2.1 Speech-based analysis for Parkinson’s disease

Speech impairment is a well-established manifestation of PD, and acoustic analysis of voice signals has emerged as a promising non-invasive biomarker for disease assessment [23,24]. Early studies demonstrated that sustained vowel phonations contain discriminative information capable of distinguishing individuals with PD from healthy controls using handcrafted acoustic features and classical machine learning techniques [15,25,26]. In particular, Little et al. [27] and Tsanas et al. [10] showed that nonlinear dysphonia measures combined with regression and classification models can accurately estimate UPDRS scores from voice recordings. Subsequent work expanded this line of research by investigating feature selection strategies, nonlinear modeling approaches, and robustness to recording conditions. Sajal et al. [28] proposed a smartphone-based telemonitoring system that integrates voice and tremor analysis with ensemble learning methods for remote symptom assessment. Ramezani et al. [29] demonstrated that PD progression can be tracked from speech by selecting informative acoustic features using mRMRC and estimating motor UPDRS with regression models, highlighting the importance of spectral, hoarseness-related, and variability-based features. Oliveira et al. [30] showed that decomposing PD voice severity into multiple binary speech classification tasks using DDK features enables moderate multiclass discrimination of disease stages. These studies established speech as a clinically meaningful modality for PD assessment and laid the foundation for speech-based telemonitoring. However, most approaches treated speech recordings as independent observations and focused primarily on population-level inference.

2.2 Telemonitoring and longitudinal Parkinson’s disease studies

To overcome the limitations of clinic-based assessments, telemonitoring systems have been developed to enable frequent, at-home data collection. Palacios et al. [31] proposed Teca-Park, an integrated, contact-free telemonitoring framework that combines speech-based PD monitoring (MonParLoc) with acoustic neurostimulation (AcousticPar), implemented via a mobile app and scorecard, to support longitudinal remote assessment, symptom tracking, and patient management. Platforms such as the At-Home Testing Device (AHTD) demonstrated the feasibility of collecting longitudinal speech and motor data remotely and estimating symptom severity over time. Tsanas et al. [11] showed that self-administered speech recordings can accurately track PD progression by mapping dysphonia features to UPDRS scores with clinically useful precision using the Oxford Parkinson’s Disease Telemonitoring Dataset [32]. Longitudinal studies have further highlighted the importance of modeling disease progression over time. Azuma et al. [33] reported progressive cognitive decline in Parkinson’s patients, even among cognitively normal individuals, emphasizing the value of baseline behavioral markers for predicting future deterioration. Salmanpour et al. [34] demonstrated that combining longitudinal clinical data with DAT-SPECT radiomics and hybrid machine-learning models can uncover distinct progression trajectories and enable early prediction of these trajectories. These studies illustrate the potential of telemonitoring to capture disease dynamics at a finer temporal resolution than conventional clinical practice. Nevertheless, many telemonitoring approaches rely on static or weakly temporal models that do not explicitly represent disease progression, and patient-specific variability is often treated as noise rather than an informative signal.

2.3 Machine learning limitations and theoretical gaps

Recent advances in machine learning, including deep and recurrent architectures, have enabled more powerful modeling of complex biomedical time series [35]. Despite this progress, most speech-based PD models remain deterministic and provide point estimates of disease severity without quantifying uncertainty. Comparative studies have shown that classical regression models can achieve strong predictive performance. Eskidere et al. [36] reported that Least Squares Support Vector Machines (LSSVM) outperformed SVMs, neural networks, and prior state-of-the-art methods for remote UPDRS estimation. Yoon et al. [37] introduced a positive transfer learning (TL)framework that constructs patient-specific models by selectively transferring beneficial information from other subjects, significantly improving prediction accuracy while mitigating negative transfer. Chandrabhatla et al. [38] provided a comprehensive overview of how advances in sensing technologies and machine learning have enabled a shift from subjective, clinic-based assessment toward data-driven, in-home monitoring of motor symptoms.

