Uncertainty quantification in neural network-based glucose prediction for diabetes

Hai Siong Tan; Rafe McBeth

cs.LGMar 5, 2026

Uncertainty quantification in neural network-based glucose prediction for diabetes

Authors: Hai Siong Tan, Rafe McBeth

Organizations: Gryphon Center for A.I. and Theoretical Sciences, Singapore · University of Pennsylvania, Perelman School of Medicine, Philadelphia, USA

Abstract

In this work, we investigate uncertainty-aware neural network models for blood glucose prediction and adverse glycemic event identification in Type 1 diabetes. We consider three families of sequence models based on LSTM, GRU, and Transformer architectures, with uncertainty quantification enabled by either Monte Carlo dropout or through evidential output layers compatible with Deep Evidential Regression. Using the HUPA-UCM diabetes dataset for validation, we find that Transformer-based models equipped with evidential output heads provide the most effective uncertainty-aware framework, achieving consistently higher predictive accuracies and better-calibrated uncertainty estimates whose magnitudes significantly correlate with prediction errors. We further evaluate the clinical risk of each model using the recently proposed Diabetes Technology Society error grid, with risk categories defined by international expert consensus. Our results demonstrate the value of integrating principled uncertainty quantification into real-time machine-learning-based blood glucose prediction systems.

Figures & tables

Model	zA	MARD	${}^{70}S$	${}^{70}B$	${}^{70}A$	${}^{180}S$	${}^{180}B$	${}^{180}A$	MCE	$\rho$	$\rho_{z}$
LSTM	96.7	4.52	0.80		0.91
$\text{LSTM}_{d}$	96.6	4.66	0.88	0.018	0.89	0.92	0.023	0.95	0.10	0.15	0.073
$\text{LSTM}_{e}$	96.6	4.24	0.94	0.016	0.93	0.96	0.020	0.98	0.04	0.67	0.201
Transf	96.7	4.44	0.78			0.91
$\text{Transf}_{d}$	96.8	4.50	0.87	0.018	0.90	0.93	0.022	0.95	0.09	0.23	0.098
$\text{Transf}_{e}$	96.8	4.14	0.94	0.015	0.94	0.96	0.019	0.99	0.03	0.68	0.208

Table 1: Models trained on heart rate-included inputs (30 min horizon). Abbreviations: zA - zone A accuracy; MARD - mean absolute relative difference;

{}^{70}S

- hypoglycemia sensitivity;

{}^{70}B

- hypoglycemia Brier score;

{}^{70}A

- hypoglycemia PR-AUC;

{}^{180}\{S,B,A\}

- the corresponding metrics for hyperglycemia; MCE - mean calibration error;

\rho

- Spearman’s correlation between ucertainty and error; model subscripts d, e - equipped with Monte Carlo dropout and evidential regression respectively;

\rho_{z}

- Spearman’s correlation between uncertainty and clinical risk zones as defined in Klonoff et al. (2024) . Each shaded cell pertains to the best-performing model for each metric column.

Figure 1: Plot of empirical coverage probabilities (ECP) vs nominal coverage probabilities (NCP) for three types of models trained on heart rate-included inputs and defined by a 30 min prediction horizon. The ideal plot is characterized by the ECP curve being very close to the nominal straight line joining the origin to the point (1,1). MCE denotes the mean calibration error which is the average of the absolute value of deviation between ECP and NCP.

Panel of Figure 2 — Figure 2: The rolling forecast plot for TEM model (a) and Transformer-based model with Monte Carlo dropout (b) trained on basal insulin-included inputs with 1 hour horizon for Patient with ID ‘3’ in the HUPA dataset Hidalgo et al. (2024) , with hypoglycemia ( $<70$ mg/dL) and hyperglycemia ( $>180$ mg/dL) thresholds being represented by red, horizontal dashed lines. Dashed ellipses locate examples of regions where model would fail to detect hypoglycemia events unless uncertainty estimates are used for detection thresholds.

Panel of Figure 3 — Figure 3: Single long horizon prediction windows for a couple of points near hypo- and hyperglycemia thresholds with the vertical lines in each diagram marking the start of the prediction horizon.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Precision-Recall curves for hypoglycemia detection performed by various models trained on heart rate-included inputs. Similar relative trends are also observed for the hyperglycemia case - see AUC values collected in Tables 1 - 8 .

