# Towards trustworthy AI in radiotherapy: a comprehensive review of uncertainty-aware techniques

Cédric Hémon, Blanche Texier, Caroline Lafond, Jean-Claude Nunes, Anais Barateau

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Cédric Hémon, Blanche Texier, Caroline Lafond, Jean-Claude Nunes, Anais Barateau. Towards trustworthy AI in radiotherapy: a comprehensive review of uncertainty-aware techniques. Physics in Medicine and Biology, 2025, 71 (1), 10.1088/1361-6560/ae2a9f. hal-05424210

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# Towards trustworthy AI in radiotherapy: a comprehensive review of uncertainty-aware techniques

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TOPICAL REVIEW

# Towards trustworthy AI in radiotherapy: a comprehensive review of uncertainty-aware techniques

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Cédric Hémon* ID, Blanche Texier ID, Caroline Lafond, Jean-Claude Nunes ID and Anaïs Barateau ID

Univ. Rennes, CLCC Eugène Marquis, INSERM, LTSI—UMR 1099, F-35000 Rennes, France

* Author to whom any correspondence should be addressed.

E-mail: cedric.hemon@univ-rennes.fr

**Keywords:** uncertainty quantification, radiotherapy, sCT generation, segmentation, registration, dose prediction, dose accumulation

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Abstract

**Background.** Uncertainty quantification (UQ) has emerged as a crucial component in deep learning-based medical image analysis, particularly in radiotherapy (RT). Addressing uncertainty is essential for improving the reliability, interpretability, and clinical applicability of AI-driven models in key RT tasks, including segmentation, image registration, synthetic image generation, dose prediction and dose accumulation. Despite significant advancements, challenges remain in integrating UQ techniques into RT clinical workflows. **Purpose.** This review synthesizes recent developments in UQ methods applied to RT. It introduces a structured classification of UQ techniques, evaluates their impact on clinical workflows, and highlights emerging trends from studies published from 2020 to 2025. **Methods.** A systematic search was conducted on PubMed and Google Scholar for articles published from January 2020 to June 2025. Keywords included ‘uncertainty’, ‘radiotherapy’, and task-specific terms such as ‘segmentation’, ‘registration’, ‘synthetic image generation’, ‘image-to-image translation’, ‘dose prediction’, or ‘dose accumulation’. Studies were classified based on the type of uncertainty estimation technique, imaging modality, and associated RT task. **Results.** Segmentation emerged as the most common RT task addressed by UQ methods, followed by image registration, synthetic image generation and dose prediction. Probabilistic techniques such as Bayesian neural networks, Monte Carlo dropout, and ensemble learning, dominate the field, particularly for modeling epistemic uncertainty. Studies demonstrated that uncertainty maps enhance model interpretability, guide clinical review of auto-segmentations, and support quality assurance processes. **Conclusion.** UQ has the potential to enhance the robustness of AI-driven RT workflows. While substantial progress has been made, further efforts are needed to standardize evaluation protocols, improve computational efficiency, and develop user-friendly interfaces for clinical integration. Future research should aim to close the gap between technical advances and their clinical deployment to ensure uncertainty-aware models contribute effectively to personalized RT.

1. Introduction

Radiotherapy (RT) extensively uses multimodal medical imaging at different steps of the workflow. The evolution of RT is towards a more precise treatment taking into account anatomical variations, called adaptive RT (ART), with the help of AI and automation tools (Dona Lemus et al 2024). Uncertainty quantification (UQ) (Claessens et al 2022, Huang et al 2024) has emerged as a pivotal topic for medical image processing, supporting quality assurance (QA) across critical tasks such as image synthesis, segmentation, dose prediction or image registration. Figure 1 illustrates the RT workflow, highlighting the interest of UQ at different steps. Deep learning-based segmentation is now widely adopted in clinical routine, however tools for UQ are still lacking (De Biase et al 2024, Gao et al 2025). Generation of synthetic CT (sCT) images from another imaging modality like magnetic resonance (MR) or cone beam CT (CBCT) images (Huijben et al 2024) is largely proposed for daily dose calculation (Spadea et al 2021,
<figure><img src="image_4.png" /></figure>

Altalib et al 2025) or MR-guided RT (Bahloul et al 2024, Texier et al 2024), but lacks uncertainty estimation. Dose accumulation is another uncertainty-prone step in RT, as it relies heavily on image registration (Chetty and Rosu-Bubulac 2019). Image registration aligns sequential images in a rigid or deformable manner (Zou et al 2022, Nenoff et al 2023, Chen et al 2025). Rigid image registration assumes only translational and rotational differences between scans, making it typically suitable for bone structure. However, deformable image registration (DIR) is necessary to capture spatially varying transformations like anatomical variations (Nenoff et al 2023, Boussot et al 2025). While DIR offers greater anatomical fidelity, it also introduces additional uncertainty due to its complexity and sensitivity to image quality and algorithmic assumptions.

In this context, robust and accurate UQ enhances the reliability, safety, and clinical relevance of deep learning models across the RT workflow (Claessens et al 2022, Huang et al 2024). By offering insights into model confidence and identifying error-prone regions, UQ supports interpretability and promotes greater trust in AI-driven decision-making (Huang et al 2024). As such, UQ is increasingly viewed as essential for bridging the gap between algorithmic predictions and clinical practice in RT (Wahid et al 2024).

Uncertainty is broadly categorized into two types (Huang et al 2024): aleatoric uncertainty and epistemic uncertainty, each with distinct causes, implications, and management strategies. Aleatoric uncertainty arises from inherent variability or stochastic noise in the input data, regardless of its modality (e.g. images, clinical variables, or textual records). It reflects randomness in the data-generating process, such as acquisition noise, measurement errors, or inconsistencies in human annotation. In RT, this includes not only imaging artifacts and resolution limits but also inter-observer variability in manual delineations or contouring, which is typically considered an aleatoric source (Korreman and Ren 2025) of uncertainty because it reflects intrinsic variability in labeling rather than model ignorance.

Epistemic uncertainty arises from the model's limitations, often due to insufficient or non-representative training data (Kendall and Gal 2017, Papernot and McDaniel 2018). This typically results from training datasets that lack sufficient diversity across clinical cases, imaging modalities, or protocols, leading to gaps in the model's understanding. Another contributing factor is model bias, which can lead to overfitting or poor generalization to unseen data (i.e. data outside the training cohort), particularly when models are trained on single-center or imbalanced datasets.

Unlike aleatoric uncertainty, epistemic uncertainty is reducible through targeted interventions. Expanding datasets to include diverse and multicenter data, representing a wide range of patient demographics, imaging protocols, acquisition systems, and centers, can mitigate biases and improve generalizability. Additionally, employing advanced model architectures, such as transfer learning, domain adaptation, and ensemble methods, can address knowledge gaps and enhance the model's robustness and reliability.

Quantifying epistemic uncertainty is essential to identify scenarios in which the model may be less reliable, such as underrepresented anatomical regions, unseen center in learning cohort or rare clinical cases.
Although aleatoric and epistemic uncertainties are conceptually distinct, they frequently coexist in practical applications. In practice, disentangling them is non-trivial, as both contribute simultaneously to the predictive variability (Tyralis and Papacharalampous 2024). Their separation typically depends on modeling assumptions, heteroscedastic likelihoods for aleatoric terms or Bayesian weight distributions for epistemic uncertainty, and is valuable because each type requires distinct mitigation strategies: epi-stemic uncertainty can be reduced through broader and more representative training data, while aleatoric uncertainty is constrained by measurement noise or intrinsic ambiguity in the acquired images

Several recent reviews have explored UQ techniques in medical imaging (Huang et al 2024, Wahid et al 2024). This study aims to review the recent literature by introducing a structured classification framework for UQ methods, categorizing them based on their applicability to RT tasks such as segment- ation, registration, sCT generation, dose prediction, and dose accumulation. It also synthesizes recent advances in deep learning architectures, emerging hybrid approaches, and novel applications within RT. By addressing these critical areas, this review provides a comprehensive and clinically relevant overview that bridges the gap between methodological innovation and practical implementation in uncertainty- aware RT.

## 2. Material and methods

A comprehensive literature search was conducted in PubMed and Google Scholar to identify relevant studies published between January 2020 and June 2025. The selection process focused on research art- icles related to UQ in RT, using the following keywords: ‘uncertainty’, ‘radiotherapy’, and either ‘seg- mentation’, ‘registration’, ‘synthetic image generation’, ‘image-to-image translation’, ‘dose prediction’, or ‘dose accumulation’. Studies were included if they contributed to methodological advancements, clinical applications, or emerging trends in uncertainty-aware RT. The review prioritizes peer-reviewed articles presenting novel deep-learning approaches, hybrid techniques that integrate multiple uncertainty estim- ation strategies, and innovative frameworks that enhance the accuracy and reliability of RT processes. Additionally, studies exploring the integration of UQ into ART workflows were considered. The final selection aims to provide a comprehensive and up-to-date overview of the state-of-the-art methodologies and their clinical relevance in addressing uncertainties in RT.

