🤖 AI Summary
This study addresses the problem of determining whether high-frequency monitoring data return to their pre-intervention baseline distribution following an intervention. The authors propose a sequential testing procedure that requires no assumptions about the underlying data distribution. The method constructs a discrepancy measure via universal inference and combines it with individualized empirical calibration to form a non-negative supermartingale, yielding an e-process that enables valid detection of the recovery time at any arbitrary stopping point without specifying a null model. Theoretical analysis provides finite-sample bounds on the calibration error, and both simulations and a clinical case study demonstrate the method’s superior performance in accurately identifying the time at which baseline conditions are restored.
📝 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.