Return-to-Baseline Testing via Empirically Calibrated e-processes

Marta Regis; Paulo Serra

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arXiv · 2606.01960

Return-to-Baseline Testing via Empirically Calibrated e-processes

Marta Regis·Paulo Serra

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Abstract

We consider the problem of detecting a Return to Baseline (RtB) in high-frequency monitoring data preceding and following an intervention, where the aim is to identify the time at which the data-generating distribution realigns with its pre-intervention distribution. We propose a sequential, distribution-free testing procedure that does not rely on specifying a null model and provides anytime-valid error control. The method relies on ideas from universal inference to define a discrepancy measure that is aggregated into a non-negative super-martingale, and is then empirically cal- ibrated to form an e-process. The calibration is performed using the baseline data, and is thus subject-specific. We establish finite-sample bounds for the calibration error (under a flexible non-parametric assumption), discuss the impact of tuning parameters and computational complexity, and illustrate through simulations and a clinical case study that the procedure accurately detects RtB from monitoring data.

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Marta Regis, Paulo Serra. 2026-06-01. Return-to-Baseline Testing via Empirically Calibrated e-processes. https://arxiv.org/abs/2606.01960

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