an inference framework. We derive a model of the dynamic interference effect that arises in linear time-invariant dynamical systems. We show that a family of causal estimands analogous to those studied in potential outcomes are estimable via a standard estimator derived from the method of moments. We derive formulae for higher moments of this estimator and describe conditions under which N-of-1 designs may provide faster ways to estimate the effects of interventions in dynamical systems. We also provide conditions under which our estimator is asymptotically normal and derive valid confidence intervals for this setting.

翻译：在特定医疗语境中，以同一单元在不同时间窗口内作为自身对照与处理的单病例随机对照试验（N-of-1实验）已应用数十年。然而，由于长期时间窗口内累积效应及干预措施的复杂演化，缺乏稳健推断工具限制了此类N-of-1设计方案的广泛应用。本研究融合因果推断中的实验设计方法与控制理论的系统辨识技术，构建了此类推断框架。我们推导出线性时不变动力系统中动态干扰效应的模型，并证明：一类与潜在结果研究中相似的因果估计量，可通过基于矩估计的标准估计量进行估计。本文推导了该估计量高阶矩的解析表达式，阐明N-of-1设计在动态系统中加快干预效应估计的条件，同时给出了估计量渐近正态性的成立条件，并推导了该场景下有效的置信区间。