Participants

The participants included in [6] were the same in the current study. The participants were 92 adult HA users (38 men) with SNHL, in the age range 18 to 60 years (distribution of age is shown in Fig 1 in S1 File), with mean (SD) of 50.35 (9.07) years and with mean (SD) of 42.96 (13.58) PTA. The included participants had acquired bilateral SNHL not exceeding 70 dB HL at low to mid frequencies (i.e., between 250 and 2000 Hz) in the better ear or in the aided ear; and they used at least one HA for 3 months minimum. The participants had no history of learning difficulties, neurological disorders, or cognitive impairments. The study was approved by the National Health Services Research Ethics Committee, England (IRAS ID: 226216). All participants provided written informed consent.

Hearing evaluation and HA fitting

Hearing assessment.

Otoscopy, tympanometry and pure tone audiometry were performed on both ears in each participant. Ears were examined following the BSA recommended procedure [24]; and tympanometry was performed using the Interacoustics Titan device with a 226-Hz probe tone [25]. Air conduction pure tone thresholds were measured at octave and interoctave frequencies from 250 to 8000 Hz (Fig 1). Bone conduction pure tone thresholds were measured at octave frequencies from 500 to 4000 Hz [26].

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Fig 1.

Test-ear (left panel, partially reproduced from [6]) and nontest-ear (right panel) mean (±1 SD) pure tone thresholds (black) with pure tone thresholds for each of the 92 participants (grey).

https://doi.org/10.1371/journal.pone.0260090.g001

Behavioural measures

Speech-ABRs

Decision trees

In the original work, BinKhamis et al. [6] included only aided speech-ABR F0 encoding amplitude and latency as possible predictors in the regression model. However, these two variables represent only a part of the information that is encoded in ABRs. Since regression trees are robust with missing data and can handle highly correlated predictors, it was possible to extend the analysis including also unaided speech-ABR F0 encoding and aided and unaided speech-ABR peaks. In this way, each of the three behavioural measures was used to fit two regression trees. The purpose was to explore all possible predictors.

Six regression trees were fitted to evaluate if the BKB-SIN, VCV and SSQ-Speech could be predicted using either speech-ABR peaks or speech-ABR F0 encoding. The non-ABR variables included in each tree were: participant age, DS-F, DS-B, and PTA; then three trees were fitted with amplitudes and latencies of speech-ABR peaks, and the other three trees were fitted with F0 encoding amplitude and latency. BinKhamis et al. [6] evaluated three multiple linear regression models using only speech-ABR aided-quiet and aided-noise conditions. Here, we used the data from all four speech-ABR conditions (aided-quiet, aided-noise, unaided-quiet, and unaided-noise).

All the regression trees were performed in R (version 3.6.3, [35]) using the package rpart [20], which implements the classical classification and regression tree algorithms developed by Breiman et al. [14]. The complexity parameter was set 0.0001 allowing growing a large tree [14, 15], which then was pruned obtaining the smallest tree that minimized the cross-validation error. The other parameters of the fitting were set to their default values, i.e., the number of cross-validations was 10 [14, 20], the minimum number of observations in any terminal node was taken as seven [20], and surrogate splits were used as recommended by Breiman et al. [14].

We had data from 92 participants. In order to obtain as stable as possible trees, it was decided to fit the trees with all observations, and to use the internal cross-validation procedure to evaluate the performance of the trees [20]. The cross-validation estimated the relative error and cross-validation error (xerror) of each tree. The latter is used for pruning because it is related to the predicted residual error sum of squares (PRESS) statistic [20, 36, 37]. The relative error is a measure of accuracy of the tree that, using the linear regression analogy, is equal to the 1-R², which is the proportion of variance not explained by the model [14, 20]. The Root-Mean Square Error (RMSE) between the actual and predicted behavioural measures was calculated. Furthermore, the variable importance for each tree was also evaluated. The measure of importance is based on the sum over all nodes of the decrease of the error produced by splits of a given variable [14, 20]. For an easy interpretation, the importance of the variables was scaled to sum 100 [20].