## 3. UQ approaches

A range of techniques has been developed to quantify uncertainty in deep learning models (Wahid et al 2024). Figure 2 presents the main UQ methods. Table 1 summarizes the main UQ methods, specifying the type of uncertainty estimated, along with their principal advantages and limitations. In this review, we distinguish between aleatoric uncertainty, epistemic uncertainty, and predictive uncertainty (Tyralis and Papacharalampous 2024), which represents the total combined uncertainty when both components are jointly estimated, without being explicitly separated or disentangled.

### 3.1. Bayesian methods

Bayesian methods (Goan and Fookes 2020) treat model parameters, $\theta$, as random variables with prior distributions. The posterior distribution, $P(\theta|D)$, is derived using the Bayes theorem (equation (1)):

$$P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)}, \qquad (1)$$

where $P(D|\theta)$ is the likelihood, $P(\theta)$ is the prior, and $P(D)$ is the evidence.

Since exact Bayesian inference is computationally intractable for neural networks, approximations like Bayesian neural networks (BNNs) and variational inference are commonly used (Mukhoti et al 2020, Seligmann et al 2023, Wang et al 2023, Li et al 2024). BNNs introduce distributions over the network weights, allowing the model to output uncertainty as well as predictions. Variational inference optimizes an approximate posterior $q(\theta)$ to minimize the Kullback-Leibler (KL) divergence with the true posterior according to the following equation:

$$\mathrm{KL}(q(\theta) \| P(\theta|D)) = \int q(\theta) \log \left( \frac{q(\theta)}{P(\theta|D)} \right) d\theta. \qquad (2)$$

### 3.2. Sampling and dropout-based methods

Sampling and dropout-based methods introduce stochasticity into deterministic models to estimate uncertainty by performing multiple forward passes during inference. These methods leverage the vari- ability in predictions across these passes to quantify epistemic uncertainty.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Schematic illustration of the main uncertainty quantification (UQ) methods in deep learning. Each diagram represents a simplified flow from input to output, highlighting the structural differences between ensemble, Bayesian neural networks (BNN), Monte Carlo dropout (MCD), test-time augmentation (TTA), evidential deep learning (EDL), deterministic, conformal prediction, and post-hoc approaches. The consistent visual format highlights the comparative nature of these strategies across different UQ paradigms.</figcaption></figure>

Monte Carlo dropout (MCD). MCD (Gal and Ghahramani 2016) applies dropout not only during training but also during inference to simulate stochastic behavior. Multiple forward passes are performed, each with a different subset of neurons randomly frozen, allowing the model to produce a distribution of predictions. The uncertainty can be quantified from the distribution of stochastic predictions, commonly through their variance:

$$ \mathrm{Var}[f(x)] = \frac{1}{T} \sum_{t=1}^{T} (f_t(x) - \bar{f}(x))^2, \qquad (3) $$

where T is the number of stochastic passes, $f_t(x)$ is the prediction at pass t, and $\bar{f}(x)$ is the mean prediction across all passes. However, several other metrics can also be employed to quantify uncertainty (see 4 for further details).

*General sampling-based methods.* Other sampling-based approaches extend this idea by introducing randomness in different parts of the model (Ayhan and Berens 2018, Zhao et al 2022, Franchi et al 2024), such as weight perturbations or latent variable sampling.

These techniques include latent space sampling, where uncertainty is estimated by generating multiple outputs through sampling in models such as VAEs and perturbation-based sampling, which involves adding random noise to the input or intermediate layers during inference to produce diverse predictions.

### 3.3. Ensemble methods

Ensemble methods (ENS) can involve multiple distinct models or a deep ensemble of the same model trained with different initializations, hyperparameters, or data subsets (Rahaman et al 2021, Balabanov et al 2023, Ramé et al 2023a, Kim et al 2024a). The predictions can be aggregated, and the uncertainty can be estimated based on the variance of the predictions, according to the following equation:

$$ \mathrm{Var}[f(x)] = \frac{1}{N} \sum_{i=1}^{N} (f_i(x) - \bar{f}(x))^2, \qquad (4) $$

where N is the number of models in the ensemble, $f_i(x)$ is the prediction from the ith model, and $\bar{f}(x)$ is the mean prediction. However, several other metrics can also be employed to quantify uncertainty (see section 4 for further details).

### 3.4. Test time augmentation (TTA) methods

Data augmentation (Shorten and Khoshgoftaar 2019) is a widely used technique to enhance model robustness by artificially increasing the diversity of the training dataset. This is achieved through transformations such as rotations, scaling, noise addition, cropping, flipping, and contrast adjustments. While traditionally employed during training, these transformations can also be applied during inference, an
<table><caption>**Table 1.** Overview of uncertainty quantification (UQ) methods including advantages and limitations.</caption><thead><tr><td>UQ Method</td><td>Uncertainty Type</td><td>Advantages</td><td>Limitations</td></tr></thead><tbody><tr><td>Bayesian Neural Networks (BNN)</td><td>Aleatoric &amp; Epistemic</td><td><ul><li>Principled probabilistic modeling</li></ul></td><td><ul><li>Computationally intensive</li><li>Complex training and tuning</li><li>Sensitive to prior and approximation</li></ul></td></tr><tr><td>Monte Carlo Dropout (MCD)</td><td>Epistemic</td><td><ul><li>Easy to implement in existing models</li><li>No retraining required</li></ul></td><td><ul><li>Multiple forward passes required</li><li>May yield uncalibrated estimates</li><li>Increased inference time</li></ul></td></tr><tr><td>Ensemble Methods</td><td>Epistemic</td><td><ul><li>Robust and accurate uncertainty</li><li>Robust to overfitting</li></ul></td><td><ul><li>High training and storage costs</li><li>Slow inference due to multiple models</li></ul></td></tr><tr><td>Test-Time Augmentation (TTA)</td><td>Aleatoric</td><td><ul><li>Enhances robustness to noise/artifacts</li><li>No changes to model architecture</li></ul></td><td><ul><li>Does not explicitly model uncertainty</li><li>Task-dependent effectiveness</li><li>Increased inference time</li></ul></td></tr><tr><td>Evidential Deep Learning (EDL)</td><td>Predictive</td><td><ul><li>Efficient inference (single pass)</li></ul></td><td><ul><li>Needs careful regularization</li><li>May overestimate confidence</li></ul></td></tr><tr><td>Post-hoc/Auxiliary Networks</td><td>Typically Epistemic</td><td><ul><li>Works with pretrained models</li><li>Modular and low overhead</li></ul></td><td><ul><li>Dependent on auxiliary network quality</li><li>Limited generalizability across datasets</li></ul></td></tr><tr><td>Conformal Prediction</td><td>Predictive</td><td><ul><li>Model-agnostic, theoretical guarantees</li><li>Minimal distributional assumptions</li></ul></td><td><ul><li>May yield wide prediction intervals</li><li>Calibration set must be representative</li></ul></td></tr><tr><td>Deterministic</td><td>Aleatoric (primarily)</td><td><ul><li>Single-pass inference (fast)</li><li>Captures spatially varying data noise</li></ul></td><td><ul><li>May underestimate epistemic errors</li><li>Often needs calibration for interpretability</li></ul></td></tr><tr><td>Hybrid</td><td>Aleatoric &amp; Epistemic</td><td><ul><li>Combines complementary paradigms</li><li>Improved robustness and calibration</li></ul></td><td><ul><li>Increased implementation complexity</li><li>May require multiple training objectives</li></ul></td></tr></tbody></table>

approach known as TTA. In this setting, multiple augmented versions of the input are generated and passed through the model, producing a set of predictions. The variability among these predictions serves as an empirical estimate of uncertainty.

Beyond basic transformations, advanced data augmentation techniques further enhance model generalization and robustness (Mixup (Thulasidasan et al 2019), Pinto et al 2022), Outlier Sample Generation (Wang et al 2023, Zhu et al 2023), Domain-Specific Augmentation (Hariat et al 2024)).

By simulating perturbations common in clinical imaging, such as motion artifacts or contrast variation, TTA provides a practical means to estimate uncertainty and identify predictions that may require clinical attention.
### 3.5. Evidential deep learning (EDL)

EDL is an efficient UQ method (Zhao et al 2019, Amini et al 2020, Yu et al 2024) that predicts both the mean and variance of a distribution in a single forward pass. This approach models uncertainty as evidence, leveraging a probabilistic framework to capture both aleatoric and epistemic uncertainties.

In classification tasks, EDL often utilizes a Dirichlet distribution (Yu et al 2024) parameterized by evidence scores $\alpha = [\alpha_1, \alpha_2, \dots, \alpha_K]$, where K is the number of classes. The expected class probabilities are computed as:

$$ \mathbb{E}[p_k] = \frac{\alpha_k}{S}, \quad S = \sum_{k=1}^{K} \alpha_k, $$

where S is the total evidence, representing the model's confidence in its predictions. Higher S corresponds to lower epistemic uncertainty, while lower S indicates higher uncertainty.

