A Multinomial Model for Identifying Significant Pure-Tone Threshold Shifts

Abstract

Purpose Significant threshold differences on retest for pure-tone audiometry are often evaluated by application of ad hoc rules, such as a shift in a pure-tone average or in 2 adjacent frequencies that exceeds a predefined amount. Rules that are so derived do not consider the probability of observing a particular audiogram. Methods A general solution for evaluating threshold differences on retest was developed on the basis of multinomial probabilities. The model uses the standard deviation of inter-test differences for 1 frequency as a parameter of the underlying Gaussian distribution of test results. The number of test frequencies, the categories of threshold change, and the probability of each category’s occurrence are used to calculate the probability that a given pattern of threshold differences on retest (or 1 rarer) could occur by chance. Results The multinomial model was compared with 2 other methods for identifying threshold shifts in persons exposed to high sound pressure levels during concerts. The multinomial model identified the same audiograms as the ad hoc methods. Conclusion Tables developed using a multinomial model can provide a clinical tool for evaluating audiograms by identifying statistically significant patterns of test–retest differences in hearing thresholds.