Counterfactual inference in sequential experiments
Raaz Dwivedi, Katherine Tian, Sabina Tomkins, Predrag Klasnja, Susan Murphy, Devavrat Shah
The Annals of Statistics · 2025 · Volume 53 · Issue 6
Abstract
We consider after-study statistical inference for sequentially designed experiments wherein multiple units are assigned treatments for multiple time points using treatment policies that adapt over time. Our goal is to provide inference guarantees for the counterfactual mean at the smallest possible scale—mean outcome under different treatments for each unit and each time—with minimal assumptions on the adaptive treatment policy. Without any structural assumptions on the counterfactual means, this challenging task is infeasible due to more unknowns than observed data points. To make progress, we introduce a latent factor model over the counterfactual means that serves as a nonparametric generalization of the nonlinear mixed effects model and the bilinear latent factor model considered in prior works. For estimation, we use a nonparametric method, namely a variant of nearest neighbors, and establish a nonasymptotic high probability error bound for the counterfactual mean for each unit and each time. Under regularity conditions, this bound leads to asymptotically valid confidence intervals for the counterfactual mean as the number of units and time points grows to ∞ together at suitable rates. We illustrate our theory via several simulations and a case study involving data from a mobile health clinical trial HeartSteps.
Keywords
62G20, 62K05, 62L05, 62L10, Adaptive randomization, counterfactual inference, Mixed effects model, nearest neighbors, nonlinear factor model, sequential experiments
Enable JavaScript for citation tools and additional paper interactions.