Despite these advances, existing methods typically decouple continuous severity estimation from clinically meaningful severity staging, despite the ordinal nature of PD progression. Moreover, uncertainty arising from subjective clinical ratings and heterogeneous disease trajectories is rarely modeled explicitly. In summary, prior work has established the feasibility of speech-based PD assessment and telemonitoring but has not fully addressed the combined challenges of longitudinal disease modeling, patient-specific personalization, uncertainty quantification, and ordinal clinical interpretation. The present work seeks to bridge this gap by introducing an uncertainty-aware, personalized temporal framework that more closely reflects the clinical reality of Parkinson’s disease progression.

4.1 Dataset description

4.1.2 Data acquisition and features.

Voice data were collected weekly in participants’ homes using the Intel ATHD with a head-mounted microphone sampled at 24 kHz and 16-bit resolution. Each session comprised six sustained phonations of the vowel /a/ recorded under controlled pitch and loudness conditions. After quality screening, a total of 5,923 phonations were retained. Each recording was represented using a set of linear and nonlinear dysphonia measures, producing scalar features used to predict motor and total UPDRS scores. A summary of the dataset characteristics is provided in Table 1.

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Table 1. Summary of the Parkinson’s telemonitoring dataset [32].

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4.2 Exploratory data analysis

An Exploratory Dataset Analysis (EDA) was conducted to characterize the longitudinal structure of the dataset and to assess variability in both observation frequency and disease severity across subjects. Fig 1 summarizes key properties of the data at the patient, temporal, and population levels.

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Fig 1. Exploratory analysis of the Parkinson’s telemonitoring dataset.

(A) Distribution of the number of visits per subject. (B) Distribution of motor UPDRS scores across all visits. (C) Individual longitudinal motor UPDRS trajectories plotted against time since recruitment. (D) Population-level scatter showing a weak global temporal trend.

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Fig 1(A) shows the distribution of the number of recording sessions per subject. While all included participants contributed a sufficient number of visits, notable variability in visit counts is observed, reflecting irregular and subject-specific sampling schedules. This heterogeneity motivates modeling approaches that can accommodate unequal temporal resolution and leverage subject-wise history rather than assuming uniformly sampled trajectories. Fig 1(B) illustrates the distribution of motor UPDRS scores across all visits. The scores span a wide range of disease severity and exhibit a multimodal structure, suggesting the presence of distinct severity regimes. This observation supports modeling disease severity as a continuous latent variable while also motivating the use of ordinal stratification into clinically meaningful stages.

Individual disease trajectories are shown in Fig 1(C), where motor UPDRS is plotted against time since recruitment for each subject. Substantial inter-individual variability is evident in both baseline severity and progression patterns. Some subjects exhibit gradual monotonic worsening, while others show fluctuating or weakly increasing trends. This diversity supports the assumption of patient-specific progression dynamics rather than a shared global temporal model. At the population level, Fig 1(D) aggregates all observations and reveals only a weak average temporal trend in motor UPDRS over time. The absence of a strong global progression pattern indicates that population-level temporal models are insufficient to capture disease dynamics and further motivates personalized temporal representations conditioned on individual histories.

Overall, the exploratory findings support the theoretical assumptions that PD’s severity evolves heterogeneously across individuals, that observed UPDRS scores represent noisy measurements of an underlying latent disease state, and that uncertainty-aware, patient-specific temporal modeling is required for accurate severity estimation.

4.3 Data preprocessing

Let denote the acoustic feature vector extracted from the t-th voice recording of subject i, where d = 16 corresponds to the selected dysphonia measures. All recordings were temporally ordered by test time for each subject. Each acoustic dimension was standardized using z-score normalization for feature comparability,

(5)

where and denote the mean and standard deviation of feature j computed over the training data.

Motor UPDRS scores were used as continuous regression targets. In addition, ordinal disease severity stages were derived via quantile-based discretization of the motor UPDRS distribution. Let q_0.33 and q_0.66 denote the 33rd and 66th percentiles, respectively. The ordinal stage label was defined as

(6)

Fixed-length sliding windows were constructed independently for each subject to capture temporal dependencies. For a window size W, the model input at time t was defined as

(7)

with the corresponding regression and ordinal targets given by and . Windows were generated without overlap across subjects, preserving subject-wise temporal ordering.