BKB-SIN trees

In the F0 encoding tree (R² = 0.43; RMSE = 3.64), there were three terminal nodes and two splits, both of which were based on PTA. The tree predicted that the mean BKB-SIN was -0.15 dB SRT-50 for the participants with PTA < 43 dB HL (47 participants, 51% of the total), 3.3 dB SRT-50 for those with PTA between 43 and 60 dB HL (34, 37%), and 9.7 SRT-50 for those with PTA ≥ 61 dB HL (11, 12%). The three most important variables were PTA, aided Fo encoding amplitude in quiet and then in noise (Fig 9 in S1 File). In the speech-ABR peaks tree (R2 = 0.45; RMSE = 3.56), the first two splits were based on PTA and were identical to the splits in the F0 encoding tree; however, the right branch of the second node (PTA between 43 and 60 dB HL) was further split by aided latency of peak F in quiet as the participants with peak F < 40 ms had mean of 2.5 dB SRT-50 (23, 25%), whereas the participants with peak F ≥ 40 ms had a mean of 5.1 dB SRT-50 (11, 12%). Fig 5 shows the relationship between BKB-SIN, PTA and aided latency of peak F. The three most important variables were PTA, aided amplitude of peak VA in noise, aided amplitude of peak E in quiet (Fig 10 in S1 File).

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Fig 5. Relationship between BKB-SIN, PTA and aided latency of peak F.

Missing peaks are indicated with crosses at 0 ms for graphical convenience. The colour code is the same as used in Fig 2.

https://doi.org/10.1371/journal.pone.0260090.g005

VCV trees

In the F0 encoding tree (R² = 0.49; RMSE = 3.69), there were four terminal nodes given by the split of the PTA and aided latency in quiet. The participants with PTA < 39 dB HL showed a mean performance of -2.7 dB SRT-50 (33 participants, 36% of the total), with PTA between 39 and 46 dB HL had mean performance of 0.43 dB SRT-50 (23, 25%), participants with PTA ≥ 47 dB HL and F0 encoding latency < 14 ms in quiet had mean performance of 3.2 dB SRT-50 (27, 29%), whereas the 9 participants with later latency ≥ 14 ms had mean performance of 9.5 dB SRT-50. The three most important variables were PTA, aided F0 encoding amplitude and latency in quiet (Fig 11 in S1 File). In the speech-ABR peaks tree (R2 = 0.57; RMSE = 3.41), the first and second nodes were PTA and were identical to the F0 encoding tree, the split of the third node was due to the aided amplitude of peak VA in quiet at 0.25 μV. The left branch (i.e. ≥ 0.25 μV) was further split by age where participants younger than 55 years had mean performance of 1.2 dB SRT-50 (17, 18%) while the older ones had mean performance of 6.2 dB SRT-50 (9, 10%). The 10 participants with amplitude < 0.25 μV had mean performance of 9.4 dB SRT-50. After PTA, the next most important variables were the aided amplitude of peaks VA and E in quiet (Fig 12 in S1 File).

SSQ-Speech trees

Both the F0 encoding and speech-ABR peaks tree (R2 = 0.16; RMSE = 1.56) had only one node that split the participants by PTA at 50 dB HL where worse hearing thresholds predicted an average score of 4.4 (31 participants, 34% of the total) while the better hearing thresholds predicted an average score of 5.8 (61, 66%). After PTA, the next most important variables were F0 encoding aided amplitude in quiet and unaided latency in quiet in the F0 encoding tree (Fig 13 in S1 File); and the aided amplitude of peak E in quiet and aided amplitude of peak F in noise in the speech-ABR peaks trees (Fig 14 in S1 File).

Accuracy of the regression trees

In order to evaluate whether the regression trees were accurate or, in other words, worthwhile [38], two metrics are generally used: Root Mean Square Error (RMSE) and R² [15]. The RMSE measures the lack of fit of the model relative to the data [15]. Since the MSE can be broken down into variance and squared bias of the data [15, 21], in the case of unbiased estimator of the mean, the MSE of the model and variance of the data are the same [15], and so are their square roots, namely RMSE and standard deviation (SD). However, a predictor with low bias may have high variance (that is the bias-variance trade-off, [15]). Nevertheless, the RMSE of the model and SD of the data can be compared and, being the same unit, are easily interpretable. Instead, R² is the proportion of variance explained by the model; it is a-dimension with a range between 0 and 1.

The SSQ-speech trees were root node trees, i.e., with only the root, which lead to a poor accuracy as the RMSE was slightly better than SD (1.56 vs. 1.71 score) and the variance accounted by the trees was small (R² = 0.16).

