1. Revisiting the quartic model for early identification of Noise Induced Hearing Loss William J. Murphy and John R. Franks, National Institute for Occupational Safety and Health
Abstract:
In a 1976 article by Cooper and Owen [Audiologic profile of noise induced hearing loss, Arch. Otolaryngol. 102: ], they advanced a quartic model to perform a least-squares fit to an audiogram for the purpose of identifying a noise-induced notch indicative of the early onset of noise-induced hearing loss. This model has been revisited for the purpose of better quantification of a set of rules that will best identify the presence or absence of a noise notch. A subset of 1660 subjects’ right and left audiograms collected for the National Health and Nutrition Examination Survey (NHANES IV) were fit with a quartic model. As well, several hearing scientists and audiologists within NIOSH examined and classified the audiograms as having a notch or not. Preliminary results suggest that the choice of notch criteria dramatically affects the identification accuracy when correlated with clinical judgments. This paper will present how these rules were developed and how the quartic model may be interpreted and applied in a hearing conservation program.
Problem:
In hearing conservation programs, audiologists and technicians are required to report incidents when a worker’s hearing exhibits a standard threshold shift (STS). An STS is defined in OSHA and MSHA regulations as a shift of 10 decibels (dB) or more for either ear in the average of the pure-tone hearing thresholds at 2000, 3000 and 4000 Hz. NIOSH recommends that a Significant Threshold Shift be defined as a 15-dB shift in pure-tone threshold in either ear for the frequencies 500 to 6000 Hz and immediate retesting of the worker to confirm the threshold shift.
The underlying difference between the two definitions is the ability to identify the occurrence of a substantial change in hearing capability. Analysis of the historical rates of identification of a substantial change has demonstrated that the NIOSH criterion identifies more workers with a significant threshold shift [NIOSH, 1988]. While a higher rate of identification may seem at face value to be a positive effect, it still represents the documentation of a worker’s progression to hearing impairment.
Given that most of the workers in the United States in a hearing conservation program are tested by a technician who records the hearing thresholds in a database, the development of tools that can analyze and identify early indicators of hearing loss should be a priority. A recent article in Spectrum [Dobie and Rabinowitz, 2003], motivated an investigation of a cross-sectional population sample of hearing collected by the NHANES IV survey. This investigation compared the choice of rules that technicians and audiologists used to evaluate the presence of a noise-induced notch in the audiogram
Background:
Rabinowitz and Dobie (2003) discussed four different approaches to identification of a noise-induced notch. The first paper they examined was Niskar et al who utilized a set of criteria that were tailored to notch identification in a young adolescent population. First, the audiogram was required to have normal hearing in the low frequencies, 500 and 1000 Hz < 15 dB HL. Second, the notch (3000, 4000 or 6000 Hz) must be more than 15 dB above the worst threshold between 500 and 1000 Hz. Third the improvement of hearing at 8000 Hz must be 10 dB or more. These criteria are rather restrictive and provide a form of benchmark for audiograms that exhibit a notch.
The second paper [Cooper and Owen, 1976] examined the prevalence of the noise notch and used a 4th order polynomial (quartic) in their analysis. While Cooper and Owen did not develop any specific parameters for identifying the notch, the quartic model provides a curve that can be fit to most any audiogram. The quartic model can create several general shapes, among which are a characteristic M or W-shaped curve.
The third approach that Rabinowitz and Dobie discussed was a piecewise fit of the audiogram to a combination of a linear model for the low frequency portion and a parabola for the notch region [Gates et al. (2000)]. The interpretation of the Gates model is straightforward, the width of the parabolic portion describes the extent of impaired hearing and the depth of the parabola relates to the magnitude of the notch. Borrowing this concept allows an interpretation of Cooper and Owens quartic model.
