Modeling the antidepressant treatment response to transcranial magnetic stimulation using an exponential decay function

Recovery from depression often demonstrates a nonlinear pattern of treatment response, where the largest reduction in symptoms is observed early followed by smaller improvements. This study investigated whether this exponential pattern could model the antidepressant response to repetitive transcranial magnetic stimulation (TMS). Symptom ratings from 97 patients treated with TMS for depression were collected at baseline and after every five sessions. A nonlinear mixed-effects model was constructed using an exponential decay function. This model was also applied to group-level data from several published clinical trials of TMS for treatment-resistant depression. These nonlinear models were compared to corresponding linear models. In our clinical sample, response to TMS was well modeled with the exponential decay function, yielding significant estimates for all parameters and demonstrating superior fit compared to a linear model. Similarly, when applied to multiple studies comparing TMS modalities as well as to previously identified treatment response trajectories, the exponential decay models yielded consistently better fits compared to linear models. These results demonstrate that the antidepressant response to TMS follows a nonlinear pattern of improvement that is well modeled with an exponential decay function. This modeling offers a simple and useful framework to inform clinical decisions and future studies.