4.4 Model architecture

The proposed model estimates PD severity using a personalized stochastic latent representation derived from longitudinal speech features. For each subject i, a sequence of standardized acoustic feature windows is provided as input.

Temporal dependencies within each window are modeled using a recurrent encoder. Specifically, an LSTM processes the input sequence and produces a hidden state corresponding to the final time step,

(8)

Then, each subject is associated with a learnable embedding vector , which is concatenated with the temporal representation,

(9)

These embeddings are learned only for training subjects and remain fixed during inference; they are not adapted online for previously unseen patients. The combined representation is mapped to the parameters of a latent disease state distribution. The latent variable is modeled as a Gaussian random variable with mean and diagonal covariance ,

(10)

where and are linear transformations. Sampling is performed via the reparameterization trick,

(11)

Continuous motor UPDRS estimation is obtained through a linear regression head,

(12)

where denotes a fully connected layer. In parallel, ordinal disease severity is estimated using an ordinal regression head with K ordered stages. The probability that the latent state exceeds threshold is given by

(13)

where is the logistic sigmoid function, is a shared projection vector, and are learnable ordered thresholds.

The model outputs the continuous severity estimate , ordinal stage probabilities, and the parameters of the latent disease state distribution for each input window.

4.5 Training objective

Model parameters are learned by minimizing a composite loss function that jointly accounts for continuous severity estimation, ordinal stage prediction, latent state regularization, and cross-task consistency. For continuous motor UPDRS prediction, a mean squared error (MSE) loss is used,

(14)

where and denote the true and predicted motor UPDRS scores, respectively. Ordinal disease severity is modeled using a cumulative link formulation. Let denote the predicted probability that the latent disease state exceeds ordinal threshold k. The ordinal loss is defined as

(15)

where denotes binary cross-entropy and is the indicator function. To regularize the stochastic latent disease state, a Kullback–Leibler divergence [42] term is included,

(16)

encouraging the approximate posterior to remain close to a standard normal prior.

To enforce consistency between continuous predictions and ordinal stage assignments, a constraint-based loss is applied. For each ordinal stage k with interval , the consistency loss [43] is defined as

(17)

The total training objective is given by a weighted sum of the individual components,

(18)

where , , and are fixed hyperparameters. In all experiments, these weights were set to , , and . The proposed framework is illustrated in Fig 2.

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Fig 2. Overview of the proposed Parkinson’s disease progression framework using longitudinal voice biomarkers.

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4.6 Experimental setup

All experiments were conducted using a strict patient-wise data split to prevent subject leakage between training and evaluation. Let denote the set of all subjects. A subset comprising 25% of the subjects was randomly selected and held out for testing, while the remaining subjects formed the training set. All recordings from a given subject were assigned exclusively to either the training or test set. Summary statistics for the resulting splits are reported in Table 2.

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Table 2. Summary statistics of the patient-wise training and test splits.

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The distributions of motor UPDRS scores in the training and test sets were examined to investigate a systematic shift in disease severity. Fig 3 shows that both subsets exhibit comparable coverage across the severity range, with overlapping density profiles and no pronounced distributional bias. Sliding windows of fixed length W = 10 were constructed independently for each subject, as described in the preprocessing stage. Models were trained using mini-batch stochastic optimization with a batch size of 32 and the Adam optimizer. Training was performed for 100 epochs with a fixed learning rate of 10⁻³.

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Fig 3. Distribution of motor UPDRS scores for training and test sets under the patient-wise split.

Histogram and kernel density estimates indicate comparable severity coverage and overlapping distributions, supporting the validity of the evaluation protocol.

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4.7 Evaluation metrics

Model evaluation was performed exclusively on the held-out test subjects defined in the patient-wise split. All reported metrics were computed using predictions generated without gradient updates. The proposed framework is compared with several naive baselines, including a global mean predictor, subject-specific mean prediction, and a last-observation-carried-forward (LOCF) [44] strategy to better understand the influence of temporal continuity.

Regression performance.

Continuous motor UPDRS estimation was evaluated using mean absolute error (MAE), root mean squared error (RMSE), and the coefficient of determination (R²),

(19)

(20)

(21)

where and denote the true and predicted motor UPDRS scores, respectively, and is the mean of the ground truth scores.