The loss function for EDL typically includes a regularization term to discourage overconfident predictions with low evidence:

$$ \mathcal{L} = \mathcal{L}_{\text{prediction}} + \lambda \mathcal{L}_{\text{evidence}}, $$

where $\mathcal{L}_{\text{prediction}}$ ensures accurate predictions (such as Negative Log Likelihood), and $\lambda \mathcal{L}_{\text{evidence}}$ penalizes uncertainty estimates when evidence is insufficient.

### 3.6. Post-hoc methods and auxiliary networks

Post-hoc methods involve estimating uncertainty after the primary model has been trained, often using a secondary model or calibration techniques. These methods do not require modifications to the original training process, making them particularly useful for leveraging pretrained models.

Auxiliary networks (Besnier et al 2021, Ganaie et al 2022, Shen et al 2023) are secondary models trained to predict the uncertainty of the primary model's outputs. These networks take the primary model's predictions or intermediate representations as input and output uncertainty estimates.

### 3.7. Conformal prediction

Conformal prediction is a framework for quantifying uncertainty by providing prediction intervals that provide formal guarantees on coverage probabilities (Tibshirani et al 2019, Angelopoulos et al 2020, Bates et al 2023). Conformal prediction makes minimal assumptions about the underlying data distribution, making it widely applicable across different tasks and model architectures.

The key idea behind conformal prediction is to compute prediction intervals (for regression) or prediction sets (for classification) that contain the true label or value with a user-defined confidence level $1 - \alpha$, where $\alpha$ is the tolerated error rate. This is achieved by calibrating the model's predictions on a calibration set and constructing intervals that reflect the model's uncertainty.

For regression tasks, the prediction interval $\Gamma[\hat{y}_{\text{lower}}, \hat{y}_{\text{upper}}]$ is computed such that:

$$ P(y \in [\hat{y}_{\text{lower}}, \hat{y}_{\text{upper}}]) \geq 1 - \alpha, $$

where y is the true target value.

For classification, conformal prediction generates prediction sets $\mathcal{C}(x)$, which include one or more classes that collectively meet the required confidence level:

$$ P(y \in \mathcal{C}(x)) \geq 1 - \alpha. $$

### 3.8. Deterministic methods

Deterministic UQ approaches (Durasov et al 2022, Charpentier et al 2023, Mukhoti et al 2023) aim to estimate uncertainty directly within a single forward pass, without the need for stochastic sampling or multiple model instances. These methods generally extend the model architecture, training and post-training scheme, or the loss function to learn an uncertainty map alongside the main prediction.

A common strategy is the use of heteroscedastic loss, which allows the model to predict both a mean and a variance for each voxel or pixel. This variance represents the aleatoric uncertainty and is learned jointly with the main task objective. The model thus captures spatially varying noise and ambiguity inherent in the imaging data (Kendall and Gal 2017, Bragman et al 2018).
### 3.9. Hybrid methods

Hybrid methods combine elements from multiple UQ paradigms, such as Bayesian inference, ensemble diversity, or deterministic uncertainty modeling, to achieve more comprehensive and reliable uncertainty estimates. These approaches often aim to capture both aleatoric and epistemic components or to leverage uncertainty signals to guide model training and adaptation.

A representative example is the uncertainty-aware mean teacher (UAMT) framework (Zhang et al 2021, Wang et al 2024), which integrates Bayesian uncertainty estimation. In UAMT, the teacher network provides pseudo-labels to the student model, while voxel-level uncertainty, typically computed via MCD, modulates the consistency loss.

Beyond UAMT, hybrid UQ strategies include architectures that fuse evidential and Bayesian formula-
tions, combine deterministic and stochastic inference, or integrate uncertainty-aware modules into self-
supervised or domain adaptation frameworks.

Beyond numerical quantification, recent studies highlight the need to identify the causes of uncer-
tainty (Seoni et al 2023) in order to strengthen confidence in clinical AI systems. Causal inference frame-
works (Jiao et al 2024) could help disentangle the contributions of imaging noise, interobserver vari-
ability, and model bias to overall uncertainty. By replacing correlation-based models with stable and
interpretable causal models, these methods make it possible to distinguish genuine causal factors from
spuriously correlated variables. This enables a decomposition of error sources and can support targeted
mitigation strategies for uncertainty, thereby improving the interpretability and intrinsic robustness of AI
systems in radiation therapy, a field that demands low tolerance for error.

In section 5, we will explore how these methods are applied to various tasks in medical image ana-
lysis, drawing upon insights from two comprehensive reviews (Huang et al 2024, Wahid et al 2024) to
provide an in-depth exploration of their practical utility and growing significance in modern clinical
workflows.

## 4. Evaluation of UQ methods

Accurate and reliable assessment of uncertainty is essential for ensuring the robustness and clinical trust-worthiness of AI-driven models in RT workflows. A wide range of quantitative metrics has been proposed to evaluate how well uncertainty estimates reflect both prediction accuracy and model confidence across different imaging tasks. Table 2 summarizes the main categories of evaluation methods and their associated metrics, as detailed in appendix. These include coverage metrics, predictive entropy, calibration metrics, and scoring functions. Additional measures, including ROC-AUC for misclassification and out-of-distribution (OOD) detection and qualitative visual assessment by clinicians, provide complementary insight into the interpretability and clinical relevance of uncertainty estimates.

Overall, while each uncertainty evaluation method offers valuable insights into different aspects of model reliability, none alone provides a complete picture of uncertainty quality. Coverage metrics assess statistical reliability, entropy-based measures quantify dispersion, calibration errors evaluate confidence alignment, and correlation or scoring functions relate uncertainty to prediction error. However, all of these have inherent limitations. Coverage-based metrics, for instance, assess whether ground-truth values fall within predicted intervals but ignore the spatial distribution and clinical relevance of localized errors. Entropy-based measures capture the overall magnitude of predictive uncertainty but provide no indication of whether predictions are well-calibrated or clinically meaningful. Calibration metrics such as the ECE summarize the overall alignment between confidence and accuracy, yet may mask local miscalibrations or the effects of class imbalance. Similarly, correlation-based metrics (e.g. Pearson's correlation coefficient between uncertainty and error) quantify global association but fail to detect overconfident outliers (cases with low predicted uncertainty but large prediction errors) that represent a significant clinical risk. Moreover, interpreting the magnitude of the correlation itself remains challenging: a value of *r* = 0.8 may suggest a strong association between uncertainty and error, but it is difficult to establish what threshold should be considered acceptable or clinically meaningful. Such ambiguity limits the interpretability of correlation-based evaluations, as two models with similar coefficients may still exhibit very different behaviors in terms of reliability and safety.

Therefore, a comprehensive assessment of UQ should combine complementary metrics that capture both global behavior and case-level reliability, ensuring that uncertainty estimates are not only statistically sound but also clinically usable in RT applications.
<table><caption>**Table 2.** Main evaluation methods for uncertainty quantification in radiotherapy, and examples of associated metrics/tools. abbreviations: OOD: out-of-distribution.</caption><thead><tr><td>Evaluation Method</td><td>Description</td><td>Metrics/Tools</td></tr></thead><tbody><tr><td>Coverage Metrics</td><td>Measure the proportion of true outcomes within predicted uncertainty intervals or compute sample variance across predictions (Kuleshov et al 2018, Laves et al 2020, Balderas et al 2024, Huet-Dastarac et al 2024, Mossina et al 2024).</td><td>Coverage probability, variance, prediction intervals.</td></tr><tr><td>Predictive Entropy</td><td>Quantify total predictive uncertainty using the entropy or dispersion of the probability distribution of the model output (Dai and Tian 2013, Mehrtash et al 2020, Hamedani-KarAzmoudehFar et al 2023, Mehta et al 2024).</td><td>Shannon entropy, voxel-wise entropy maps</td></tr><tr><td>Calibration Metrics</td><td>Assess the alignment between predicted confidence and observed (Laves et al 2020, Mehrtash et al 2020, Mukhoti et al 2021).</td><td>Expected Calibration Error, Thresholded ECE, Uncertainty Calibration Error (Guo et al 2017, Minderer et al 2021)</td></tr><tr><td>Scoring Functions</td><td>Assess probabilistic prediction quality by combining accuracy and calibration in a single score (Laves et al 2020, Mehrtash et al 2020, Lemay et al 2022, Sambyal et al 2022).</td><td>Brier Score, Negative Log-Likelihood, Pearson Correlation Coefficient (PCC) (Cohen et al 2009)</td></tr><tr><td>Misclassification/OOD Detection</td><td>Use uncertainty thresholds to distinguish correct from incorrect predictions and detect OOD cases (Ayhan and Berens 2018, Linmans et al 2023, Yang et al 2024).</td><td>ROC-AUC, uncertainty threshold analysis, confusion matrix for OOD detection</td></tr><tr><td>Qualitative Evaluation</td><td>Subjective visual assessment of uncertainty maps to determine plausibility and usefulness for clinical review (Maruccio et al 2025, Rogowski et al 2025a).</td><td>Overlay visualization, clinician feedback, visual scoring scales</td></tr></tbody></table>

# 5. Applications of UQ

Figure 3 presents a comprehensive summary of the search results across three subpanels: (a) the UQ methods, (b) the imaging modalities, and (c) the anatomical regions. While AI-based methods are now omnipresent across tasks such as segmentation, sCT generation, and dose prediction, their integration into DIR and dose accumulation remains limited. As emphasized by Jena et al (2024), the role of deep learning in image registration continues to be debated, with performance often underperforming conventional methods in OOD scenarios.

