Authors: Jason Lien¹
¹University of Cambridge
Introduction: With the growing interests in consumer-grade assistive listening devices (e.g., AirPods), an automatic, accurate, and fast hearing test is highly desirable. Pure-Tone Audiometry (PTA) is the mainstream method adopted clinically that utilises the 2 alternatives forced-choice paradigm. In the process, the presentation levels are determined by the listener’s responses and vary in fixed step sizes of 5 or 10 dB. In this study, an algorithm, efficient noisy binary search (ENBS), is proposed to determine the step size maximising the information gain per presentation.
Method: The ENBS Algorithm – The algorithm adopts a Bayesian framework to update the belief of the threshold and stops when the credible interval is smaller to a pre-specified size, or the number of presentations reaches a limit (stop criteria). The algorithm starts the presentations with the expected value of the prior and updates the prior distribution depending on the response from the listener. The presentations continue until the stop criteria is met. The estimated threshold is the expectation of the latest updated prior distribution (posterior).
Monte Carlo Simulation – Each listener’s response is modelled as a draw from a normal distribution with a mean of the true threshold, theta, and a standard deviation, sigma, representing the noise (both internal and external) while doing the hearing test. In 100000 simulations, theta was estimated with the two methods, British Society of Audiology (BSA) recommended procedure for PTA and ENBS under different noise levels. In addition, several conditions such as listener misses to respond, different ways of estimating the noise level, and the true threshold is not on 5 dB step, were simulated to test if either of the methods works better.
Results: In simulations, with the same average number of presentations, the absolute error of ENBS was significantly smaller by 0.6 dB on average and most (>95%) errors were smaller than 5dB. This advantage was robust across different noise levels.
Discussion: The Bayesian framework allows ENBS to grow with the number of tests conducted as the prior can be updated periodically. Also, depending on the use case, the stopping criteria can be adjusted to balance the time and accuracy.
