Variants of relative frequency methods for determining transcranial magnetic stimulation motor threshold do not provide accurate estimation of threshold

Relative frequency methods such as five-out-of-ten have been used for a long time to determine motor threshold of transcranial magnetic stimulation (TMS), despite known severe limitations both in accuracy and speed. Variants of relative frequency methods have been developed to improve performance, such as adaptive staircasing and the recent RMT-Finder using binary search. However, they do not solve the fundamental problem underlying the use of relative frequencies to approximate the 50% TMS response rate at threshold. We demonstrate that the probability of false decisions using relative frequency due to at least half the pulses resulting in responses at subthreshold intensities or more than half the pulses resulting in no responses at suprathreshold intensity cannot be sufficiently reduced unless an impractically high pulse count is used, which substantially increases the duration of the thresholding procedure. Simulations in a virtual population of 25,000 subjects reveal that the accuracy of relative frequency methods is not improved by the adaptive staircasing or binary search variants. Although these variants reduce the number of pulses required to reach an estimate compared to the conventional relative frequency method, they are still slower and less accurate than more advanced thresholding methods such as stochastic approximation or maximum likelihood estimation. Therefore, these faster and more accurate methods should become the standard for motor thresholding of TMS, and the use of methods based on relative frequency should be discouraged.