Principal components analysis on audiograms from a hearing aid clinic

In this study we describe a Principal Components Analysis (PCA) of 11,462 audiograms recorded at the hearing aid clinic at James Cook University Hospital in Middlesbrough between 1992 and 2001. PCA is a multivariate statistical technique which starts with an n x p matrix in which n subjects are each evaluated on each of p variables (Woods et al, 1986). In our case the n subjects were represented by the 11,462 audiograms, and the p variables were the six air conduction thresholds and five bone conduction thresholds typically obtained in an audiogram. Although the patients were originally tested at 11 thresholds, the principle of PCA is that certain hearing thresholds tend to vary together, and thus can be grouped into a smaller number of underlying variables called principal components (PC). Each PC has a set of coefficients in the range -1 to +1, corresponding to the degree of influence of each of the original thresholds on that PC. The coefficients of the first PC were all negative and approximately equal. This suggests that the main source of variation between the patients was simply the overall degree of hearing loss. The coefficients of the second PC were negative for frequencies at or below 1000Hz, but positive for higher frequencies, for both air and bone conduction, and thus differentiate patients according to whether they have a predominanty high frequency or low frequency hearing loss. The coefficients of the third PC were negative for air conduction at all frequencies, but positive for bone conduction, showing a contrast between patients with and without an air-bone gap. The fourth component is similar to the second, but corresponds to a sensorineural hearing loss with a sharper dip at 2000 – 4000 Hz rather than a general high frequency hearing loss. No clear patterns were seen for the fifth or subsequent principal components. The percentage of the overall variability in the data explained by the first four principal components respectively was 59.5, 13.4, 9.7, and 5.2, giving a total of 87.8%. We performed PCA using the MATLAB statistical toolbox.