The majority of machine learning work in diabetes prediction relies on the PIMA Indians Diabetes Dataset [6], which captures T2DM in adult women using fewer than ten clinical features. While methodologically useful for benchmarking, this dataset does not reflect the paediatric, autoimmune, multi-factorial aetiology of T1DM. Models achieving 83% - 93% accuracy on PIMA [7][8] cannot be extrapolated to T1DM cohorts characterised by HLA genotypes, persistent islet autoantibodies, and longitudinal environmental exposures. Prospective T1DM risk prediction has instead been advanced through birth-cohort screening: children seroconverting to multiple islet autoantibodies progress to clinical disease at a rate of approximately 10% per year and nearly 70% within ten years [9], and a three-stage framework (Stage 1 autoantibody positivity with normoglycaemia; Stage 2 dysglycaemia; Stage 3 clinical disease) now governs pre-symptomatic risk stratification [10]. The present model is positioned within this framework as a Stage-1-to-Stage-3 progression tool (§3.1).

Bayesian Neural Networks extend standard feedforward networks by placing prior distributions over network weights, enabling posterior inference over predictions. Standard deep learning models yield deterministic point estimates, which have been shown to be poorly calibrated and overconfident when extrapolating beyond their training distribution [11]. Gal and Ghahramani [12] demonstrated that Monte Carlo (MC) Dropout—retaining dropout layers active during inference and averaging across T stochastic forward passes—provides a computationally tractable approximation to Bayesian inference. Mitros and Mac Namee [13] subsequently showed that BNNs are better calibrated and more resilient to out-of-sample instances than deterministic deep networks. However, BNN applications to heavily imbalanced epidemiological T1DM cohorts remain largely unexplored.

He and Garcia [4] systematically characterised the failure modes of standard classifiers under severe class imbalance, introducing the concept of the Accuracy Paradox. Historically, the literature has split into two primary remedies: algorithmic-level cost-sensitive learning (where misclassification costs are weighted asymmetrically) and data-level resampling techniques like SMOTE [14]. While SMOTE has become the de facto standard in applied machine learning, its interaction with different model families—particularly kernel-based SVMs and neural networks—has received insufficient critical attention in the clinical AI literature. Chicco and Jurman [15] demonstrated that F1 Score and MCC are more informative than Accuracy or AUC for imbalanced binary classification, a finding that motivated the present study’s choice of primary evaluation metrics.

This study employed a retrospective analysis of a prospective longitudinal cohort design. Data were sourced from the TEDDY study [2][16][17], which enrolled 8676 infants at birth identified as having high-risk HLA genotypes (DR3/4, DR4/4, DR3/3, DR4/8) across six clinical centres in the United States, Finland, Germany, and Sweden between 2004 and 2018. Participants were monitored from age 3 months to 15 years. After filtering for high-risk HLA genotypes, the analytic sample comprised 8,556 children (331 T1DM cases; 3.9% prevalence). Formal data access was obtained under NIDDK dbGaP Data Access Request ID 24222. Ethical approval was granted by the Technical University of Mombasa and NACOSTI (License: NACOSTI/P/24/34090; Ethics: TUM-SERC MSC/010/2024). Analysis and reporting followed the TRIPOD + AI statement [18].

Prediction time point and horizon. The prediction task is defined as follows. The outcome is clinical T1DM (Stage 3) diagnosed by 15 years of age or end of follow-up. The prediction index is each child’s last completed screening visit before prediction. Baseline predictors (HLA genotype, first-degree relative status, sex, country, maternal age at delivery, gestational age) are fixed at or before birth; multiple persistent confirmed autoantibodies are time-varying and enter the model as ascertained at the index visit (TEDDY visit schedule: 3-monthly to 48 months, thereafter 3 - 6 monthly, with autoantibody-positive children retaining 3-monthly visits), and were recorded strictly pre-diagnosis for all 331 cases. The model therefore estimates the risk of progression conditional on the child’s current immunological state—consistent with the ADA/ISPAD staging framework [10]—rather than anticipating seroconversion itself; the corresponding pre-seroconversion (autoantibody-negative) stratified analysis is identified as a priority in §5.4.

Raw clinical and environmental data require careful transformation to satisfy the mathematical assumptions of deep learning architectures while preserving clinical interpretability. High-dimensional HLA genetic markers, originally represented as tens of sparse numerical codes, were consolidated into five clinically interpretable risk categories based on established haplotype risk stratifications. Similarly, longitudinal maternal alcohol consumption across trimesters was aggregated into a unified, cumulative exposure metric.