A least squares fit of the model to each audiogram was performed. The fitting parameters were not directly relatable to a notch or no-notch condition. Instead, using the properties of minima and maxima (dy/dx = 0 and d2y/dx2 < > 0 ), the respective minima and maxima of the fit were determined. The location of a maxima was constrained to be within Hz. Each of the curves could then be evaluated as to whether or not the notch rule was satisfied. In this case, the amount of a shift from the low-frequency minima to the maxima was varied in 1-dB steps. Similarly, the amount of recovery was evaluated in 1-dB steps.
0.34
0.41
0.43
0.29
0.59
Discussion:
This research was undertaken as an opportunity to evaluate the performance of the Notch Index and to develop improvements to the problem of early indicators of noise-induced hearing loss. Several aspects of the quartic model could be improved. As noted, the evaluation is currently performed on the fit to the data and not on the actual audiometric data. The fit to a 4th order polynomial provides well-defined features such as minima and maxima that can be found. Finding minima and maxima in the audiometric data presents situations where the audiogram is noisy and potentially ill-defined. If the quartic model is used to identify the frequencies of the minima and maxima, then a modified algorithm could look up the audiometric values of the nearest frequencies. Once the frequencies are selected, the rule can easily be evaluated.
A second area for improvement is in the evaluation of both ears. NIHL due to occupational exposure will typically be present in both ears. The model has been developed using isolated audiograms and not binaural evaluations. The judges evaluated each ear separately, but the contralateral audiogram was plotted in the background to allow them to see both ears at the same time. For each evaluation, the judges had to confirm their evaluation as notched or not notched.
Finally if this system could be evaluated by a larger group of audiologists, preferably actively involved in occupational hearing conservation, the rule could be better refined to identify notched audiograms.
Conclusions:
These results demonstrate the utility of a more sophisticated model for identification of the noise-notch. The quartic model permitted the evaluation of numerous rules against a set of evaluations completed by experienced audiologists. The correlations showed that the audiologists used a more restrictive rule that required at least a 10-dB shift and a 5-dB recovery. None of the judges were instructed regarding what criteria they were to use in the evaluation. Furthermore, the order in which audiograms were evaluated was randomized to minimize any bias that existed in the ordering of the subject in the dataset (the subset of the NHANES data were sorted on the right ear 8 kHz threshold). As well as the quartic model, the Notch Index using different definitions was compared to the judges’ evaluations. While the Notch Index is an interesting concept that makes intuitive sense, it fails to yield a high degree of correlation with judgments of the panel of audiologists. Thus its utility for identifying NIHL is limited.
References:
Cooper J.C., and Jeffery H. Owen. Audiologic Profile of Noise-Induced Hearing Loss.1976;
Gates GA; Schmid P; Kujawa SG; Nam B, and DAgostino R. Longitudinal threshold changes in older men with audiometric notches. Hear Res. 2000; 141(1-2):
NIOSH (1998). Revised criteria for a recommended standard – occupational noise exposure. U.S. Department of Health and Human Services, Public Health Service, Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health, DHHS (NIOSH) Publication
Niskar AS; Kieszak SM; Holmes AE; Esteban E; Rubin C, and Brody DJ. Estimated prevalence of noise-induced hearing threshold shifts among children 6 to 19 years of age: The Third National Health and Nutrition Examination Survey, , United States. Pediatr. 2001; 108(1):40-43.
Rabinowitz, PM, and Dobie RA. Use of the Audiometric Configuration to Determine Whether Hearing Loss is Noise-Induced: Can “Notch Criteria Help?” NHCA Spectrum 2003; 20(1):8-11.
Correspondence:
William J. Murphy, Ph.D.,
National Institute for Occupational Safety and Health,
4676 Columbia Parkway MS C-27
Cincinnati, OH
Figure 3: Correlation matrix for the averaged non-audiologist evaluations of NHANES data. Three non-audiologists completed evaluated each of the 3320 audiograms for the right and left ears of the subjects in the NHANES data. Each audiogram was classified as either having a notch or having no notch. The judgments were stored and then the quartic model was tested using several rules. For instance, a 0 dB shift and 15 dB recovery yielded a correlation of 0.43 in the upper left corner. The best correlation was 0.59 which implies a 4 dB shift and 5 dB recovery rule was most commonly used by the three non-audiologists. The lower right corner of the correlation plot is anomalous for the non-audiologists and may represent a significant shift with a 5-dB recovery at 8 kHz.