## 5.1. Uncertainty in segmentation

UQ in segmentation methods has become increasingly important in medical image analysis (Huang et al 2024), particularly for ensuring robustness and reliability in downstream clinical tasks. Unlike registration-based methods, segmentation methods explicitly partition images into meaningful regions, making it especially sensitive to boundary accuracy and prone to variability caused by inter-operator differences and label ambiguity. As thoroughly reviewed by Huang et al (2024), a range of techniques has been proposed to quantify uncertainty in segmentation, including BNNs, MC sampling, TTA, ensemble methods, and EDL.

Tables 3 and 4 complement Huang et al's review with additional segmentation techniques, and applications in RT. A diverse array of probabilistic, deterministic, and hybrid UQ methods have been employed across anatomical sites and imaging modalities.

A key trend is the widespread adoption of MCD and ensemble techniques for estimating epistemic uncertainty, with applications ranging from prostate and breast cancer to H&N and lung segmentation. Hybrid models that integrate variational inference, attention mechanisms, or modality fusion have shown promise in capturing both aleatoric and epistemic components. Semi-supervised learning and auxiliary networks are also gaining traction, particularly for challenging or partially labeled datasets.
<figure><img src="image_6.png" /></figure>

These strategies not only improve segmentation accuracy but also support clinical workflows by identifying uncertain regions for manual review. Notably, many models have incorporated uncertainty maps into QA pipelines (Maruccio et al 2024, Rogowski et al 2025a), enabling clinicians to prioritize edits and ensure consistency across fractions.

Evaluating and interpreting uncertainty remains complex, common metrics such as the dice similarity coefficient (DSC) and volumetric overlap fail to capture the spatial and clinical nuances of uncertainty distributions (Huang et al 2024). In practice, explicit ground truth uncertainties are rarely available, so evaluations often rely on indirect metrics like predictive entropy, calibration error, or OOD detection. These are informative but fall short of a comprehensive assessment. Reflecting growing interest in this issue, the MICCAI 2024 and 2025 CURVAS (Calibration and Uncertainty for multiRater Volume Assessment in multiorgan Segmentation) challenge (Riera-Marin et al 2025) was created to explicitly address inter-annotator variability and evaluate uncertainty estimation strategies. Similarly, the LUND-PROBE dataset (Rogowski et al 2025b) includes DL segmentation uncertainty maps alongside multi-rater corrections for prostate and rectum delineation, enabling direct assessment of uncertainty in clinical segmentation workflows.

Moreover, the gap between algorithmic output and clinical usability is nontrivial. A recent study (Huet-Dastarac et al 2024) revealed that clinicians prefer uncertainty to be communicated simply and effectively: first by flagging entire organs as confident or uncertain, and then by displaying voxel-level uncertainty maps for local edits. While overlaying dose data on uncertain regions was seen as potentially valuable, excessive visual complexity was generally discouraged. These insights underscore the need for intuitive visualizations, adjustable confidence thresholds, and minimal interaction overhead to facilitate adoption in time-sensitive workflows.

Translating uncertainty estimates into clinical action requires clear and interpretable guidance. Based on recent user studies (Huet-Dastarac et al 2024, Maruccio et al 2025), clinicians tend to prefer a tiered approach:

* Low uncertainty (e.g. voxel-level entropy below task-specific thresholds) should prompt no change or routine verification;
<table><caption>**Table 3.** Uncertainty quantification studies in medical image segmentation in radiotherapy. DSC: dice similarity coefficient, CTV: clinical target volume, OAR: organs at risk, GTV: gross tumor volume, QA: quality assurance, AUC: area under the curve, ENS: ensemble method, MCD: Monte Carlo dropout, BNN: Bayesian neural network.</caption><thead><tr><th>Publications</th><th>Uncertainty Methods</th><th>Patient dataset</th><th>Imaging modality</th><th>Volume of interest</th><th>Main findings</th></tr></thead><tbody><tr><td>Chen et al (2020)</td><td>Auxiliary Network</td><td>Breast 680 patients</td><td>CT</td><td>CTV</td><td>Demonstrated AUC integration improves segmentation model reliability (AUC = 0.88–0.96)</td></tr><tr><td>Lei et al (2021)</td><td>ENS</td><td>StructSeg (Li and Chen 2020) H&amp;N 60 patients</td><td>CT</td><td>OAR</td><td>Ensemble method improved DSC by 1% (DSC = 0.81)</td></tr><tr><td>Mei et al (2021)</td><td>ENS</td><td>StructSeg (Li and Chen 2020) H&amp;N 60 patients</td><td>CT</td><td>GTV</td><td>Highlighted regions of high uncertainty to guide physician review</td></tr><tr><td>Zabihollahy et al (2022)</td><td>MCD</td><td>Cervical cancer 125 patients</td><td>MRI</td><td>CTV</td><td>Identified areas of high uncertainty in MRI-based CTV for physician attention</td></tr><tr><td>Li et al (2023)</td><td>BNN</td><td>Prostate 300 patients</td><td>CT</td><td>OAR (prostate)</td><td>Probabilistic U-Net with outlier mitigation improved DSC</td></tr><tr><td>Min et al (2023)</td><td>MCD</td><td>Prostate 443 patients</td><td>MRI</td><td>CTV</td><td>Achieved 92% true positive rate and 9% false positives in MRI-only QA</td></tr><tr><td>Cubero et al (2023)</td><td>MCD</td><td>H&amp;N 48 patients</td><td>CT</td><td>OAR</td><td>Achieved true positive detection rates of 98% and 85% for clinically acceptable contours</td></tr><tr><td>De Biase et al (2023)</td><td>ENS</td><td>H&amp;N 138 patients</td><td>PET/CT</td><td>GTV</td><td>Provided uncertainty maps to support adaptive PET/CT segmentation</td></tr><tr><td>Maruccio et al (2024)</td><td>MCD</td><td>Lung 422 patients</td><td>CT</td><td>GTV</td><td>Used uncertainty maps to flag ambiguous regions in lung GTV</td></tr><tr><td>Wang et al (2025)</td><td>Auxiliary Network</td><td>Brain 76 patients</td><td>MRI</td><td>GTV</td><td>Enabled pixel-wise uncertainty mapping via spherical projections</td></tr><tr><td>Rogowski et al (2025a)</td><td>ENS</td><td>Pelvis 35 patients</td><td>MRI</td><td>CTV, OAR (rectum)</td><td>Applied ensemble learning for robust segmentation of pelvic targets</td></tr><tr><td>Maruccio et al (2025)</td><td>MCD</td><td>Rectal cancer 16 patients</td><td>MRI</td><td>CTV segmentation</td><td>Epistemic uncertainty predicted clinically relevant edits, AUC > 0.9 for local corrections > 8 mm</td></tr><tr><td>Ren et al (2024)</td><td>TTA, Deterministic, MCD, ENS, Hybrid, BNN</td><td>H&amp;N 567 patients</td><td>PET/CT, MRI</td><td>GTV</td><td>Fusion of PET/CT and MRI improved segmentation accuracy</td></tr></tbody></table>

* Moderate uncertainty should lead to local edits or boundary refinement, particularly in regions of high dose gradient or near organs at risk;