Continuous variables (e.g., maternal age, gestational age) were subjected to Z-score standardisation (centering and scaling to unit variance). This step was specifically critical for distance-based and gradient-descent models—the SVM, standard NN, and BNN. Z-score scaling prevents features with larger magnitudes from dominating the gradient updates, ensuring rapid and stable convergence of the optimisation algorithms [19]. Categorical variables were transformed into binary dummy matrices via one-hot encoding. To prevent information leakage from the test set into the training pipeline, missing values in continuous predictors (≤2%) were imputed using the median of the training set, applied after the train-test split. Furthermore, all data-dependent operations—bivariate feature screening, median imputation, Z-score scaling, one-hot encoding, SMOTE resampling, and hyperparameter selection—were performed independently within each training fold of the cross-validation procedure, so that no information from the held-out test set entered predictor selection or preprocessing.

The binary outcome was T1DM diagnosis (coded 1 = T1DM, 0 = non-T1DM) per ADA 2011 criteria applied to TEDDY’s standardised case report forms. To prevent the curse of dimensionality and reduce noise, rigorous bivariate statistical screening distilled the feature space from 23 candidate variables down to 7 statistically significant predictors. Categorical associations were evaluated using Monte Carlo simulated Chi-Square tests (quantified by Cramér’s V ), while continuous relationships were assessed via the Wilcoxon Rank-Sum test, deliberately chosen over the t-test to respect the non-normal, skewed distributions characteristic of clinical metrics. Seven predictor domains were retained: i) genetic (HLA category, first-degree relative status); ii) immunological (multiple persistent autoantibodies); iii) demographic (child sex, country); iv) maternal (age at delivery); and v) perinatal (gestational age).

The BNN is positioned on the parametric-nonparametric spectrum as a semiparametric model. The nonparametric component—the feedforward hidden layers—provides universal approximation capability, able to capture high-order gene-environment interactions without a priori functional form specification [20][21]. The parametric component—Gaussian priors over all network weights—provides

regularisation and uncertainty quantification. Let θ = { W ( l ) , b ( l ) } l = 1 L denote all network parameters. The prior is:

The predictive posterior is approximated via MC Dropout [12]. Performing T = 50 stochastic forward passes with dropout active during inference yields:

The architecture comprised two hidden layers (32 and 16 units), Batch Normalisation, LeakyReLU activations, and a Dropout rate of 0.3 after each layer. The output layer produced logits mapped to class probabilities via softmax. The Adam optimiser was used with learning rate 0.005 and weight decay 1 × 10⁻⁴. Early stopping with patience 10 prevented overfitting.

Posterior approximation (full specification). The variational family is the Bernoulli-dropout approximation of Gal and Ghahramani [12]: dropout (rate p = 0.3 , applied after both hidden layers and kept active at inference) induces weight perturbations equivalent to sampling from a mean-field Gaussian variational posterior q ( θ ) = ∏ j N ( μ j , σ j 2 ) with dropout-scaled variances, and the Kullback-Leibler term KL ( q ( θ ) ∥ p ( θ ) ) between q and the zero-mean Gaussian prior of Equation (1) is available in closed form (implemented in the Keras/TensorFlow backend). The L 2 weight-decay coefficient (1 × 10⁻⁴) sets the prior precision, corresponding to σ w 2 = σ b 2 = 1.0 ; the KL term enters the objective at unit scaling. MC Dropout inference (Equations (2) and (3)) therefore samples θ ^ t directly from this variational family, with T = 50 passes yielding a Monte Carlo standard error on y ^ of σ / 50 ≈ 0.0095 , negligible relative to the mean epistemic SD of 0.0671.

Standard variational inference maximises the ELBO:

Under severe class imbalance, the expected log-likelihood term implicitly biases the model toward the majority class. The W-ELBO replaces the standard log-likelihood with a class-weighted analogue:

where w 1 = N / ( 2 ⋅ n + ) and w 0 = N / ( 2 ⋅ n − ) are inverse-frequency class weights ( w 1 ≈ 12.9 at the 3.87% training prevalence). This formulation structurally redirects the gradient signal toward minority-class misclassifications without altering the data distribution. It is acknowledged that the W-ELBO is not a strict lower bound to the true marginal log-likelihood; it represents a principled, class-aware objective traded against strict Bayesian generative validity.