Figure 5: Correlation of Notch Index calculated using 2, 3 & 4 kHz with the audiologist and non-audiologist evaluations. The Notch Index was calculated as the difference between the pure-tone average for 2, 3 & 4 kHz and the pure-tone average for 1 and 8 kHz [Rabinowitz and Dobie, 2003]. As can be seen, the Pearson correlation coefficient with the two groups of judges reached a maximum of about 0.2 when the Notch Index was set at 3 to indicate the presence of a notch. Such a low correlation indicates poor performance for this definition of the Notch Index.
In Figure 6, definition of the Notch Index was modified to include 6 kHz in the calculation. The correlations were calculated for different values of the notch index and the clinical evaluations.
Figure 1: The least squares fit, minima and maxima plotted for three audiograms. The maximum that is located between 2 and 8 kHz is identified and the adjacent minima are identified. The algorithm for notch identification evaluates the minima on either side of a maximum threshold that falls between 2000 and 8000 Hz.
In the left panel for Subject 45, a maximum exists below 1 kHz and is ignored. The minimum was located at about 2000 Hz. Since no minimum exists in the plot above 8 kHz, the value at 8 kHz serves as the minimum. In the middle panel for Subject 175, a minimum was found at about 1600 Hz and the value at 8 kHz was used as the minimum. The maximum threshold occurred at about 6 kHz. In the right panel for Subject 1051, a minimum was found at about 1600 Hz, but no other minimum was found beyond the maximum threshold at 8 kHz. 8 kHz was used as the maximum and the high-frequency minimum.
0.68
0.53
0.51
0.32
0.49
Figure 4: Correlation matrix for the averaged audiologist evaluations of NHANES data. Three audiologists evaluated each of the 3320 audiograms for the right and left ears of the subjects in the NHANES data. These results indicate that the rule that best matches the evaluations performed by the audiologists was a 13-dB shift from the low-frequency minima to the notch and a 5-dB recovery. The reader should note that although the audiogram is measured with a 5-dB step size, the fit is performed on a continuous scale, thus the rule can be adjusted to find the best correlation with the audiologist evaluations.
A similar correlation analysis was performed for the Notch Index using 2, 3, & 4 kHz and for the Notch Index using 2, 3, 4 & 6 kHz.
Figure 6: Correlations of Notch Index calculated using 2, 3, 4 & 6 kHz for both audiologist and non-audiologist evaluations. The modified calculation of the Notch Index provides a much more pronounced peak in the correlation plots. These results suggest that if the Notch Index is positive that a notch is present in the audiogram. A correlation of 0.4 is still lower than one would desire to algorithmically identify the presence of a notch.
When these results are compared to the results using the quartic model, the model improves the correlation to about 0.68 for the audiologists. Given the differences between the audiologists and non-audiologists, the algorithm should be based upon obtaining a best match to the performance of trained audiologists.
Figure 2: In this figure, the rules are displayed on the graph as vertical bars. If the distance from the maxima to the adjacent minima exceed the rule, then the maxima is marked as a notch. If not, the audiogram does not have a notch. For Subjects 45 and 175, the bars do not intersect the plot. However, for subject 1051 in the right panel, the bar at 8000 Hz intersects the plot and therefore the fit did not satisfy the notch criteria. Each of the 3320 audiograms were fit and evaluated against shifts ranging from 5 to 15 decibels for both the low frequency and high frequency sides. In the next portion of the research, 3 non-clinical hearing scientists and three audiologists evaluated the audiograms for the presence or absence of a notch.