## 4 Discussion  
Although the only existing longitudinal study [31] is different in the interval between sessions (32.5 vs. 24.0 months), we are going to compare our findings with the results reported by these authors. In contrary to [PERSON] et al., who observed significant change in shimmer of the sustained phonation of vowel /a/, we have not identified any significant differences in this vowel. Nevertheless, we identified significant changes in the same feature extracted from vowels /e/, /i/, /u/. In addition, we monitored some significant changes in jitter and FLUF. Based on these results, we can conclude that, for two years, patients' voices became more aperiodic with increased micropperturbations of frequency and amplitude. Figure 2: Feature importance graphs for trained XGBoost models. Each column shows graphs for the models trained to estimate the change (\(\Delta\)) in values of a particular clinical rating scale (UPDRS III, UPDRS IV, RBDSQ, FOG-G). Each row shows graphs for the models trained using the features extracted from the recordings of a particular vowel phonation (/a/, /e/, /i/, /o/, /u/). The scale of the graphs is unified so that it is easier to compare the values among the models. None of the acoustic features at baseline significantly correlated with a change in UPDRS III, which supports the results of the clinical scales' estimation where the lowest estimation error was above 25%. However, we identified some significant correlations between changes of phonatory features and the clinical scale. Surprisingly, except tremor of lips (F3 (CV)), acoustic noise (ER (Q2)), and variation of voice quality (GNE (SD)), worsening in UPDRS III (motor performance) was associated with improvement in phonatory characteristics. This could be explained by the fact that HD belongs to axial symptoms [9; 31] that do not play significant part in UPDRS III. In other words, although several significant correlations were identified, we hypothesize that some underlying pathophysiological mechanism are involved and a direct interpretation is not possible. Regarding the change in complications of therapy (as assessed by UPDRS IV), although the most significant correlations were observed with baseline features extracted from the vowel /a/, the lowest estimation error (11%) was based on vowel /o/. In this case, low aperiodicity, but increased lips tremor and increased acoustic noise at baseline, was associated with increased complications in the follow-up examination. Only three significant correlations are reported between baseline acoustic parameters (quantifying microperturbations of frequency/amplitude and variation in voice quality) and change in RBDSQ. Although we have not identified any significant correlations based on vowel /i/, the XGBoost algorithm reached the lowest error (16%) including features calculated from this vowel. This result could originate from the ability of XGBoost to model complex interdependencies that are not evident at first sight [47]. Regarding the partial correlations between changes in RBDSQ and phonatory features, we can conclude that mainly changes in voice aperiodicity and voice quality are linked with changes in sleep disorders. HD and freezing of gait (FOG) are both axial symptoms of PD [55]. In our recent work, we have found out that these symptoms share some pathophysiological mechanism [56]. More specifically, we proved that FOG is mainly linked with improper articulation, disturbed speech rate and with intelligibility. We did not identify any significant relations between FOG and phonatory features. On the other hand, we analyzed only the sustained vowel /a/ and partial correlations were calculated only with some baseline FOG-Q sub-scores. The current study provides deeper and more complex results in terms of FOG and phonatory features relations. The first correlation analysis (baseline features vs. \(\Delta\)FOG-Q) identified just a few significant correlations.