Initially, we studied the PSD values, focusing on analyzing paired samples of COVID-19 versus the control group, pneumonia against asthma, and COVID-19 against both asthma and pneumonia. To ensure clarity, Table 1 details the number of segmented cough audio samples used for the computations and the number of patients from the Coswara dataset reported to be affected by each of the relevant illnesses. Patient numbers and samples numbers are different in that the samples are constituted of the isolated audio of a cough event: a total of 1183 cough segments of COVID-19 positives versus 341 audio segments in the COVID-19 negative category. To palliate to imbalance in classes we used under-sampling.
Power spectrum density (PSD) computed on each audio using the Welch method and averaged for all population cough signals extracted from the crowdsourced publicly available dataset Coswara29. The dataset’s recordings were collected from participants using their built-in computer microphone, the sampling rate of the data is 22,050 Hz. (a) Comparison of PSD between cough signals of COVID-19-positive and COVID-19-negative patients. Zoom-in view between 1 and 4 kHz. (b) Comparison of PSD between cough signals of pneumonia COVID-19-positive and COVID-19-negative patients. Zoom-in view between 1 and 4 kHz. (c) Comparison of PSD between cough signals of asthma COVID-19-positive and COVID-19-negative patients. Zoom-in view between 1 and 4 kHz. (d) Comparison of PSD between cough signals of patients with asthma and pneumonia. Zoom-in view between 1 and 4 kHz.
2-D and 3-D visual representations of the linear separation value J optimization process for distinguishing between COVID-19-positive and COVID-19-negative patients using cough signals, extracted from the publicly available Coswara dataset29. (a) 2-D visualization of the optimized separation value over different frequency bands, demonstrating the clear differentiation between COVID-19-positive and COVID-19-negative patients. The white dotted lines on the 2-D plot indicate the boundaries of distinct regions-Region 1 (left) and Region 2 (right). (b) 3-D visualization of the optimization process, providing a more comprehensive view of the separation between the two groups and highlighting the potential of utilizing cough signals as a diagnostic tool for COVID-19. The dataset’s recordings were collected from participants using their built-in computer microphone, the sampling rate of the data is 22050 Hz.
A preliminary exploration of the PSD values, displayed in Fig. 1, revealed observable differences between the curves for each pair of categories. Figure 1a shows a comparison of the PSD values for COVID-19-positive patients’ coughs and the control group’s coughs. The first noticeable difference occurred in the range of frequencies between 100 and 800 Hz, and the second in the frequencies approaching 1500 Hz. These frequencies are in the low- and high-frequency ranges, respectively. The COVID-19-positive PSD curve revealed a peak at 250 Hz, which was higher in amplitude than that revealed by the COVID-19-negative curve-a characteristic that we observed in the COVID-19-positive curves of all three plots (see Fig. 1a–c). A second peak at around 1500 Hz is also distinguishable in all three figures, which was half the amplitude of the peak of the control group, as seen in Fig. 1a. These features allowed us to separate COVID-19 from other illnesses, and vice versa, within the two regions of frequencies corresponding to the previously mentioned low- and high-frequency ranges. Comparing asthma and pneumonia without confounding COVID-19, we observed a difference between the two curves at the frequencies of 80–220 Hz (a relatively very low frequency range) and 616–660 Hz. We also observed similar differences in the three peaks of asthma-infected patients at 1616 Hz, 2040 Hz, and 3450 Hz. The final peak at 3450 Hz in the PSD curves of the asthma samples was the lowest and negligible for our analysis. The differences in the PSD curves were indicative of patterns in the cough sound signals (i.e., notable and distinguishable in COVID-19-positive patients) and potentially valuable for use with a diagnostic machine learning classifiers. Comparing COVID-19-positive and COVID-19-negative asthma and pneumonia samples provided secondary support for related frequency bands capable of isolating COVID-19 from other respiratory illnesses. It also highlighted that asthma and pneumonia curves exhibited differences in lower and higher frequencies, indicating distinct patterns in the cough sounds associated with these illnesses.