Ordinal severity prediction.

Ordinal disease severity prediction was evaluated using classification accuracy,

(22)

where and denote the true and predicted severity stages, respectively. Predicted stages were obtained by counting the number of ordinal thresholds exceeded by the model’s cumulative probabilities.

In addition to global metrics, patient-level robustness was evaluated by computing the mean absolute error separately for each test subject and summarizing the distribution of these errors across subjects. To assess robustness beyond short-term temporal continuity, temporal extrapolation experiments were conducted by training the model on earlier segments of each patient trajectory and evaluating performance on later visits. Additional experiments were performed using reduced temporal window sizes consisting of one or two prior recordings. Predictive uncertainty was evaluated using prediction interval coverage probability (PICP) [45] and reliability calibration analysis after variance scaling calibration. Coverage probabilities for calibrated and confidence intervals were compared against expected Gaussian confidence levels to assess global calibration behavior.

5.1 Regression analysis results

First, regression performance was evaluated on the held-out test set, where the proposed model achieved an MAE of 0.561 motor UPDRS points, an RMSE of 0.740, and an R² of 0.989, indicating accurate estimation of continuous disease severity across the full range of scores. The high (R²) should be interpreted in the context of the dataset and task formulation. The dataset consists of dense longitudinal recordings with repeated measurements per subject and relatively low short-term variability in motor UPDRS, particularly over the six-month study period. As a result, a substantial proportion of the variance is explained by subject-specific baseline severity and short-term temporal continuity. Similar levels of explained variance have been reported in prior work on the same dataset when using longitudinal or subject-aware models [10,46]. Table 3 summarizes the comparison of the proposed framework with several naive baselines.

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Table 3. Comparison with naive temporal baselines.

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The LOCF baseline achieved comparatively stronger performance, indicating substantial short-term temporal autocorrelation within the longitudinal UPDRS trajectories. Nevertheless, the proposed framework provides several additional capabilities beyond simple temporal persistence, including uncertainty quantification, latent disease representation learning, and joint continuous-ordinal severity modeling.

Fig 4(A) shows predicted versus ground truth motor UPDRS values for the test set. Predictions closely align with the identity line, with low dispersion across mild to severe severity levels, demonstrating consistent accuracy and absence of systematic bias. Performance remains stable across the severity spectrum, suggesting effective modeling of both low and high disease burden. Uncertainty-aware regression results are illustrated in Fig 4(B), where predictions are sorted by true severity. The predicted trajectory closely follows the ground truth progression, while the estimated uncertainty bands adapt to local variability in the data. Regions exhibiting greater prediction variability are associated with wider uncertainty intervals, reflecting the model’s capacity to express confidence in its estimates.

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Fig 4. Regression performance on the test set.

(A) Predicted versus ground truth motor UPDRS scores for unseen patients. (B) Uncertainty-aware regression with predictive intervals, with samples sorted by severity.

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Fig 5 presents representative longitudinal trajectories for two unseen patients. The model accurately tracks individual disease progression over time, capturing both gradual trends and short-term fluctuations. Predicted trajectories closely match observed motor UPDRS scores, demonstrating the personalized temporal model’s ability to generalize to new subjects while preserving subject-specific progression patterns.

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Fig 5. Longitudinal motor UPDRS trajectories for two representative unseen patients.

Predicted trajectories closely follow ground truth measurements across time.

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Under this substantially challenging setting of temporal extrapolation experiment, the proposed framework achieved an MAE of 2.994, RMSE of 3.946, and R² = 0.774. Although performance decreased compared to the original longitudinal evaluation, the model retained reasonably strong predictive capability, suggesting that the framework captures meaningful longer-range temporal disease structure beyond simple local persistence effects.

5.2 Ordinal classification results

Ordinal disease severity prediction was also evaluated on the held-out test set consisting of unseen patients. The model achieved an overall classification accuracy of 0.916 across the three severity stages. Table 4 reports precision, recall, and F1-score for each class, along with macro-averaged and weighted-averaged performance. Performance is balanced across classes, with high recall for mild and severe stages and slightly lower recall for the moderate stage.

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Table 4. Ordinal classification performance on the test set.