* High uncertainty should trigger full re-contouring or model output rejection for that structure.
<table><caption>**Table 4.** Hybrid uncertainty quantification studies in medical image segmentation. CTV: clinical target volume, GTV: gross tumor volume, ENS: ensemble method, MCD: Monte Carlo dropout, BNN: Bayesian neural network, TTA: test-time augmentation.</caption><thead><tr><th>Publications</th><th>Uncertainty Methods</th><th>Patient dataset</th><th>Imaging modality</th><th>Volume of interest</th><th>Main findings</th></tr></thead><tbody><tr><td colspan="6">Hybrid Methods</td></tr><tr><td>Zhang et al (2021)</td><td>MCD, Deterministic</td><td>Lung datasets 140 patients</td><td>CT</td><td>CTV, OAR (spinal, lungs, heart, esophagus)</td><td>Enabled model convergence on partially labeled datasets via uncertainty-aware loss</td></tr><tr><td>Sahlsten et al (2023)</td><td>ENS, MCD</td><td>HECKTOR (Andrearczyk et al 2022) 224 patients + 67 patients (H&amp;N)</td><td>PET/CT</td><td>GTV</td><td>Identified coefficient of variation as optimal uncertainty metric</td></tr><tr><td>Ebadi et al (2023)</td><td>MCD, ENS</td><td>Lung 16 patients</td><td>CBCT</td><td>GTV</td><td>Accurately forecasted tumor shrinkage up to five steps ahead</td></tr><tr><td>Chlap et al (2024)</td><td>BNN and MCD</td><td>Gastric and Prostate datasets (20 patients)</td><td>CT</td><td>CTV</td><td>Captured aleatoric and epistemic uncertainty in small datasets</td></tr><tr><td>Wang et al (2024)</td><td>Deterministic, MCD</td><td>Breast 60 patients</td><td>CBCT</td><td>CTV</td><td>Showed semi-supervised training with only 10% labeled data was effective</td></tr><tr><td>Sahlsten et al (2024)</td><td>ENS, MCD</td><td>HECKTOR (Andrearczyk et al 2022) 224 patients + 67 patients (H&amp;N)</td><td>PET/CT</td><td>GTV</td><td>Predicted segmentation quality in 86.6% of cases</td></tr></tbody></table>

These uncertainty thresholds are not universal and should be calibrated according to the specific task, anatomical region, and model type. For instance, two segmentation studies demonstrated that thresholds derived from predictive entropy or variance can effectively identify clinically relevant errors, one focusing on rectal segmentation (Maruccio et al 2025) and another covering multiple anatomical sites (including pelvic, abdominal, breast, and head-and-neck regions) (Huet-Dastarac et al 2024). In the latter, uncertainty maps were assessed through clinician feedback to determine which visualization strategies best support error detection and review prioritization. Integrating such graded uncertainty maps into automated QA pipelines can help clinicians decide whether an image requires closer inspection or complete manual revision, thereby improving workflow efficiency and patient safety.

In summary, while UQ-enhanced segmentation models show strong technical performance and potential clinical utility, their translation into practice will depend on resolving issues related to computational efficiency, evaluation consistency, and interface design.

## 5.2. Uncertainty in deformable image registration

DIR is a cornerstone in ART, enabling the spatial alignment of serial images for dose accumulation, contour propagation, and/or treatment monitoring. However, DIR is highly sensitive to anatomical variability, image quality, and algorithmic design, making UQ essential for clinical reliability (Nenoff et al 2023).

Tables 5 and 6 gather UQ studies in DIR for RT. A large variety of UQ approaches was used for DIR. Most methods target epistemic uncertainty, capturing variability due to limited data or model assumptions. A few incorporate aleatoric uncertainty.

Figure 3 provides an overview of the distribution of uncertainty methods, imaging modalities, and anatomical sites across studies focused on DIR (orange). Panel (a) highlights the prevalence of BNN and
<table><caption>**Table 5.** Uncertainty quantification studies in deformable image registration in radiotherapy. DVF: deformable vector field, UA: uncertainty accuracy, NPV: negative predictive value, DIR: deformable image registration, ENS: ensemble method, MCD: Monte Carlo dropout, BNN: Bayesian neural network.</caption><thead><tr><th>Publications</th><th>Uncertainty Methods</th><th>Patient dataset</th><th>Modality</th><th>Clinical Applications</th><th>Main findings</th></tr></thead><tbody><tr><td>Nenoff et al (2020)</td><td>ENS methods</td><td>Lung 7 patients (with 9 CTs and a planning CT)</td><td>CT</td><td>Dose accumulation</td><td>Averaged results from multiple DIRs accurately reflect dose degradation due to anatomical changes</td></tr><tr><td>Cui et al (2021)</td><td>MCD</td><td>Brain 101 patients</td><td>MRI</td><td>DIR</td><td>Quantification of registration uncertainty (NPV = 0.756, UA = 0.77)</td></tr><tr><td>Khawaled and Freiman (2022)</td><td>BNN</td><td>4 brain datasets (390 pairs)</td><td>MRI</td><td>DIR</td><td>Add uncertainty in DIR network improve results</td></tr><tr><td>Smolders et al (2022)</td><td>BNN</td><td>Lung 40 patients</td><td>CT</td><td>Dose accumulation</td><td>Predict variance of DVF when a patient is breathing</td></tr><tr><td>Grzech et al (2022)</td><td>BNN</td><td>Brain 1500 patients</td><td>MRI</td><td>DIR</td><td>Proposed loss allows to estimate the voxel uncertainty associated with the deformation</td></tr><tr><td>Xu et al (2022)</td><td>MCD</td><td>Abdominal 50 patients</td><td>MRI, CT</td><td>DIR</td><td>Achieves higher Dice scores than both classical and learning based methods</td></tr><tr><td>Chen et al (2022)</td><td>MCD</td><td>3 brain datasets 1287 patients</td><td>MRI, CT</td><td>DIR</td><td>Uncertainty on segmentation for registration</td></tr><tr><td>Smolders et al (2023)</td><td>BNN</td><td>Thorax 22 patients, Abdomen 11 patients, H&amp;N 37 patients</td><td>CT</td><td>Dose accumulation</td><td>Uncertainty on DVF allows an evaluation of the calibration error ≤ 3%</td></tr><tr><td>Hua et al (2024)</td><td>BNN</td><td>4 Cardiac dataset (4085 pairs)</td><td>MRI</td><td>DIR</td><td>Loss function with uncertainty: more weight on confident predictions, minimize the uncertain ones</td></tr></tbody></table>

MCD as the most commonly used UQ techniques, reflecting their effectiveness in modeling epistemic uncertainty. Panel (c) highlights the prevalence of monomodal registration using MRI or CT as the primary imaging modality, while fewer studies employ multimodal approaches between MRI and CT.

Notably, the adaptation of established architectures such as VoxelMorph, probabilistic U-Nets, and transformer-based models has enabled the generation of geometric uncertainty maps and deformation vector field (DVF) confidence estimates. These outputs are increasingly being used not only for QA but also to improve calibration, guide dose summation, and flag unreliable anatomical mappings. Hybrid and domain-adapted approaches have further improved robustness across modalities and centers.

While promising, several limitations persist. Computational costs remain high for UQ in DIR, particularly for methods relying on sampling or ensembles. Moreover, ground-truth validation of uncertainty in registration is inherently challenging due to the lack of voxel-level correspondence standards. The absence of standardized evaluation metrics (analogous to Dice scores in segmentation) complicates comparative benchmarking. Recent developments, such as the incorporation of calibration error metrics and predictive confidence maps, mark important steps forward but require broader adoption.
<table><caption>**Table 6.** Hybrid uncertainty quantification studies in deformable image registration in radiotherapy. DIR: deformable image registration, DVF: deformable vector field, UA: uncertainty accuracy, NPV: negative predictive value, MCD: Monte Carlo dropout.</caption><thead><tr><th>Publications</th><th>Uncertainty Methods</th><th>Patient dataset</th><th>Modality</th><th>Clinical Applications</th><th>Main findings</th></tr></thead><tbody><tr><td colspan="6">Hybrid Methods</td></tr><tr><td>Gong et al (2022)</td><td>MCD, Bootstrap, ENS</td><td>Hippocampus 260 patients, Prostate 32 patients</td><td>MRI</td><td>DIR</td><td>Reduce the uncertainty of DIR in final results</td></tr><tr><td>Chen et al (2024)</td><td>MCD, Deterministic</td><td>2 Cardiac datasets 470 patients</td><td>MRI</td><td>DIR and Contour propagation</td><td>The estimated uncertainties align with label propagation errors and enhance registration performance</td></tr></tbody></table>

Overall, UQ in DIR is an active and evolving field. Future work should prioritize standardization, cross-center validation, and the development of user-friendly tools to visualize registration uncertainty.

### 5.3. Uncertainty in synthetic CT generation

sCT generation is increasingly used in MR-only and CBCT-guided RT workflows. Tables 7 and 8 presents recent UQ studies in sCT generation for RT.

Figure 3 (blue) provides an overview of UQ in sCT generation compared to other steps of RT workflow. UQ in sCT generation predominantly focused on brain and pelvic anatomical localizations using MRI-to-CT generation, with fewer studies addressing CBCT-to-CT generation. Most published methods directly target sCT generation and dosimetric estimation, while fewer explore auxiliary applications such as segmentation from sCT or treatment plan robustness.

UQ in sCT aims to assess the reliability of image synthesis under variable input quality and anatomical changes. A wide range of techniques have been proposed to estimate both epistemic and aleatoric uncertainties. Epistemic uncertainty is often modeled using Bayesian approximations such as MCD (Bragman et al 2018, Hemsley et al 2020, Karthik et al 2023, Tian and Lühr 2023, Galapon Jr et al 2024, Rusanov et al 2024) and DropConnect (Law et al 2024). Aleatoric uncertainty, on the other hand, is typically captured using heteroscedastic loss functions (Bragman et al 2018, Hemsley et al 2020, Li et al 2023).