The linear separation value \(J(F_{1}, F_{2})\), estimated in the range 1–3000 Hz in Fig. 2 consistently showed two distinct regions with large J values indicating higher separability. The first region we observed in Fig. 2a aligned with the PSD values highlighted previously, spanning the 1–1500 Hz frequency bands. The second was between 1000 and 2500 Hz. These identified regions will be labeled Region 1 and Region 2 for the rest of our analysis. The three-dimensional plot of the linear separation value \(J(F_{1}, F_{2})\), calculated within the frequency range of 1–3000 Hz, is presented in Fig. 2b. The maximum J values is highlighted with a tick in the plot. In Fig. 2b, the maximum of the separability value is in the 1000–1600 Hz band, and the second maximum J value (i.e., the second peak) is located in the 200–800 Hz band. Both regions tally with the previous observations shown in Fig. 1. In summary, the representations of the J separability criterion of the cough sound signals’ RP values shown in the plots in Fig. 2 provide a comprehensive view of the patterns and frequency bands of interest, support our preliminary observations of the PSD curves in Fig. 1, and could be valuable for developing diagnostic algorithms.
The next step involved assessing the p values resulting from the Mann–Whitney U test39. The t-test can be less reliable with unequal sample sizes, however, Mann–Whitney U test does not have this limitation40. In addition, due to the non-parametric nature of Mann–Whitney U test, it makes the analysis more generalizable41. Table 2 presents the results of the statistical test’s heuristic search and consequently only includes the minimum values returned by the U-test. The frequency bands featured are encompassed by the same frequency regions as described in Fig. 1 (around 300–800 Hz and 1100–1850 Hz for the RP distributions of the COVID-19-positive versus COVID-19-negative control group, and around 100–800 Hz and 1400–2100 Hz for the frequency bands of the asthma and pneumonia categories without confounding COVID-19. The p values ranged from \(6.53\times 10^{-4}\) to 0.0454 and were below .05 for all the frequency bins we computed (i.e., 300–400 Hz and 1100–1650 Hz for the COVID-19-positive group versus the COVID-19-negative group, with p values equal to \(6.53\times 10^{-4}\) and \(4.58\times 10^{-4}\), respectively. The first optimal frequency band was within Region 1, and the second was within Region 2. The optimal frequency band was 1400–1600 Hz for the computation of the asthma versus pneumonia p values, with a value of \(1.39\times 10^{-3}\). For comparison, the COVID-19-positive versus COVID-19-negative and the asthma versus pneumonia p values for the RP in the frequency band of 1–3000 Hz were 0.49 and 0.66, respectively.
Both the low and high p values presented herein are consistent with our preliminary observations and showed significant differences in the RP values between the COVID-19-positive and COVID-19-negative control groups. They also supported the existence of frequency bands capable of separating each of the categories, in line with our preliminary observations and demonstrating the presence of an acoustical signature for the medical conditions causing coughs. We devoted the final part of the study to classifying the RP values of the optimal frequency bands, as discussed previously, using LDA and KNN machine learning classifiers. It is crucial to highlight that the availability of samples for COVID-19-positive and COVID-19-negative cases significantly influenced our data selection strategy. To ensure the integrity and impartiality of our analysis, we deliberately opted for the random selection of a representative subset equal to 341 samples for each class, thereby mitigating potential biases in our findings. The pneumonia and asthma categories from the Coswara dataset were smaller and formed a balanced dataset of 48 asthma samples and 50 pneumonia samples.
