Randomization inference when N equals one

• 成果类型: Article
• 署名作者: Liang, Tengyuan; Recht, Benjamin
• 署名单位: University of Chicago; University of California System; University of California Berkeley
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaf013
• 发表日期: 2025
• 关键词: Causal Inference; models; identification; exposure

摘要

For decades, $ 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. 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 experimental 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.