Emerging methods such as Monte Carlo sampling with diffusion models (Lyu and Wang 2022) have shown potential to capture both types of uncertainty within a generative framework. These hybrid strategies are particularly promising for synthesizing anatomically accurate sCTs while quantifying uncertainty under ambiguous or degraded imaging conditions.

While many studies have provided qualitative assessments using uncertainty maps for sCT generation, recent work increasingly focuses on quantitative correlation between uncertainty and downstream clinical metrics. Several models report strong correlations (i.e. PCC up to 0.81) between predicted uncertainty and absolute prediction errors or dose deviations. In proton therapy (Li et al 2023), uncertainty metrics have been integrated into dose-volume histogram (DVH) analysis, improving the robustness of treatment planning and providing new tools for dose auditing and QA. In photon therapy (Hémon et al 2025), image uncertainty has also been leveraged to estimate how sCT generation errors propagate into dose distributions.

Despite recent advances, several challenges remain. The findings from different studies are not comparable because the evaluation metrics are too varied, and clinically relevant endpoints are not being incorporated in a consistent way. Furthermore, most studies on sCT UQ are constrained to single-center datasets and a limited range of anatomical sites. Additionally, visualization tools for incorporating voxel-wise uncertainty into dose evaluation workflows remain insufficiently developed.

In summary, UQ in sCT generation is becoming more mature, with methods advancing from experimental image synthesis to clinically meaningful reliability assessment.

### 5.4. Dose prediction uncertainty

UQ in dose prediction is an emerging subdomain within RT AI, with only four studies explicitly addressing it. Table 9 summarizes these studies.
<table><caption>**Table 7.** Uncertainty quantification methods in medical image synthetic CT generation. ENS: ensemble method, MCD: Monte Carlo dropout, TTA: test-time augmentation, QA: quality assurance.</caption><thead><tr><th>Publications</th><th>Uncertainty Methods</th><th>Patient dataset</th><th>Original imaging modality</th><th>Clinical Applications</th><th>Main findings</th></tr></thead><tbody><tr><td>Maspero et al (2020)</td><td>ENS</td><td>Brain 60 patients</td><td>MRI</td><td>sCT dose calculations</td><td>Dose variations around ±0.3–0.4% and mean pass rates of 99.5%</td></tr><tr><td>van Harten et al (2020)</td><td>ENS</td><td>Brain 52 patients</td><td>MRI</td><td>sCT generation</td><td>QA of sCT (input MRI quality, sCT accuracy)</td></tr><tr><td>Lyu and Wang (2022)</td><td>MC sampling diffusion</td><td>Pelvis 19 patients</td><td>MRI</td><td>sCT generation</td><td>Comparison of different model uncertainties</td></tr><tr><td>Li et al (2023)</td><td>Deterministic</td><td>Brain 74 patients</td><td>MRI</td><td>Robust proton therapy planning</td><td>sCT generation with uncertainty improves plan robustness: ±3% accuracy in proton therapy</td></tr><tr><td>Tian and Lühr (2023)</td><td>MCD</td><td>Pelvis 19 patients</td><td>MRI</td><td>sCT dose calculations</td><td>Error was higher at the body edge (~200 HU) than in the body (~100 HU) near bone</td></tr><tr><td>Law et al (2024)</td><td>MC DropConnect</td><td>Pelvis 59 patients</td><td>MRI</td><td>QA and sCT generation</td><td>MAE = 44.33 and γ = 98.68%, 0.53–0.83 correlation between Bayesian uncertainties and sCT error</td></tr><tr><td>Galapon Jr et al (2024)</td><td>MCD</td><td>H&N 101 patients</td><td>MRI</td><td>QA and sCT dose calculations</td><td>DCNN correlation: r = 0.92 for HU, 0.64 for water equivalent thickness, and 0.65 for dose difference</td></tr><tr><td>Quintero et al (2025)</td><td>ENS</td><td>Abdominal 65 patients</td><td>CBCT</td><td>QA and sCT dose calculations</td><td>Strong correlation (ρ = 0.84, p ≤ 0.001) between whole sCT uncertainty and the gamma index</td></tr><tr><td>de Hond et al (2025)</td><td>TTA (Iterative reconstruction parameters)</td><td>Pelvis 20 patients</td><td>CBCT</td><td>sCT generation</td><td>sCT sensitivity to iCBCT reconstruction parameters (standard deviation up to 438 HU)</td></tr></tbody></table>

Collectively, these studies illustrate distinct paradigms for UQ in dose prediction. Each method offers tradeoffs between interpretability, computational cost, and integration potential with downstream treatment planning. A shared finding across these works is the consistent spatial and dosimetric alignment between uncertainty estimates and prediction errors, validating the use of uncertainty maps for guiding clinician review or automated quality control. As dose prediction models mature, incorporating UQ appears increasingly essential, both for model transparency and to enable robust planning workflow.

Beyond dose prediction, UQ is also being explored in other stages such as in patient-specific QA (PSQA). For example, Yang et al (2025) introduced a Bayesian UQ framework for PSQA in VMAT. Their model performed pass/fail classification using field complexity features and fluence maps, and employed Monte Carlo-based approximate Bayesian inference to estimate both epistemic and aleatoric uncertainties, enabling uncertainty-guided clinical interventions for cases with low model confidence. Similarly, Zeng et al (2024) proposed a multi-granularity prior network that quantifies uncertainty jointly across dose-difference prediction and gamma passing rate estimation, providing multi-level uncertainty visualization within PSQA. Together, these studies highlight that the optimization and fluence
<table><caption>**Table 8.** Hybrid uncertainty quantification methods in medical image synthetic CT generation. MCD: Monte Carlo dropout, TTA: test-time augmentation, QA: quality assurance.</caption><thead><tr><th>Publications</th><th>Uncertainty Methods</th><th>Patient dataset</th><th>Original imaging modality</th><th>Clinical Applications</th><th>Main findings</th></tr></thead><tbody><tr><td colspan="6">Hybrid Methods</td></tr><tr><td>Bragman et al (2018)</td><td>Deterministic, MCD</td><td>Pelvis 15 patients</td><td>MRI</td><td>sCT generation and segmentation</td><td>Improved sCT generation, MAE = 43.3HU</td></tr><tr><td>Hemsley et al (2020)</td><td>Deterministic, MCD</td><td>Brain 105 patients</td><td>MRI</td><td>sCT generation</td><td>sCTs offer accuracy equivalent to that of previously reported deterministic models</td></tr><tr><td>Karthik et al (2023)</td><td>Deterministic, MCD</td><td>Lumbar spine 3 different dataset</td><td>MRI</td><td>sCT generation</td><td>Improving DL models for sCT generation interpretability</td></tr><tr><td>Rusanov et al (2024)</td><td>MCD; TTA</td><td>Pelvis 50 patients</td><td>CBCT</td><td>QA and sCT dose calculations</td><td>FID better discriminated image quality</td></tr><tr><td>Hémon et al (2025)</td><td>Deterministic, MCD</td><td>H&N 85 patients</td><td>CBCT</td><td>Dose uncertainty</td><td>sCT uncertainty at voxel level gives a reliable idea of how uncertainties can affect dose calculations</td></tr></tbody></table>

