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Summary 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. 

Abstract: This commentary proposes a framework for understanding the role of statistics in policy-making, regulation, and bureaucratic systems. I introduce the concept of “ex ante policy,” describing statistical rules and procedures designed before data collection to govern future actions. Through examining examples, particularly clinical trials, I explore how ex ante policy serves as a calculus of bureaucracy, providing numerical foundations for governance through clear, transparent rules. The ex ante frame obviates heated debates about inferential interpretations of probability and statistical tests, p-values, and rituals. I conclude by calling for a deeper appreciation of statistics’ bureaucratic function and suggesting new directions for research in policy-oriented statistical methodology. 

We investigate adaptive protocols for the elimination or reduction of the use of medications or addictive substances. We formalize this problem as online optimization, minimizing the cumulative dose subject to constraints on individual well-being. We adapt a model of addiction from the psychology literature and show how it can be described by a class of linear time-invariant systems. For such systems, the optimal policy amounts to taking the smallest dose that maintains well-being. We derive a simple protocol based on integral control that requires no system identification, only needing approximate knowledge of the instantaneous dose response. This protocol is robust to model misspecification and is able to maintain an individual's well-being during the tapering process. Numerical experiments demonstrate that the adaptive protocol outperforms non-adaptive methods in terms of both maintenance of well-being and rate of dose reduction.