Considering the trees for the BKB-SIN and VCV, their RMSE’s were below 4 dB SRT-50 and smaller relative to the standard deviation of the behavioural measures. Looking at the proportion of variance explained by the trees, the values of R² laid between 0.43 (BKB-SIN with F0 encoding) and 0.57 (VCV with the speech-ABR peaks). Overall, the regression trees had good accuracy. Other statistical learning algorithms, such as Random Forest [39] or Boosting [40, 41], may give better predictive accuracy than the regression trees [15]. However, the accuracy was not the critical objective of the current study, but rather we were interested to understand the structural relationships between behavioural and speech-ABR measures; the aim was to assess if speech-ABRs are a clinically applicable objective outcome measure in HA users.

Variable importance

The most important variable was PTA in each of the six trees. This was in line with the results obtained by BinKhamis et al. [6], who studied a subset of our predictors. The first splits from the root were always due to PTA. This suggests that PTA is more informative than any of the speech-ABR measures.

Putting to one side the SSQ-Speech trees as they had only one node, we extrapolated the three most important variables for each tree, for a total of 12 variables. Of the eight variables with speech-ABR measures, six were in the quiet condition and two in background noise, and all were aided. So, the most informative condition was aided quiet. The SIN tests were performed aided and in noise. The trees may rely mainly on quiet condition because the speech-ABR in quiet is more detectable than in noise [6, 7] as the former condition allowed to have both more inter-subject variability (i.e. more information available for modelling) and less missing data points relative to the speech-ABR in noise.

Some of the variables ranked as important but were not used in the trees. In the F0 encoding VCV tree, the aided F0 encoding amplitude, despite not being a node, was more important than the aided F0 encoding latency, which was a tree node. This was because, in the root node, the optimal split was given by PTA while the best suboptimal split was due to the F0 encoding amplitude. So, being suboptimal has contributed to its importance [14].

Prediction of behavioural measures with speech-ABRs

Two studies were able to correlate SIN tests performance with F0 amplitude estimated in the Fourier domain from the steady-state region of the 170-ms [da]. It was reported that F0 amplitude in quiet for older adults (mean 63.1 years old) and F0 amplitude in noise for young adults (mean 24 years old) were larger for the participants with better SIN tests performance relative to those with worse performance [42, 43]. The older adults had normal or near-normal hearing up to 4 kHz and some degree of hearing loss at higher frequency [42], whereas the young adults had normal hearing [43]. Others did not find the association between speech-ABRs and SIN test performance in adults with normal or near-normal absolute thresholds up to 4 kHz. For instance, the correlation between F0 through the fifth harmonic recorded in older adults (mean 70 years old, and audiometric thresholds ≤ 20 dB HL up to 4 kHz) and SIN tests performance was not significant [44]. Interestingly, Coffey et al. [45] reported a positive correlation between F0 and SIN tests using magnetoencephalography (MEG) but not using EEG in normal-hearing adults. In one of the few studied with HA users, Easwar et al. [12] observed a positive correlation between EFR amplitudes and both speech discrimination scores and sound quality ratings. Seol et al. [46] investigated the effects of HA noise reduction algorithms for speech understanding and speech-ABRs both in quiet and in noise. They reported a positive correlation between F0 amplitudes and SIN tests performance irrespective of the background (quiet or noise), however it was not clear how the speech-ABRs were recorded (unaided or aided, cf. their Figs 5 and 6) or how the presence/absence of a speech-ABR was established as several F0 amplitudes were close to 0 μV. In the current study, the F0 encoding latency in quiet was a node in the VCV tree, splitting the performance of the participants with PTA ≥ 47 dB HL. The delayed F0 measures were associated with the nine poorest performers. Because our CV stimulus was shorter relative to those in the above-mentioned studies, our frequency resolution was lower and this may have an effect on the estimation of F0. Indeed, the EFR amplitude in [12] was the sum of the response amplitudes across the eight formant carrier of the stimulus, whereas our F0 was based on one carrier. This may explain the lack of F0 measures as a strong predictor in our case. Furthermore, stimuli with a sustained component (such as [susa∫i] or 170-ms [da]) can provide information about temporal fine structure, which might be important for speech perception in noise [47, 48]. However, a longer stimulus will result in a longer recording session [7], which has to be kept to a minimum for a clinical setting, and in the degradation of the temporal characteristics of speech-ABRs [5]. Overall, taken together, these mixed results do not clarify the role of F0 measures in the SIN prediction, and further studies are required, in particular involving HA users.