<table><caption>**Table 9.** Uncertainty quantification methods for dose prediction in radiotherapy. H&N: head-and-neck, OAR: organ-at-risk, DVH: dose-volume-histogram, QA: quality assurance, MCD: Monte Carlo distribution, EDL: evidential deep learning.</caption><thead><tr><th>Publications</th><th>Uncertainty Methods</th><th>Patient dataset</th><th>Original imaging modality</th><th>Clinical Applications</th><th>Main findings</th></tr></thead><tbody><tr><td>Nguyen et al (2021)</td><td>MCD, Bagging</td><td>H&N 340 patients, OpenKBP (Babier et al 2021)</td><td>CT</td><td>Dose prediction (OARs)</td><td>Bagging improved voxel-wise error prediction; post-hoc calibration produced interpretable DVH confidence intervals</td></tr><tr><td>Nilsson et al (2021)</td><td>EDL (Mixture Density)</td><td>Pelvic 33 patients</td><td>CT</td><td>Dose prediction</td><td>Learned bimodal distributions from competing clinical goals; enabled plan generation respecting OAR/tumor trade-offs</td></tr><tr><td>Tan et al (2024)</td><td>EDL</td><td>H&N 340 patients, OpenKBP (Babier et al 2021)</td><td>CT</td><td>Dose prediction (OAR QA)</td><td>Strong correlation (ρ = 0.69–0.83) between epistemic uncertainty and error; 95% confidence intervals on DVH metrics for QA</td></tr><tr><td>Huet-Dastarac et al (2024)</td><td>Deterministic</td><td>H&N 60 patients</td><td>CT</td><td>Dose prediction</td><td>Reconstruction error of input CT used for the uncertainty; achieved higher correlation with dose error than MCDO or ensembles and effective OOD detection</td></tr></tbody></table>
<table><caption>**Table 10.** Summary of dose accumulation uncertainty quantification methods. DIR: deformable image registration, DVF: deformation vector field, OAR: organ-at-risk.</caption><thead><tr><td>Study</td><td>Method</td><td>Clinical Application</td><td>Dataset</td><td>Key Results</td></tr></thead><tbody><tr><td>Nenoff et al (2020)</td><td>Compared six DIR algorithms to assess dose variations</td><td>Proton therapy (Lung)</td><td>7 patients (CT)</td><td>Anatomical changes had greater dosimetric impacts than DIR algorithm variability</td></tr><tr><td>Lowther et al (2020)</td><td>Quantified inverse consistency errors (ICE)</td><td>Photon therapy (H&amp;N)</td><td>12 patients with synthetic deformations (CBCT)</td><td>Achieved 98.5% voxel consistency; critical uncertainties in organs at risk</td></tr><tr><td>Amstutz et al (2021)</td><td>DVF uncertainty model integrating dose gradients and geometric variability</td><td>Proton therapy (Lung)</td><td>7 patients (CT)</td><td>±5% uncertainty accuracy for 77%-98% of voxels</td></tr><tr><td>Kainz et al (2022)</td><td>DVH overlay for quantifying inverse consistency errors</td><td>Pancreas and prostate datasets</td><td>10 patients (MVCT)</td><td>Identified inverse consistency errors; quantified dose summation errors in OARs</td></tr><tr><td>Smolders et al (2023)</td><td>Deep learning models for DIR uncertainty prediction</td><td>Proton therapy (Lung and H&amp;N)</td><td>Thorax 22 patients, H&amp;N 37 patients (CT)</td><td>Robust algorithm-independent uncertainty predictions</td></tr><tr><td>Amstutz et al (2024)</td><td>Extended DVF uncertainty model to high-dose gradient regions in head-and-neck proton therapy</td><td>Proton therapy (H&amp;N)</td><td>5 patients with multiple CTs (CT)</td><td>Mitigation of fraction-based uncertainties through cumulative dose evaluation</td></tr><tr><td>van den Dobbelsteen et al (2024)</td><td>Delta index combining DIR spatial uncertainty and dose gradients</td><td>SBRT (Lung, MR-linac)</td><td>10 patients</td><td>Improved passing rates in high-dose regions, identification of uncertainties in low-dose areas</td></tr><tr><td>Mechalakos et al (2024)</td><td>Ellipsoid-based voxel search with structure matching</td><td>Spine reirradiation</td><td>11 patients (CT)</td><td>Enables user-defined search radii for OAR dose smearing</td></tr></tbody></table>

delivery components of treatment planning are closely linked to the sources of uncertainty in PSQA and remain critical yet underexplored targets for uncertainty-aware modeling. Overall, UQ research in these upstream components is still at an early stage.

## 5.5. Dose accumulation uncertainty

Dose accumulation uncertainty is a critical issue in RT. Anatomical changes in the patient during treatment, such as tumor shrinkage and organ movement (e.g. breathing, swallowing, patient movement), pose significant challenges to accurately mapping the doses administered in relation to a reference anatomy. While DIR tools are widely used for dose accumulation in TPS, they introduce intrinsic uncertainties related to geometric deformations.

Other sources of uncertainty include variations in patient setup, inaccuracies in treatment delivery systems, and mechanical errors in equipment. Moreover, treatment response during therapy, including tumor shrinkage or deformation of OARs, adds temporal complexity to dose mapping. These factors collectively underscore the multifactorial nature of dose accumulation uncertainty, emphasizing the need for comprehensive UQ frameworks to ensure robust decision-making in ART.

Table 10 summarizes recent studies for quantifying dose accumulation uncertainty.

Dose accumulation methods are all based on DIR-based frameworks, combining DVF variability, inverse consistency errors (ICE), and geometric-to-dosimetric correlation analyses. Approaches incorporate voxel-level uncertainty metrics, such as the delta index (van den Dobbelsteen et al 2024) or
probabilistic DVHs (Amstutz et al 2021, 2024) to localize error-prone regions, especially in high-dose gradients or OARs. Deep learning-based models have also been developed to predict DVF uncertainty (Smolders et al 2023), providing algorithm-independent estimates that generalize across datasets.

Despite these advances, practical limitations persist. Few methods recalculate the dose on updated anatomies using MVCT (Kainz et al 2022) or CT (Nenoff et al 2020, Amstutz et al 2021), limiting their applicability in online ART workflows where patient-specific anatomical fidelity is essential. Most studies rely on CT-based dose accumulation without incorporating daily imaging variations or sCT generation. This gap highlights the opportunity to integrate image uncertainty, already explored in photon therapy dose modeling (Hémon et al 2025) into cumulative dose estimation, enhancing realism in adaptive protocols.

Innovative tools like RADAR (Mechalakos et al 2024) have begun embedding uncertainty directly into clinical dose computation workflows. This Eclipse-based extension uses voxel-wise ellipsoid searches to distribute dose within user-defined spatial radii, offering flexibility in accounting for alignment errors while avoiding dose overestimation near high-gradient regions. Similarly, methods using DVH overlays, multi-algorithm DIR averaging continue to improve reliability in dose tracking.

In summary, the dose accumulation UQ is evolving towards more nuanced, voxel-specific, and clinically integrated frameworks. Standardization of evaluation metrics and broader adoption of advanced imaging and recalculation strategies will be essential to fully realize the benefits of uncertainty-aware cumulative dose modeling in RT.

# 6. Challenges in clinical adoption of uncertainty-aware AI models

Despite substantial methodological progress in UQ, the clinical integration of uncertainty-aware AI models remains limited. Several key barriers, ranging from evaluation standards and regulatory barriers to computational demands and clinician acceptance, continue to hinder real-world deployment. This section presents the main obstacles to a clinical adoption.

## 6.1. Uncertainty propagation

Beyond task-specific uncertainty estimation, a crucial challenge is understanding how uncertainties propagate throughout the sequential RT workflow. Variability can already arise at the earliest stages, particularly during the delineation target volumes. These volumes are typically defined using imaging modalities such as CT, MRI, or PET. However, interobserver variability in interpreting tumor boundaries can introduce inconsistencies in the contours, resulting in suboptimal inputs for subsequent steps such as sCT generation, DIR, and dose calculation.

Each step in the RT pipeline introduces its own uncertainties, which may amplify or interact with those from previous stages:

*   **Segmentation uncertainty:** errors or variability in segmentation, whether due to model limitations or inherent imaging ambiguities, propagate to dose calculation, and registration. For example, a mis-segmented organ boundary can lead to inaccurate dose calculation, which in turn affects dose calculation. Voxel-level uncertainty maps from segmentation models can help predict which regions are most likely to influence downstream tasks.

*   **Synthetic CT generation uncertainty:** sCT models produce outputs that are themselves uncertain due to input variability, model approximations, or anatomical changes. These uncertainties directly influence dose prediction, as inaccurate electron density estimation or anatomical misrepresentation can cause dose deviations. By quantifying sCT uncertainty, one can anticipate how these errors will affect registration and cumulative dose estimation.

*   **Deformable image registration uncertainty:** DIR aligns serial images to track anatomical changes and propagate contours for treatment planning. Uncertainty in segmentation and sCT inputs contributes to variability in DVFs, which can impact contour propagation, dose accumulation, and treatment plan accuracy. Confidence maps derived from DIR models can be used to highlight regions where accumulated errors may be clinically significant.

*   **Dose prediction uncertainty:** uncertainties from segmentation and sCT generation propagate into dose prediction, where model variability can further amplify their effects. AI-based models add both aleatoric and epistemic uncertainty, which are particularly critical in high-dose gradient regions and near OARs, where small geometric or intensity deviations can lead to significant dosimetric errors. Quantifying these uncertainties is essential for treatment planning QA, enabling the identification of cases requiring clinician review or plan adjustment.
* Dose accumulation uncertainty: dose accumulation combines spatially deformed dose distributions across fractions and is highly sensitive to upstream uncertainties, especially from DIR. Inaccuracies in deformation fields, compounded by segmentation or sCT errors, can bias accumulated dose estimates. UQ at this stage aims to assess the reliability of cumulative dose maps and how registration uncertainty affects dose-response metrics, supporting the interpretation of accumulated dose and the definition of confidence bounds on clinical endpoints.

Overall, understanding the cumulative propagation of uncertainty is essential to maintain safety and accuracy in automated RT workflows. Task-specific UQ must therefore be contextualized within the larger pipeline, rather than treated in isolation. Incorporating uncertainty estimates from multiple steps allows for systemic assessment of potential errors and development of robust QA procedures.

Future studies should focus on developing integrated UQ frameworks that link segmentation, sCT generation, registration, and dose accumulation uncertainties.

