🤖 AI Summary
This paper addresses individual-time-point-level counterfactual inference under adaptive treatment strategies in multi-unit, multi-period sequential experiments, aiming to relax strong prior assumptions on intervention policy structure. We propose a nonparametric latent factor model that unifies nonlinear mixed-effects and bilinear factor models. Integrating nonparametric nearest-neighbor estimation with sequential experimental design, we derive the first non-asymptotic, high-probability error bound for individual-time-point-level counterfactual means. We establish theoretical consistency of the estimator and asymptotic validity of associated confidence intervals. The method is validated via simulations and the HeartSteps mobile health clinical trial, demonstrating both statistical accuracy and practical utility. Our core contribution lies in breaking the traditional reliance on restrictive parametric or structural assumptions about treatment policies—enabling high-precision, assumption-light, fine-grained causal inference at the individual-time-point level.
📝 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 non-parametric generalization of the non-linear mixed effects model and the bilinear latent factor model considered in prior works. For estimation, we use a non-parametric method, namely a variant of nearest neighbors, and establish a non-asymptotic 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 $infty$ together at suitable rates. We illustrate our theory via several simulations and a case study involving data from a mobile health clinical trial HeartSteps.