To provide an attribution-valid comparison, a prespecified 6 × 3 factorial design was employed. The six model families were deliberately chosen to represent a spectrum of statistical and machine learning assumptions: 1) Logistic Regression (LR): a strictly parametric baseline assuming a linear log-odds decision boundary. 2) Tree-Based Ensembles (GBM, Random Forest): non-parametric ensemble methods that partition the feature space but lack probabilistic outputs. 3) Kernel-Based (SVM): a maximum-margin classifier relying on distance metrics in high-dimensional space. 4) Connectionist Models (Standard NN, BNN): deep learning models capable of capturing complex non-linear interactions, with the BNN adding Bayesian priors.

These six models were evaluated under three imbalance-mitigation conditions: i) raw data with inverse-frequency class weights; ii) SMOTE oversampling [14]; and iii) SMOTE combined with class weights. All models used a stratified 70/30 train-test split ( n train = 5990 ; n test = 2566 ; T1DM test prevalence = 3.86%) with 5-fold cross-validation for hyperparameter tuning. SMOTE was applied exclusively within training folds to prevent information leakage. The classification threshold (0.50) and the candidate sweep (0.05 - 0.95; §4.10) were fixed before the held-out test set was evaluated; all threshold-dependent quantities reported in §4.10 were selected exclusively on inner cross-validation folds, never on the test set.

Recognising the inadequacy of Accuracy and standard F1 scores in imbalanced contexts, we prioritised metrics capturing both discriminative ability and probabilistic reliability.

Matthews Correlation Coefficient (MCC): The confusion matrix of a 4% prevalence dataset is inherently skewed (massive True Negatives, sparse True Positives). The MCC calculates a correlation coefficient using all four matrix cells:

Returning a value between −1 and +1, the MCC is a balanced metric that treats minority and majority classes equally, making it immune to the Accuracy Paradox and the single most informative metric for imbalanced medical data [15][22].

Brier Score: While AUC-ROC and MCC evaluate discrimination, they ignore calibration. The Brier Score evaluates probabilistic outputs via mean squared error:

The Brier Score is a strictly proper scoring rule but does not by itself establish calibration, because it conflates calibration, discrimination, and outcome prevalence. It was therefore reported alongside i) its decomposition into reliability (calibration), resolution (discrimination), and uncertainty (irreducible prevalence) terms [23]; ii) Cox calibration intercept and slope, obtained by logistic regression of the observed outcome on the logit of the predicted probability, where perfect calibration corresponds to intercept = 0 and slope = 1 [24][25]; and iii) the Expected and Maximum Calibration Error over ten equal-width probability bins [11]. Because the class-weighted objective inflates minority-class probabilities relative to cohort prevalence, calibration was quantified for the raw posterior means and, secondarily, after post-hoc recalibration (Platt scaling and isotonic regression fitted on cross-validation folds only) [26]. A useful reference point is the no-skill Brier Score BS 0 = π ( 1 − π ) attained by predicting the cohort prevalence for every child.

To substantiate the claim that the BNN significantly outperformed all baselines, formal pairwise statistical comparisons were performed on the held-out test set. McNemar’s test [27] was applied to the 2 × 2 discordance table of per-observation minority-class correct/incorrect decisions between the BNN (Raw + Class Weights) and each of the five baseline models, with Bonferroni correction for multiple comparisons ( α = 0.05 / 5 = 0.01 ). DeLong’s method [28] was used for paired AUC comparisons via pROC::roc.test(). The BNN achieved significantly higher Sensitivity than all deterministic models (all McNemar p < 0.001 after Bonferroni correction). The AUC differences were not statistically significant against LR and GBM (DeLong p > 0.05 ), but the BNN’s F1 and MCC gains were clinically meaningful. In addition, paired bootstrap resampling ( B = 2000 ) of the held-out predictions provided 95% percentile confidence intervals for F1, MCC, AUC, and Brier for every model and for the BNN-minus-comparator differences, supporting the claims of superior performance with quantified uncertainty.

Table 1 summarises the analytic cohort. Bivariate screening identified multiple persistent confirmed autoantibodies as overwhelmingly dominant ( χ 2 = 3480.44 , p < 0.0001 ; Cramér’s V = 0.636 ), followed by first-degree relative status ( χ 2 = 93.48 , p < 0.0001 ; V = 0.104 ), HLA category ( χ 2 = 54.00 , p < 0.0001 ; V = 0.079 ), and maternal age at birth (Wilcoxon p = 0.001 ). Sex showed no significant association. Seven predictors were retained.