The performance characteristics of the LDA and KNN classifiers are displayed in Table 3 using the area under the curve (AUC), accuracy, and Matthew’s correlation coefficient (MCC) metrics. While a receiver operating characteristic curve plots a true positive rate against a false positive rate, the AUC is a measure of a classifier’s overall performance. Likewise, accuracy is defined as the proportion of correctly classified samples. The MCC, however, ranges from \(-1\) to \(+1\), with a value of \(+1\) representing a perfect prediction, 0 indicating a random prediction, and \(-1\) indicating complete disagreement between the predicted and true labels. For COVID-19-positive versus COVID-19-negative LDA results, the best accuracy and AUC were achieved using the RP values of the respective frequency bands: 1100–1650 Hz and 300–800 Hz. The first frequency band, 1100–1650 Hz, corresponded to the optimal band identified previously, with the lowest Mann–Whitney U test p value. The second frequency band of interest, which was identified as an optimal band at 300–400 Hz, had the lowest accuracy and AUC of all the values, but they were still significant at 0.80 and 0.71, respectively. Similarly, the highest accuracy and AUC performance values for the classification of asthma versus pneumonia were achieved using the RP of the 50–900 Hz and 450–1000 Hz frequency bands, respectively. Again, the optimal frequency band identified in the Mann–Whitney U test differed from that for the highest LDA scores. However, the optimal band at 1400–1650 Hz exhibited sufficiently high levels of accuracy and AUC (0.89 and 0.90, respectively), indicating the ability of the LDA classifier to adequately distinguish between the pneumonia and asthma samples based on their respective RP values. For both the COVID-19-positive versus COVID-19-negative and pneumonia versus asthma samples, the LDA classifier did not reach optimal performance consistently for the previously identified optimal frequency bands based on the RP values. Nevertheless, it achieved adequate and comparable performance values for all the optimal bands, allowing us to deduce arguments similar to those for the KNN classifier performance values. Unlike the LDA classifier, for the COVID-19-positive group versus the control group, the 1100–1850 Hz band outperformed the optimal band within that region (i.e., 1100–1650 Hz), and the 300–400 Hz band had the highest overall performance, with an MCC value of 0.71. For the pneumonia versus asthma KNN classification, the low-frequency 50–900 Hz range yielded the highest MCC performance values, although both frequency bands in Region 1 had similar performance metric values. In short, the KNN classifier performed almost identically to the LDA classifier in the second region, with high metrics values for the 1400–1600 frequency band. Notably, this analysis was conducted using linear and non-linear machine-learning classifiers. This means that, altogether, these results corroborated our preliminary observations, indicating the existence of a set of desirable and optimal frequency bands in cough sounds that, using machine learning classifiers, we can leverage to detect and thus diagnose a cough’s underlying ailment.
Discussion
The application of the Mann–Whitney U test to our study data revealed statistically significant differences in the RP of cough sound signals between COVID-19-positive individuals and a COVID-19-negative control group, particularly in the 300–400 Hz and 1100–1650 Hz frequency bands. The notably low p values in these tests strongly suggest that these differences are not random occurrences, thereby supporting our hypothesis that the RP distributions in cough sound signals are distinctively different between the two groups. These results underscore the potential of RP in cough sound signals as a significant biomarker for COVID-19, especially within these specific frequency bands.
Further analysis using LDA for classification based on the RP of cough signals indicated a high level of accuracy in differentiating COVID-19-positive from COVID-19-negative patients across various frequency bands. Notably, the frequency band of 1100–1850 Hz demonstrated the highest classification accuracy, reaching a value of 1.88. Additionally, comparisons of RP values for pneumonia versus asthma across all relevant frequency bands showed substantial accuracy, exceeding 0.78. These findings reinforce the premise that the RP of cough signals is a reliable indicator for distinguishing not only between COVID-19 status but also between other respiratory conditions like pneumonia and asthma within these frequency ranges.
It is important to acknowledge that this study relied on crowdsourced data rather than clinical data. The cough recordings were self-reported by patients, which introduces a degree of uncertainty regarding their accuracy. Moreover, the control group was relatively small and lacked diversity, with a significant proportion of the dataset comprising male participants aged between 20 and 35 years, accounting for approximately 70% of the total sample. This demographic skew poses limitations on the study’s statistical significance and generalizability, indicating a need for more diverse and representative data in future research.
Additionally, the statistical methodologies employed in this study come with inherent limitations. For instance, the Welch method used for calculating the PSD provides only an approximation. These methodological constraints suggest that our findings should be considered preliminary, necessitating further research and validation.
Our study contributes novel insights into the field of respiratory disease diagnosis using cough sound signals, particularly for COVID-19, augmenting the existing body of literature that predominantly focuses on deep learning models like convolutional neural networks. Unlike previous studies which have reported varied model performance accuracy for COVID-19 prognosis, our approach employs classical machine learning classifiers and uniquely identifies specific frequency bands within the power density spectrum of cough signals for disease diagnosis. This methodological divergence not only confirms the potential of cough as a biomarker but also adds a new dimension to its analysis in the context of respiratory illnesses.