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Fig 6(A) shows the confusion matrix. Most predictions lie on the diagonal, indicating correct stage assignment, while misclassifications primarily occur between adjacent severity levels. Fig 6(B) visualizes the learned latent disease representations projected using t-SNE, where samples are colored according to true severity stage. The latent space exhibits structured separation between stages, with smooth transitions between neighboring severity levels.

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Fig 6. Ordinal classification results on the test set.

(A) Confusion matrix for three-stage disease severity classification. (B) Two-dimensional t-SNE projection of the learned latent disease states, colored by true severity stage.

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5.3 Feature importance analysis

A permutation-based feature importance analysis was conducted to assess the relative contribution of individual acoustic features to prediction. For each feature, values were randomly permuted across samples while keeping all other features unchanged, and the resulting increase in MAE was recorded.

Fig 7 shows the change in MAE induced by permuting each feature, averaged across permutations. Larger increases in MAE indicate greater importance for prediction. Features related to harmonicity and nonlinear vocal dynamics, including HNR, RPDE, and PPE, exhibit the largest impact on performance. Measures of jitter and shimmer also contribute substantially, indicating sensitivity to both frequency and amplitude perturbations in sustained phonation.

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Fig 7. Permutation-based global feature importance analysis.

Bars indicate the increase in MAE after permuting each acoustic feature, with larger values corresponding to greater importance for motor UPDRS prediction.

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5.4 Model analysis and uncertainty characterization

Further analysis of the proposed personalized latent framework focuses on its sensitivity to key architectural hyperparameters and on the properties of the learned latent disease representation and associated predictive uncertainty.

Hyperparameter sensitivity.

Fig 8 summarizes model performance as a function of temporal window length, latent state dimensionality, and patient embedding size. Increasing the temporal window initially yields substantial performance gains, reflecting the benefit of incorporating short-term longitudinal context, after which performance saturates for window lengths beyond approximately 10 recordings. A similar trend is observed for the latent state dimensionality and patient embedding size, where performance improves up to an intermediate capacity and then plateaus. These results indicate that the proposed model is robust to hyperparameter selection and does not rely on excessively large representations to achieve strong performance.

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Fig 8. Hyperparameter sensitivity analysis.

(A) Temporal window length. (B) Latent state dimensionality. (C) Patient embedding size. Performance is reported in terms of MAE and R² on the held-out test set.

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Uncertainty-aware error analysis.

To characterize the behavior of predictive uncertainty, test samples were stratified into uncertainty levels based on the posterior standard deviation of the latent disease state. Fig 9(A) shows the distribution of absolute prediction error across low, medium, and high uncertainty groups. While predictions associated with higher uncertainty exhibit somewhat broader error distributions, the median prediction error remains relatively similar across groups. This observation is consistent with the quantitative calibration analysis, which showed only a weak association between predictive uncertainty and sample-wise prediction error. Consequently, the current uncertainty estimates should be interpreted as reflecting overall predictive variability rather than as validated indicators of individual prediction reliability.

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Fig 9. Properties of the learned latent disease representation.

(A) Distribution of absolute prediction error across uncertainty levels. (B) Relationship between latent disease severity and motor UPDRS scores.

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5.5 Uncertainty calibration analysis

Uncertainty calibration was further evaluated using PICP and reliability calibration analysis. Table 5 summarizes the quantitative calibration results.

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Table 5. Quantitative uncertainty calibration results after variance scaling calibration.

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Fig 10 illustrates the calibration behavior of the uncertainty estimates after post-hoc uncertainty scaling. Fig 10(A) compares expected and observed prediction interval coverage probabilities for and confidence intervals. The calibrated intervals achieved empirical coverage probabilities reasonably close to the expected Gaussian confidence levels, although mild undercoverage remained at higher confidence intervals. Fig 10(B) presents the reliability calibration curve across multiple nominal confidence levels. Observed coverage followed the ideal calibration trend consistently but remained slightly below the diagonal, indicating residual underestimation of predictive uncertainty after calibration. While the scaling procedure improved global interval calibration, the near-zero correlation between predictive uncertainty and sample-wise prediction error () suggests that the current latent uncertainty representation remains weakly associated with local prediction difficulty.