Figure 5: DTS error grids for two patients with marked difference in their risk zone distributions. The various pairs of solid lines defined away from the dashed diagonal mark the boundaries of the five risk zones.

Figure 6: Boxplots showing the distribution of per patient MARD values for each class of input features. Friedman test was significant $(p<0.01)$ for the short horizon setting, with post-hoc Wilcoxon signed-rank tests with Holm correction indicating heart rate-trained models to achieve better MARD than those trained on steps and calories (Holm-adjusted $p\sim 0.01$ ).

Figure 7: Boxplots showing the distribution of per patient DTS zone A accuracy for each class of input features. Friedman test indicated no statistically significant difference among various models.

Model	zA	MARD	${}^{70}S$	${}^{70}A$	${}^{70}B$	${}^{180}S$	${}^{180}A$	${}^{180}B$	MCE	$\rho$	$\rho_{z}$
LSTM	96.7	4.46	0.79			0.90
$\text{LSTM}_{d}$	96.6	4.64	0.88	0.88	0.018	0.92	0.95	0.023	0.10	0.16	0.071
$\text{LSTM}_{e}$	96.6	4.26	0.94	0.88	0.016	0.96	0.95	0.020	0.04	0.68	0.192
Transf	96.9	4.36	0.79			0.90
$\text{Transf}_{d}$	96.7	4.53	0.86	0.90	0.018	0.93	0.95	0.022	0.08	0.25	0.097
$\text{Transf}_{e}$	96.8	4.20	0.94	0.94	0.015	0.96	0.99	0.020	0.02	0.68	0.205

Appendix

Table 2: Models trained on basal insulin-included inputs (30 min horizon). Abbreviations: zA - zone A accuracy; MARD - mean absolute relative difference;

{}^{70}S

- hypoglycemia sensitivity;

{}^{70}B

- hypoglycemia Brier score;

{}^{70}A

- hypoglycemia PR-AUC;

{}^{180}\{S,B,A\}

- the corresponding metrics for hyperglycemia; MCE - mean calibration error;

\rho

- Spearman’s correlation between ucertainty and error; model subscripts d, e - equipped with Monte Carlo dropout and evidential regression respectively;

\rho_{z}

- Spearman’s correlation between uncertainty and clinical risk zones as defined in Klonoff et al. (2024) . Each shaded cell pertains to the best-performing model for each metric column.

Model	zA	MARD	${}^{70}S$	${}^{70}A$	${}^{70}B$	${}^{180}S$	${}^{180}A$	${}^{180}B$	MCE	$\rho$	$\rho_{z}$
LSTM	87.9	8.96	0.63			0.80
$\text{LSTM}_{d}$	88.0	8.92	0.73	0.71	0.035	0.82	0.87	0.046	0.22	0.14	0.100
$\text{LSTM}_{e}$	88.7	8.33	0.88	0.82	0.028	0.90	0.95	0.038	0.02	0.67	0.322
Transf	88.5	8.63	0.62			0.80
$\text{Transf}_{d}$	88.4	8.70	0.72	0.73	0.033	0.83	0.88	0.044	0.20	0.27	0.180
$\text{Transf}_{e}$	89.2	8.14	0.90	0.84	0.027	0.90	0.95	0.037	0.004	0.68	0.334

Appendix

Table 3: Models trained on basal insulin-included inputs (60 min horizon).

Model	zA	MARD	${}^{70}S$	${}^{70}A$	${}^{70}B$	${}^{180}S$	${}^{180}A$	${}^{180}B$	MCE	$\rho$	$\rho_{z}$
LSTM	96.7	4.48	0.80			0.90
$\text{LSTM}_{d}$	96.6	4.64	0.88	0.89	0.018	0.92	0.95	0.023	0.10	0.15	0.074
$\text{LSTM}_{e}$	96.6	4.24	0.94	0.93	0.016	0.96	0.98	0.020	0.04	0.68	0.196
Transf	96.9	4.38	0.79			0.90
$\text{Transf}_{d}$	96.7	4.52	0.87	0.90	0.018	0.93	0.95	0.022	0.09	0.24	0.103
$\text{Transf}_{e}$	96.8	4.18	0.94	0.94	0.015	0.96	0.99	0.020	0.02	0.67	0.208

Appendix

Table 4: Models trained on steps-included inputs (30 min horizon).