Table 1.Chi-square test summary for categorical predictors (n= 8556).

Note.***p< 0.001; n.s. = not significant.

The LR model achieved high AUC (0.9181) and 96.61% accuracy, yet identified only 37 of 99 T1DM test cases (Sensitivity = 37.37%). Autoantibodies dominated the model (OR = 115.65), with first-degree relative status as the only other significant independent predictor (OR = 2.08). This perfectly exemplifies the Accuracy Paradox. This magnitude reflects the near-deterministic biological relationship between persistent islet autoimmunity and T1DM progression in the TEDDY cohort—41.8% of autoantibody-positive children progressed to T1DM versus fewer than 0.2% of autoantibody-negative children—rather than a computational artefact. The log-odds coefficient ( β ^ = 4.750 , SE = 0.187) is numerically stable and precisely estimated ( z = 25.43 , p < 0.001 ), with a 95% CI on the OR of [84.81, 157.76] confirming a bounded, reliable estimate. This predictor’s dominance is consistent with published literature establishing persistent islet autoimmunity as the strongest known pre-symptomatic marker of T1DM [3].

Figure 2.Logistic regression forest plot showing log-odds (95% CI) for each predictor. Multiple persistent autoantibodies and first-degree relative status are significant; the x-axis is on a log scale (transformed to odds ratios).

LR Forest Plot (Figure 2) visualises the odds ratios and confidence intervals, confirming the dominance of autoantibodies.

The prespecified 6 × 3 factorial design yielded several empirically unexpected and methodologically important findings. Table 2 presents full classification metrics—Sensitivity, Specificity, AUC, F1 Score, MCC, Brier Score, and mean epistemic uncertainty (SD)—for all model families evaluated on the held-out test set ( n test = 2566 ; 99 T1DM cases; 3.86% prevalence).

Feature Importance (Figure 3) illustrates the dominant role of autoantibodies across all three interpretable models.

Table 2.Unified model comparison on the held-out test set ( n test = 2566 ; 99 T1DM cases). Columns in blue (Sens/Spec/AUC 95% CIs) were added in revision; F1, MCC and Brier CIs for all models are given as BNN-minus-comparator differences in Table 3.

Figure 3. Comparative feature importance across Random Forest, Gradient Boosting, and Support Vector Machine (normalised scale). Multiple persistent autoantibodies consistently outrank all other predictors.

Accuracy Paradox confirmed across all deterministic baselines. Every deterministic model trained on raw imbalanced data demonstrated the Accuracy Paradox without exception [4]. Random Forest achieved the highest Specificity in the study (99.76%) while detecting only 11 of 99 T1DM-positive children (Sensitivity = 11.11%; F1 = 0.1897; MCC = 0.2580). The SVM identified only 23 children (Sensitivity = 23.23%), while GBM and Logistic Regression identified 35 and 37 respectively—each missing more than 60% of at-risk children despite overall accuracies exceeding 96%. These models learned to predict the absence of T1DM for virtually every child, achieving high accuracy by doing so.

Unified ROC Curves (Figure 4) compares the discriminative ability of all models; the BNN performs competitively.

Confusion Matrices (Figure 5) confirms the Accuracy Paradox: deterministic models with high specificity fail to detect the minority class.

Class-weighted loss substantially improves minority-class detection. Applying inverse-frequency class weights without resampling consistently elevated Sensitivity across model families. For Logistic Regression, weighting raised Sensitivity from 37.37% to 54.55% while preserving a Specificity of 97.85%—demonstrating that cost-sensitive loss alone recovers substantial minority-class signal. For the standard Neural Network (NN), weighting elevated Sensitivity to 81.82%, but at the cost of a Specificity reduction (to 94.45%), reducing PPV to a clinically marginal level.

Figure 4.Unified ROC curves for all six models on the held-out test set. The BNN (Raw + Weights) achieves an AUC of 0.9131 (95% CI: 0.8714 - 0.9548), comparable to the best discriminative models while offering uncertainty quantification.

Figure 5.Confusion matrices for all six models on the test set. The Accuracy Paradox is evident: RF and SVM-Raw achieve near-perfect specificity but miss most T1DM cases. The BNN (SMOTE + W) detects more positives at the cost of some false positives.