Beside the features extracted in the frequency domain, such as the F0 measures, the amplitude and latency of speech-ABR peaks are the key temporal features to evaluate. In this framework, Parbery-Clark et al. [49] examined speech-ABRs evoked by 170-ms [da] within multi-talker babble (the SNR was 10 dB as in this study) in normal-hearing adults and their performance on a SIN test. Using the speech-ABR peaks elicited by the stimulus onset (at 9–11 ms) and the formant transition period (at 43–45 ms) as features, they observed positive correlations between the latency of both peaks and SIN test performance. In the current study, the onset peak was labelled as peak VA. In the BKB-SIN tree, the amplitude of peak VA in noise was among the important variables. In the VCV tree, the amplitude of peak VA in quiet was a predictor for the subgroup of participants having the worst PTA and performance. Furthermore, their formant transition peak can be associated with our peaks D, E, and F [8, 9]. The amplitude of peak E in quiet was among the important variables for both the BKB-SIN and VCV trees. In the BKB-SIN tree, latency of peak F in quiet was a predictor only for the participants with PTA between 43 and 61 dB HL.

For a subgroup of participants, both the onset (i.e. peak VA) and the FFR (i.e. peaks E and F, and the F0 encoding measures) of speech-ABRs appeared to be relevant for SIN performance. The speech onsets and, in turn, the speech-ABRs onset, have been theorised to be linked to phoneme identification and language literacy [50]. Therefore, abnormal amplitude or timing may indicate less robust phoneme identification resulting in reduced speech understanding in noise. Abrams & Kraus [50] proposed that FFR measures represent frequency transitions, which are important for suprasegmental cues (e.g. speaker’s gender and emotion) and for consonant identification. Consequently, impairment in the FFR may be linked to a deficit in utilising these cues and, hence, to a difficulty to understand speech in noise.

The effects of age on speech-ABRs and SIN performance were examined by Heidari et al. [51] and Mamo et al. [44]. In both studies, the comparison between younger and older adults showed that the latter had worse SIN performance and lower speech-ABR amplitude than the younger groups. Age was among the predictors for the VCV in the speech-ABR peaks tree, but only when aided amplitude of peak VA in quiet was ≥ 0.25 μV. The VCV performance worsened as a function of age but without a strong group division as in the previous studies [44, 51]. Clinard & Tremblay [52] observed that the amplitudes of the onset responses (waves V and A) degraded significantly as age increased.

Regarding SSQ-Speech, Anderson et al. [30] reported that latency of the peak O (i.e. offset) and the ’response morphology’ (i.e., cross-correlation between stimulus and response waveforms) of speech-ABR were significant predictors for the SSQ-Speech score. As in our study, the speech-ABRs were evoked by a 40 ms [da]. Differently to the current study, Anderson et al. [30] obtained speech-ABR monaurally through insert earphones (we used loudspeakers) in adults with both normal-hearing and hearing loss (we had only adults with SNHL), having average PTA (0.5–4 kHz) from 2.5 to 44.5 dB HL (in our case from 12 to 68 dB HL). In their study, the PTA was not a significant predictor, instead, in the SSQ-Speech trees, the only node split the participants at a PTA of 50 dB HL, that is near their worst PTA. So, the two results may be reconciled assuming that as PTA has larger variance or range, it may give a stronger contribution to explain the SSQ-Speech score.

In the current study, the PTA range was wider relative to the above-mentioned studies. The wide range of PTA means that the PTA is the most relevant feature. However, the wide range of PTA is an asset here as it allowed assessing the speech-ABR as a possible objective measure for HA users in a clinically plausible scenario, given that a wide variability in PTA is common in a clinical setting.

Non-linearity and sub-groups

One of the reasons for using regression trees was to disclose plausible non-linear boundaries between the predictors. Instead, the models predicted monotonic relations for BKB-SIN and VCV trees. Considering for instance the tree fitted to VCV with speech-ABR peaks: worse hearing threshold led to worse performances, younger participants outperformed the older ones, and smaller speech-ABR amplitudes were associated with worse performance. However, the tree allowed pinpointing the sub-groups of participants for which the prediction was based on speech-ABR features. In the case of the BKB-SIN tree, the aided latency of peak F in quiet can be used for the participants with PTA between 43 and 61 dB HL, this feasibility within a range of only 18 dB HL would not be useful as a clinical tool. In the case of the VCV trees, F0 encoding and speech-ABR measures split the participants with PTA ≥ 47 dB HL in two sub-groups, pointing-out the nine/ten participants with the poorest performance, as such a method aimed at a niche group of participants may not be clinically relevant but is promising for future research. It will also be worthy to explore if speech-ABRs evoked by other stimuli (e.g., longer than those used here) would model and predict behavioural measures in HA users with a wide range of PTA.