Model	zA	MARD	${}^{70}S$	${}^{70}A$	${}^{70}B$	${}^{180}S$	${}^{180}A$	${}^{180}B$	MCE	$\rho$	$\rho_{z}$
LSTM	87.6	9.17	0.63			0.80
$\text{LSTM}_{d}$	88.1	8.92	0.73	0.72	0.034	0.82	0.87	0.046	0.21	0.14	0.096
$\text{LSTM}_{e}$	88.8	8.31	0.88	0.82	0.028	0.90	0.95	0.038	0.02	0.67	0.326
Transf	88.6	8.63	0.62			0.80
$\text{Transf}_{d}$	88.5	8.70	0.71	0.74	0.033	0.83	0.88	0.044	0.20	0.31	0.180
$\text{Transf}_{e}$	89.3	8.12	0.89	0.85	0.026	0.90	0.95	0.037	0.007	0.68	0.338

Appendix

Table 5: Models trained on steps-included inputs (60 min horizon).

Model	zA	MARD	${}^{70}S$	${}^{70}A$	${}^{70}B$	${}^{180}S$	${}^{180}A$	${}^{180}B$	MCE	$\rho$	$\rho_{z}$
LSTM	96.7	4.58	0.79			0.90
$\text{LSTM}_{d}$	96.4	5.04	0.87	0.88	0.019	0.91	0.94	0.025	0.147	0.15	0.072
$\text{LSTM}_{e}$	96.6	4.26	0.94	0.93	0.016	0.96	0.98	0.020	0.043	0.67	0.194
Transf	96.5	4.76	0.78			0.90
$\text{Transf}_{d}$	96.4	4.85	0.87	0.89	0.019	0.92	0.95	0.024	0.12	0.24	0.101
$\text{Transf}_{e}$	96.9	4.19	0.94	0.94	0.015	0.96	0.99	0.020	0.015	0.68	0.205

Appendix

Table 6: Models trained on calories-included inputs (30 min horizon).

Model	zA	MARD	${}^{70}S$	${}^{70}A$	${}^{70}B$	${}^{180}S$	${}^{180}A$	${}^{180}B$	MCE	$\rho$	$\rho_{z}$
LSTM	87.9	9.08	0.62			0.80
$\text{LSTM}_{d}$	87.7	9.18	0.72	0.71	0.035	0.81	0.86	0.047	0.232	0.122	0.092
$\text{LSTM}_{e}$	88.8	8.33	0.88	0.82	0.028	0.90	0.95	0.038	0.013	0.673	0.322
Transf	88.6	8.70	0.64			0.80
$\text{Transf}_{d}$	88.2	8.88	0.71	0.73	0.034	0.83	0.88	0.045	0.206	0.302	0.181
$\text{Transf}_{e}$	89.1	8.17	0.88	0.84	0.026	0.90	0.95	0.037	0.014	0.682	0.338

Appendix

Table 7: Models trained on calories-included inputs (60 min horizon).

Model	zA	MARD	${}^{70}S$	${}^{70}A$	${}^{70}B$	${}^{180}S$	${}^{180}A$	${}^{180}B$	MCE	$\rho$	$\rho_{z}$
LSTM	87.5	9.26	0.63			0.80
$\text{LSTM}_{d}$	87.9	8.97	0.73	0.71	0.035	0.82	0.87	0.046	0.21	0.13	0.102
$\text{LSTM}_{e}$	88.8	8.32	0.88	0.83	0.027	0.90	0.95	0.038	0.02	0.68	0.327
Transf	88.7	8.62	0.63			0.80
$\text{Transf}_{d}$	88.4	8.77	0.72	0.73	0.033	0.83	0.88	0.044	0.19	0.29	0.167
$\text{Transf}_{e}$	89.2	8.11	0.89	0.85	0.026	0.91	0.95	0.037	0.01	0.68	0.337

Appendix

Table 8: Models trained on heart rate-included inputs (60 min horizon).

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