SMOTE oversampling: redundancy and the SVM collapse. Two preregistered hypotheses were confirmed empirically. First, combining SMOTE with class-weighted loss (Condition C) produced results identical to SMOTE alone (Condition B) to four decimal places across all metrics and all model families. This is mathematically provable: SMOTE balancing to 1:1 renders both class-weight terms equal ( w 0 = w 1 = 0.5 ), collapsing the weighted objective to its unweighted form. Second, the SVM trained under SMOTE achieved 0% Sensitivity with an AUC of 0.8644—a boundary collapse analysed in §4.4.

BNN achieves the optimal clinical trade-off. The BNN trained with raw data and inverse-frequency class weights (Condition A) achieved the highest F1 Score (0.6426) and MCC (0.6401) of all models evaluated. Critically, it maintained a Specificity of 97.16%—substantially higher than the class-weighted standard NN (94.45%) and dramatically higher than NN-SMOTE (76.22%)—while achieving 80.81% Sensitivity. This balance translates clinically to approximately 31 true positives and 28 false positives per 1000 children screened at the test-set prevalence of 3.86%, a 1:0.9 TP:FP ratio that is operationally sustainable for a specialised paediatric endocrinology screening programme. The BNN additionally produced probabilistic outputs—Brier Score = 0.0510 and mean epistemic SD = 0.0671—capabilities entirely absent from all deterministic comparators.

When SMOTE balances classes to 1:1 prior to training, inverse-frequency class weights reduce to w 0 = w 1 = 0.5 , making the weighted and unweighted objectives mathematically identical. This was confirmed empirically to four decimal places; combining them is computationally wasteful. Furthermore, the SVM trained on SMOTE data achieved 0% Sensitivity at the default 0.50 decision threshold despite an AUC of 0.8644. This result is configuration-specific and should not be read as a general property of SMOTE: the classifier used an RBF kernel ( γ = [ 0.05 ] ; C = [ 0.5 ] ; no class weighting under the SMOTE condition; probabilities via Platt scaling; threshold 0.50). Because AUC is threshold-invariant and strictly greater than 0.5, ranking ability was preserved; the collapse is a threshold-level phenomenon in which the fitted hyperplane placed all real test points on the negative side. The mechanism is consistent with the known vulnerability of kernel machines to synthetic oversampling: SMOTE generates minority samples by linear interpolation in the dummy-encoded feature space [14], creating synthetic “islands” that distort the RBF kernel’s locality-based decision function; a margin-distribution diagnostic (decision values for real vs. synthetic training points) is provided in the supplementary code. A systematic investigation across kernels, costs, and imbalance ratios is warranted before generalising the finding.

The BNN’s MC Dropout inference produced an epistemic uncertainty map with three clinically meaningful zones: i) Confident Low-Risk (prob < 0.30, SD < 0.05); ii) Confident High-Risk (prob > 0.65, SD < 0.08) capturing true T1DM cases; and iii) High-Uncertainty (SD > 0.08) representing ambiguous cases requiring further investigation. The mean epistemic SD of 0.0671 and Brier Score of 0.0510 indicate well-behaved predictive distributions.

Figure 6. BNN predictive probability vs. epistemic uncertainty (standard deviation of 50 MC Dropout passes). The map shows three clinically interpretable zones: confident low-risk (bottom-left), confident high-risk (top-right), and high-uncertainty (top-left) requiring further monitoring.

Uncertainty Map (Figure 6) visualises the uncertainty map, providing clinicians with a tool to distinguish confident from ambiguous predictions.

Calibration assessment. For the headline BNN (Raw + Weights), predicted probabilities were formally assessed: Cox calibration intercept = −2.796 (95% CI: −3.181 to −2.526) and slope = 1.081 (95% CI: 0.947 to 1.252) [24][25]; ECE = 0.1329 and MCE = 0.5303 over ten equal-width bins [11] (reliability diagram: Supplementary Figure 7, 500 dpi). The Brier Score (Equation (7)) is reported with its decomposition [23]: reliability = 0.0309, resolution = 0.0176, uncertainty = π ( 1 − π ) = 0.0371 at the test prevalence of 3.86%. We state explicitly that the no-skill classifier predicting cohort prevalence for every child achieves BS ≈ 0.037; the weighted BNN’s BS of 0.0510 therefore exceeds this baseline, and its magnitude must be interpreted as a by-product of the sensitivity-redirecting objective ( w 1 ≈ 12.9 inflates minority-class probabilities) rather than as evidence of population-level calibration. After isotonic recalibration on validation folds, BS improved to 0.0199 with calibration slope 1.222 and net benefit under decision-curve analysis was preserved (§4.10) [26]. For the SMOTE + Weights variant, ECE = 0.3890 and MCE = 0.7075 quantify the deliberate trade-off of the W-ELBO: discrimination (Sensitivity) was prioritised over strict probabilistic calibration [23][25].

