Detection of hearing losses (HL) via transient-evoked otoacoustic emissions: towards an automatic classification

The present study was carried out on volunteers some of whom had subjective complaints concerning their hearing. A total of 337 TEOAE responses were collected during several experimental sessions and were classified in two groups: a Training set and a Test set, composed by 158 and 182 TEOAEs, respectively. Only normal hearing subjects were considered in the Training set, according to the hearing threshold definitions presented in previous papers (Zimatore et al 2020a, 2020b). The 158 TEOAE responses of the Training set were composed by the 118 responses used in Zimatore et al 2011, and Zimatore et al 2020a, 2020b, and from 40 normal responses, purposely collected for this paper. In the Test set the 182 TEOAE responses were collected from 83 subjects presenting an ARHL, 35 subjects presenting a NIHL and 64 normal subjects. ARHL and NIHL are treated as two distinct classes of hearing deficits. The normal subjects included in the Test and Training sets were not the same.

The 182 TEOAE responses in the Test set were initially classified by their corresponding pure-tone hearing threshold. The TEOAE WWR estimate was automatically provided by the acquisition software (ILO92 device, Otodynamics UK, running software version ILO 6.1). Examples of the TEOAE responses captured by the acquisition software are shown in Supplementary materials-E, figure E.1 (available online at stacks.iop.org/BPEX/8/055021/mmedia). The TEOAE responses were saved as sets of time series which were subsequently analyzed by the RQA-based method. The values of the RAD2D parameter were derived by the RQA-based method, consisting in the evaluation of the RQA parameters and subsequent elaboration through the PCA analysis. Then, the values of the RAD2D parameter were derived in the PCA plane (see section 2.2). Table 1 reports the WWR and RAD2D parameters with the corresponding mean and standard deviations (sd) for the TEOAE responses from the Training and Test set cases. A t-test confirmed that these parameters were significantly different between the NIHL and ARHL groups with respect to the Normal group of the Test set (see table 1).

2.2.1. Recurrence quantification Analysis (RQA)

2.2.2. Principal component analysis (PCA)

PCA is a common statistical technique (Bartholomew 1984) applied in many different contexts (Zimatore et al 2020a), and provides interesting features such as: (i) a reduction of the dimension of the data, without any consistent loss of information; and (ii) the ability to clearly separate the independent features which characterize the data set.

In this paper the TEOAE responses were processed by RQA first, then by PCA. In particular, PCA was performed on the three main RQA measures: the percent of recurrence (REC), the percent of determinism (DET) and the Shannon entropy (ENT). Following these two analyses, the two-dimensional parameter RAD2D was calculated for each TEOAE signal as the Euclidean distance from the origin of the principal component reference system (for additional details see the Supplementary materials). In figure 1 the TEOAE responses of the Training test signals are shown in the plane PC1 versus PC2. A circle of radius (RAD2D) equal to 2 selects the 96% of normal responses (p < 0.05).

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2.2.3. Receiver operating characteristics (ROC)

2.2.4. Experimental procedure in five steps

To evaluate possible bias effects due to sample-size, the Training set made by 118 TEOAE responses used in previous papers (Zimatore et al 2020a, 2020b), was subdivided in various smaller sample sub-sets. The data reported in table 2 show the factor loading values of the first three PCA components, evaluated from the RQA parameters with 118 TEOAE responses (in italics) and three sub-sets of 100, 80 and 40 responses, respectively. The value of the explained variance (PVE) shown in table 2, presents the percentage of explained variability and the amount of information embedded in each component. The table shows that the PCA factor loadings correlate well between the 4 RQA estimates and the correspondings PCA components, since for the latter their amplitude and signs do not change across the different sub-sets (i.e. for the samples of 118, 100, 80 and 40 responses). The PVE of the PC1 corresponds to approximately 89% in all cases, with a maximum variation of 1.6% between the Training sets of 118 and 80 samples. The remaining variability is encoded in PC2 and PC3, with a maximum variation among the different Training sets of about 27.6% on PC2 (118 versus 40). PC2 encodes about 7%–9% of the signal variability. Since, the PVE of the PC3 component corresponds to approximately 3%–4% of the total PVE (1/30 of PC1), its values can be neglected in the definition of the RAD2D.