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Fig 10. Uncertainty calibration analysis after variance scaling calibration.

(A) Expected versus observed prediction interval coverage probabilities for and intervals. (B) Reliability calibration curve comparing expected and empirical coverage across multiple confidence levels.

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5.6 Robustness to synthetic label noise

To evaluate robustness against noisy clinical annotations, an additional experiment was conducted in which synthetic Gaussian noise was injected into the motor UPDRS labels during training. Noise levels with standard deviations ranging from to were evaluated, while testing was performed on clean labels. Table 6 summarizes the results. Predictive performance degraded gradually as label corruption increased, indicating that the proposed framework remained relatively stable under moderate annotation noise. Even under substantial perturbation (), the model retained strong predictive capability with R² = 0.963. In addition, predictive uncertainty increased moderately with larger noise levels, suggesting that the probabilistic latent formulation partially reflects increased ambiguity in the supervision signal.

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Table 6. Robustness analysis under synthetic Gaussian label noise added to motor UPDRS targets during training.

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5.7 Limited-history prediction analysis

Experiments were conducted using temporal windows consisting of only one or two prior recordings to assess model performance under a limited longitudinal context. With a single-recording window, the proposed framework achieved an MAE of 1.710, an RMSE of 2.292, and an R² of 0.920. Using two recordings further improved performance, yielding an MAE of 1.552, an RMSE of 2.087, an R² = 0.934, and an average predictive uncertainty of 0.112. Although performance improved with longer temporal context, as shown in Fig 8, the model remained reasonably accurate even under extremely limited history, suggesting usefulness in practical real-world settings where prior recordings are scarce, such as newly enrolled patients or sparse telemonitoring scenarios.

5.8 Ablation Analysis

An ablation study was conducted to evaluate the contribution of each major component of the proposed framework, including ordinal supervision, probabilistic latent inference, patient-specific embeddings, and temporal modeling. Results are summarized in Table 7.

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Table 7. Ablation analysis of the proposed framework.

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Removing any individual component resulted in performance degradation relative to the full model, indicating that each module contributes positively to overall prediction quality. The largest performance decrease was observed when temporal modeling was replaced with a non-temporal MLP encoder, highlighting the importance of longitudinal temporal structure for disease severity estimation. Removal of patient embeddings also reduced performance, suggesting that personalization captures subject-specific disease characteristics. In contrast, removing ordinal supervision or probabilistic latent inference produced smaller but consistent decreases in accuracy, indicating that both components provide complementary regularization and improve the stability of the longitudinal representation.

5.9 Comparison with existing works

Table 8 compares the proposed framework with prior speech-based approaches for PD severity estimation on the telemonitoring dataset [32]. Early studies by Tsanas et al. [10,11] employed classical machine learning models such as CART and LASSO, reporting MAE in the range of 5–7 UPDRS points. Subsequent work by Eskidere et al. [36] improved predictive accuracy using LSSVM, achieving an MAE of 4.87. These approaches primarily relied on cross-sectional modeling and did not explicitly account for longitudinal structure or patient-specific variability. More recent studies have explored nonlinear and hybrid learning paradigms. Nilashi et al. [46] reported strong performance using an adaptive neuro-fuzzy inference system (ANFIS), achieving a low MAE of 0.491 and an R² of 0.959. Mohammadi et al. [47] employed decision tree–based regression (REPTree), while Tang et al. [48] proposed the NoRo framework, both yielding moderate reductions in prediction error. However, these methods generally focused on point estimation and did not provide explicit uncertainty quantification or jointly model continuous and ordinal disease severity.

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Table 8. Comparison with existing speech-based PD severity estimation methods on the telemonitoring dataset.

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In comparison, the proposed framework achieves competitive predictive performance (MAE = 0.56, R² = 0.99) while incorporating personalized temporal modeling, probabilistic latent inference, ordinal severity supervision, and uncertainty-aware prediction within a unified formulation. Although direct numerical comparison should be interpreted cautiously due to differences in evaluation protocols and data splits, the results suggest that integrating temporal context and personalization can improve longitudinal speech-based assessment of Parkinson’s disease severity.