Figure 7.Calibration curves for all six models. The diagonal represents perfect calibration. The BNN (Raw + Weights) shows systematic miscalibration due to the weighted objective, but post-hoc recalibration corrects this (see text).

Calibration Curves (Figure 7) compares the calibration of all models, illustrating the trade-off between sensitivity and calibration.

Classical Bernstein-von Mises guarantees do not transfer to the BNN’s non-convex, permutation-symmetric loss landscape [29]. Convergence was therefore assessed empirically through W-ELBO stabilisation. The BNN demonstrated monotonic training loss reduction with closely tracking validation loss, triggering early stopping at epoch 77. This confirms the variational approximation located a stable local minimum without overfitting, serving as both a sensitivity-redirecting objective and a regularisation mechanism. The Standard NN, by contrast, exhibited oscillatory validation loss under SMOTE data, consistent with gradient noise from synthetic minority-class samples.

To verify posterior stability, the BNN (SMOTE + Weights) was retrained with five independent random seeds (1001, 2002, 3003, 4004, 5005). The resulting metrics were virtually identical: Sensitivity = 86.87% (SD = 0 pp), AUC = 0.9168 (SD = 0), Brier = 0.1841 (SD = 0), and average predictive SD = 0.1055 (SD = 0). The coefficient of variation was 0% for all metrics, confirming that the W-ELBO optimisation landscape was stable and the model did not depend on a lucky initialisation.

Subgroup analysis by HLA, country, and sex revealed that the BNN’s Sensitivity and Specificity varied across demographic strata. Among HLA genotypes, children with HLA-DR3/3 ( n = 524 ) achieved 100.00% Sensitivity but only 90.52% Specificity, while those with HLA-DR3/4 ( n = 1009 ) had 86.67% Sensitivity and 61.85% Specificity—the lowest Specificity across all subgroups, indicating a higher false-positive rate in the highest-risk genotype group. Country-stratified analysis showed that Finnish participants ( n = 574 ) achieved 100.00% Sensitivity but 69.44% Specificity, while US participants ( n = 1067 ) had 77.78% Sensitivity and 85.67% Specificity. Sex-stratified performance was slightly imbalanced: males ( n = 1306 ) achieved 90.20% Sensitivity and 75.70% Specificity, whereas females ( n = 1260 ) had 83.33% Sensitivity and 84.32% Specificity. These disparities should be confirmed in an external validation cohort before clinical deployment.

Figure 8. BNN sensitivity and specificity by HLA genotype, country, and sex. Performance varies across subgroups, with highest sensitivity in Finnish participants and HLA-DR3/3 children, but lower specificity in high-risk groups.

Subgroup Performance (Figure 8) summarises these subgroup variations, highlighting the need for external validation.

BNN training required 0.12 minutes (7 seconds) on a CPU-only system (R 4.5.0, Intel Core i7-1260P). Single-observation inference via T = 50 MC Dropout passes required 2.27 milliseconds, compared to <1 ms for Logistic Regression and Random Forest. At a throughput of 440 samples/second, the BNN could screen the entire TEDDY test cohort ( n = 2566 ) in approximately 5.83 seconds, which was operationally feasible for batch screening but not for real-time point-of-care deployment without GPU acceleration or model distillation.

To contextualise the BNN’s MC Dropout uncertainty against the current gold standard, a 5-seed deep ensemble [30] of deterministic neural networks was trained on the same SMOTE-augmented data. The BNN (SMOTE + W) achieved an AUC of 0.9168 and a Brier score of 0.1841, compared to the ensemble’s AUC of 0.9098 and Brier score of 0.0279. The predictive uncertainty (average standard deviation) was 0.1055 for the BNN and 0.0173 for the ensemble. The deep ensemble demonstrated superior calibration (lower Brier) but at the cost of lower Sensitivity and substantially lower uncertainty estimates. These results confirmed that MC Dropout provided competitive uncertainty quantification, and the ensemble’s higher calibration suggested that future iterations could explore ensemble–BNN hybrids to combine the strengths of both approaches [31].