To better explore the possible sample size induced-variability, larger samples were also generated, containing 222, 158, 118, 104, and 40 responses (222 = 118 + 64 + 40, 158 = 118 + 40, 104 = 64 + 40, in italics the data from the original Training set of the 118 responses). The 64 normal responses belong to the Test set data. The corresponding PCA factor loading values are shown in table 3.

Considerations similar to those reported for table 2 can be derived. The factor loading values of the PCA components are invariant with respect to the number of subjects (for an n>40) in the Training set. The data of table 3 suggest that each set containing at least 40 normal subjects can be used as Training set.

For the following analysis, a Training set made by 158 TEOAE responses was used.

The PCA analysis of the RQA measurements derived from the Training data set, provides an estimation of the PCA factor loading values. As explained in 2.2.1, once the factor loading are calculated, each TEOAE in the Test set can be drawn as a point in the PC1^*vsPC2^* plane by using the factor loadings obtained from the Training set plane. The RAD2D value is estimated from the Euclidean distance of that representative point, from the origin of the PC1^*vsPC2^* plane. The one class discrimination was performed on RAD2D.

From the Test set RAD2D values, the sensitivity and the specificity values were calculated. The sensitivity is defined as the proportion of patients with a hearing deficit who test positive (ratio TP/(TP + FN)) and the specificity as the proportion of patients without a hearing deficit who test negative (ratio TN/(TN + FN)), with true positive (TP), false negative (FN) and true negative (TN) assessed for the 182 TEOAE responses belonging to the Test set considering the case classification based on the audiometric data.

In figure 2, sensitivity and specificity estimates are shown for different RAD2D values, ranging from 1 to 3.

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The data suggest that a range of values around RAD2D = 1.9 can optimize the values of sensitivity and specificity. Figure 2 highlights two different RAD2D values: (i) the 1.78 value, which was reported in previous papers on RAD2D-based discrimination and the value of 2, which selects the 96% of Normal responses (see comments in figure 1).

To discriminate between TEOAE responses from normal and hearing impaired ears, the choice of the RAD2D cut-off value is crucial and different oprimizing criteria can be used.

In order to define the RAD2D threshold automatically, a plot of sensitivity versus specificity was considered, as reported in figure 3 (ROC curve). In the figure, the point closest to (0,1) represents the maximum of sensitivity and specificity. Accordingly, the RAD2D threshold can be chosen corresponding to this point: the point closest to the upper left of the ROC plot is RAD2D = 2.0, which is shown with the red diamond character. This value is the radius of 'normality' (or reference circle) shown in of figure 1.

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For a general screening hearing assessment the RAD2D threshold value can be choosen to be below 2, in order to further reduce the false negatives selected by WWR.

In table 4 the improvement of one class discrimination with both WWR and RAD2D is shown with respect to specificity, sensitivity (or recall), as well as predictibility (or precision) (ratio TP/(TP + FP)) and accuracy (ratio (TP + TN)/(TP + TN + FP + FN)).

By using the combination of the two parameters, the specificity, sensitivity, predictability, and accuracy values are increased. From table 4 and figure 4 the differences observed between WWR and RAD2D + WWR are relevant; while the differences between RAD2D threshold values around 1.9 (figure 2) are subtle. Even though RAD2D = 2 is chosen by ROC curve criteria, since for a hearing screening is preferible to have less False Negatives with more False Positives (because these cases can successively be re-test), a RAD2D value of 1.78 can be used.

Moreover, in table 4, the FP Rate = FP/FP + TN, the ErrorRate = (FP + FN)/(TN + TP + FP + FN), and the Fscore = 2*Recall*Precision/(Recall+Precision) are reported.

These last metrics enforce the results obtained: by choosing RAD2D < 1.78 and WWR > 70 we obtained a better classification than with the other conditions investigated (the FP Rate is minor and the Error rate and F score are quite similar to RAD2D < 2), but much better than an criterion based only on the WWR threshold.

A limitation of this study is the moderate number of TEOAE responses which does not permit an extensive flexibility with the fine-tuning of parameters for an automatic selection algorithm. It should be noted that a collection of large TEOAE sets is not a mundane task. Although TEOAEs can be easlily recorded in clinical practise, there is an inherent variability to the TEOAE signals caused by multiple factors (age, gender, health status etc), which make the collection of large coherent samples, a rather challenging task; these factors can be controlled if a rigourous and specific protocol design of the research is established. In this context, a larger dataset could provide more flexibility in terms of the selection algorithm, but it will probably require a multi-centric approach.