Hierarchical Bayesian estimation of motor-evoked potential recruitment curves yields accurate and robust estimates

We aim to develop a robust method to improve the estimation accuracy of motor-evoked potential (MEP) recruitment curves (RCs), including motor threshold, in small-sample settings which typically involve fewer than 40 stimuli.

We present a hierarchical Bayesian (HB) method to model MEP size as a rectified-logistic function of stimulation intensity. This method is designed to account for small samples, handle outliers without discarding data, quantify estimation uncertainty, and simulate synthetic data that closely matches real observations, useful for optimizing experimental design. We validate its performance on transcranial magnetic stimulation (TMS), epidural spinal cord stimulation (SCS), and synthetic TMS datasets, and provide an open-source library for Python, called hbMEP, for diverse applications.

The rectified-logistic outperformed sigmoidal functions in predictive accuracy on TMS and SCS datasets, as demonstrated through cross-validation. A mixture extension of the HB model improved robustness to outliers by further increasing its predictive accuracy. The HB model reduced threshold estimation error by up to 70% on sparse synthetic TMS data compared to non-hierarchical models. Bayesian estimation with the HB model reduced the required number of participants by at least 23% to detect a shift in threshold with 80% power, compared to frequentist testing. Empirical results on human SCS data further validated its applicability to real data.

By improving accuracy on sparse data, our method minimizes the number of stimuli needed to probe each individual's neuromuscular parameters across multiple muscles simultaneously, thereby reducing session duration and the risk of inadvertent neuromodulation. Our approach provides a more statistically powerful and conclusive framework for inferring changes in threshold, and therefore corticospinal excitability. The hbMEP library streamlines and unifies the analysis of RCs across stimulation modalities and experimental paradigms.