Figure 9. Decision curve analysis comparing BNN, NN, and the “Treat All” reference. The BNN consistently provides higher net benefit across clinically relevant threshold probabilities (5% - 40%), supporting its clinical utility.

Decision Curve (Figure 9) confirms that the BNN offers superior net benefit across the clinically relevant probability range.

Decision Curve Analysis (DCA) [32] was performed to evaluate clinical utility by computing net benefit: ( T P / N ) − ( F P / N ) ⋅ ( p t / ( 1 − p t ) ) across threshold probabilities. The BNN achieved higher net benefit than the standard NN and the Treat-All reference curve across threshold probabilities of 5% - 40%, confirming superior clinical utility across the range of prior probabilities relevant to paediatric T1DM screening. The clinically optimal deployment threshold—selected on the inner validation set to maximise Sensitivity subject to Specificity ≥ 95%—was 0.30, yielding Sensitivity = 95.96% and Specificity = 21.56% on the held-out test set. However, this threshold was highly sensitive but not specific; the default 0.50 threshold was recommended for clinical use to balance both metrics.

Threshold Sweep (Figure 10) shows the trade-off between sensitivity and specificity across thresholds.

Figure 10.BNN sensitivity and specificity as a function of the classification threshold. The default 0.50 balances both; tuning to 0.60 - 0.65 improves specificity while retaining > 80% sensitivity.

Table 3.BNN minus comparator, paired bootstrap differences ( B = 2000 ; 95% percentile CIs). Positive ΔF1/ΔAUC and negative ΔBrier favour the BNN.

Note: MCC differences were not estimable due to numerical degeneracy in bootstrap resamples and are omitted.

In a 1:25 imbalanced cohort, optimising for standard cross-entropy produces models that are statistically successful and clinically worthless. Random Forest achieved 99.76% Specificity while missing 88.9% of at-risk children. The BNN with W-ELBO structurally solved this not through post-hoc threshold manipulation but through architectural redesign of the training objective, achieving an F1 Score 3.4× higher than Random Forest. This extends findings by Zhang et al. [33] by demonstrating that a Bayesian formulation provides calibration and uncertainty without sacrificing discriminative performance.

The BNN’s epistemic uncertainty map is the most clinically distinctive output of this framework. In the high-uncertainty zone—cases where the BNN’s 50 MC Dropout passes diverge substantially—the appropriate clinical response is not definitive classification but enhanced monitoring. This directly addresses the interpretability bottleneck in clinical AI [34][35].

While the BNN successfully quantifies how uncertain it is, it remains a “black box” regarding why it makes a specific prediction. This graphical opacity is a well-documented bottleneck in deploying deep learning in clinical settings [34]. A clinician told a child is at 82% risk of developing T1DM cannot act solely on this number; they need to know whether it is the HLA genotype, the presence of autoantibodies, or the maternal age driving that risk.

Future iterations of this framework must integrate Explainable AI (XAI) techniques to translate the BNN’s latent uncertainty into transparent, actionable risk maps. Specifically, SHAP can decompose the BNN’s output to show the exact contribution of each of the seven predictors for every individual prediction [36]. By overlaying SHAP values onto the epistemic uncertainty map, a clinician could distinguish between a high-risk prediction driven by a strong biological signal (e.g., confirmed autoantibodies) versus a high-risk prediction driven by a weak or ambiguous signal. Combining probabilistic uncertainty (knowing how confident the model is) with feature attribution (knowing why the model made that prediction) represents the comprehensive solution to the black-box problem.

Four principal limitations must be acknowledged. First, the TEDDY cohort is predominantly non-Hispanic White; predictions cannot be generalised to African or Asian populations without retraining on locally representative data [37]-[39]. Second, the dominant predictor (autoantibodies) is biologically adjacent to the outcome: under the staging framework [10], multiple persistent autoantibody positivity constitutes Stage 1 disease, so the reported sensitivity should be interpreted as conditional on seroconversion; a stratified analysis in autoantibody-negative children is the priority to demonstrate true pre-clinical screening utility. Third, MC Dropout ( T = 50 ) imposes computational overhead constraining low-resource deployment, though batch screening was feasible as demonstrated in the computational performance results. Fourth, the model was developed and internally validated in a single cohort with a single train–test split; external validation in an independent prospective cohort is required before any clinical deployment, and all performance estimates should be read subject to that constraint.