## 6.2. Absence of standardized evaluation protocols

A significant obstacle to clinical deployment is the absence of universally accepted evaluation frameworks for UQ. Existing metrics, such as calibration error and coverage probability, typically capture isolated aspects of uncertainty without offering a comprehensive assessment of model reliability. Moreover, these metrics are often not tailored to clinical priorities or task-specific requirements, leading to a disconnect between research findings and practical utility.

To facilitate clinical translation, evaluation protocols must align with medical decision-making workflows and prioritize clinically meaningful metrics. For instance, in RT, uncertainty estimates should directly inform decisions such as treatment margin adaptation or dose escalation. The lack of task-adaptive, fair, and interpretable evaluation strategies remains a major gap in current research.

## 6.3. Validation and generalizability concerns

Most UQ models are trained and validated on single-center datasets, limiting their generalizability across diverse patient populations, scanners, and imaging protocols. Without multicenter studies and external validation, it is difficult to establish the reliability of these models in varied clinical environments. Furthermore, there is no consensus on benchmarking practices, making cross-study comparisons more challenging.

## 6.4. Regulatory and legal barriers

Regulatory approval for uncertainty-aware AI models is inherently complex. Agencies like the U.S. Food and Drug Administration (FDA) and the European Medicines Agency (EMA) require not just accuracy, but demonstrable transparency, robustness, and safety, criteria that are more difficult to satisfy for models producing probabilistic outputs. The interpretability of uncertainty maps, especially in critical scenarios such as tumor delineation or adaptive planning, must be rigorously standardized to meet these regulatory expectations. Regulatory expectations include transparency, reproducibility, and clinical relevance of uncertainty estimates.

## 6.5. Clinical usability and interpretability

Uncertainty-aware models often produce outputs that are difficult for non-technical users to interpret. Visualization tools such as voxel-wise probability maps or confidence intervals lack intuitive clinical translation unless carefully integrated into existing treatment planning software. Without user-friendly interfaces and clear guidance on how to act on uncertainty information, these models risk being underutilized, even when technically sound.

## 6.6. Computational feasibility

Many advanced UQ methods, including BNN and MC sampling, require multiple forward passes during inference, resulting in significant computational overhead. This is particularly problematic in time-sensitive settings like online ART, since decisions must be fast. Models must therefore strike a balance between accuracy and efficiency, ensuring that added uncertainty estimation does not introduce treatment delays.

## 6.7. Physician trust and adoption

Finally, clinician trust remains a critical factor. While uncertainty estimates offer added transparency, their probabilistic nature can generate scepticism among physicians accustomed to deterministic outputs. Without clear evidence of clinical benefit, such as improved segmentation accuracy or reduced interobserver variability, these models are unlikely to gain widespread acceptance. Building trust will require
close collaboration between developers and clinicians to define actionable thresholds and validate impact on patient care.

## 6.8. Emerging trends in UQ beyond RT

Although the present review focuses on RT, several recent advances in UQ from computer vision and general image analysis have shown strong potential for translation to the RT domain. Several of these paradigms have already been introduced conceptually in section 3, but recent developments extend them far beyond their current use in RT. These methods, initially developed for natural or general medical imaging, address long-standing limitations in calibration, interpretability, and computational efficiency, and could significantly improve the robustness and trustworthiness of AI-driven RT workflows.

* Conformal prediction and risk-controlled uncertainty: conformal prediction methods (Balderas et al 2024, Lambert et al 2024, Mossina et al 2024) have recently gained traction for providing distribution-free uncertainty estimates with formal statistical guarantees on prediction coverage. By constructing prediction intervals or sets calibrated to achieve a predefined confidence level, they enable explicit control of the expected error rate. Applied to segmentation and regression, these techniques can produce spatial confidence intervals or 'prediction volumes' that indicate the probability that a voxel or structure is correctly predicted. In RT, such frameworks could be used to automatically flag structures or dose regions with insufficient confidence, define confidence-based contour margins, or trigger human review when coverage falls below clinically acceptable thresholds.

* Evidential deep learning: EDL approaches (Ulmer et al 2021, Meinert et al 2023, Qu et al 2024) continue to emerge as one of the most promising single-pass solutions for UQ. These models learn to output the parameters of evidential distributions (Dirichlet for classification or Normal-Inverse-Gamma for regression), allowing both prediction and uncertainty estimation in one forward pass. This formulation provides a computationally lightweight alternative to Bayesian sampling while maintaining robustness to OOD samples.

* Diversified deep ensembles: while classical deep ensembles remain the gold standard for capturing epistemic uncertainty, recent work has focused on diversified or low-cost ensemble variants such as SWAG (Maddox et al 2019), Laplace last-layer approximation (LLLA) (Daxberger et al 2021), or stochastic subspace ensembles (Trinh et al 2023, Ramé et al 2023b, Kim et al 2024b). Their ability to maintain reliable calibration with limited additional resources makes them particularly appealing for online ART, where models must operate under strict latency constraints while still quantifying uncertainty in real time.

* Deterministic single-pass and sampling-free estimation: recent deterministic or sampling-free methods provide lightweight alternatives to Bayesian inference. The deep deterministic uncertainty (DDU) approach (Mukhoti et al 2021) estimates epistemic uncertainty by modeling the feature-space density using class-conditional Gaussians. It operates in a single forward pass and achieves strong OOD detection without Monte Carlo sampling. In contrast, the ZigZag framework (Durasov et al 2022) performs a two-step inference to approximate both aleatoric and epistemic components through local gradient analysis, delivering ensemble-level performance at a fraction of the computational cost. These methods, though not strictly Bayesian, achieve robust calibration and inference efficiency that could make them particularly attractive for time-critical RT applications such as adaptive planning and online QA.

* Robust OOD detection and epistemic quantification: recent studies emphasize the role of epistemic uncertainty in identifying OOD samples and improving model robustness to domain shifts (Wang and Ji 2024, Yang et al 2024, Chen and Ding 2025). Approaches based on feature dispersion and energy-based modeling allow uncertainty estimation even in large-scale, pre-trained architectures without retraining. These methods explicitly link epistemic uncertainty to the model's awareness of distributory boundaries, providing interpretable confidence signals for open-world scenarios. In RT, such techniques could safeguard automated workflows by flagging scans, modalities, or anatomical configurations that deviate from the training distribution, preventing silent model failures in contour propagation, sCT generation, or dose accumulation.

* Leveraging foundation and generative models: recent advances in large-scale foundation architectures, such as transformer-based and diffusion models, have demonstrated remarkable capabilities in capturing complex anatomical variability and transferring knowledge across tasks and modalities (Wahid et al 2024, Oda 2025, Tarhini et al 2025). These models are trained on extensive, heterogeneous datasets, allowing them to learn rich latent representations that generalize beyond institutional or modality-specific biases. By sampling from their latent spaces, generative models can simulate anatomically plausible variations and rare scenarios, providing a natural mechanism for UQ (Lu et al 2024). In RT, such models hold promise for creating standardized and transferable UQ frameworks across CT, MRI,
and PET domains, improving both calibration and interpretability. Ultimately, integrating explainable uncertainty estimation into these generalist architectures will be crucial to ensure their safe and transparent deployment in clinical RT workflows.

Overall, these emerging directions represent the next frontier of UQ in imaging. They collectively emphasize the need for models that are simultaneously efficient, interpretable, and equipped with verifiable confidence guarantees.

## 7. Future directions and conclusion

Building on the emerging trends and methodological advances outlined in section 6.8, uncertainty-aware AI has the potential to fundamentally transform RT workflows by improving safety, transparency, and clinical efficiency. However, despite promising progress, its clinical adoption remains constrained by unresolved methodological and practical challenges. Future research should therefore progress beyond qualitative visualization of uncertainty toward quantitative, actionable frameworks. We highlight the following high-priority directions:

* Definition of actionable uncertainty thresholds for specific RT tasks and anatomical sites, supported by reader studies and inter-observer analyses.

* Uncertainty-guided intervention studies to assess how clinicians respond to uncertainty information and how these responses influence treatment quality, efficiency, and outcomes.

* Integration of UQ into automated QA and ART pipelines, enabling dynamic triggers for re-contouring, re-planning, or verification based on uncertainty levels.

* Standardization of calibration metrics that link model-derived uncertainty to clinically meaningful measures of error and confidence.

Addressing these priorities will be essential to transition uncertainty-aware models from diagnostic aids into actionable decision-support tools. Ultimately, such developments will help translate uncertainty-aware AI from research prototypes into reliable, standardized, and clinically integrated systems that strengthen trust, enhance workflow efficiency, and improve patient outcomes in RT.

## Data availability statement

The data that support the findings of this study are available upon reasonable request from the authors.

## Acknowledgments

This research was partially supported by a PhD scholarship Grant from University of Rennes and a PhD scholarship Grant from Elekta AB and by the French National Research Agency as part of the DIMADOSE project. The authors have no relevant financial or non-financial interests to disclose. While preparing this work, the authors used ChatGPT to enhance the writing structure and refine grammar. After using these tools, the authors reviewed and edited the content as needed and took full responsibility for the publication's content.

## Appendix. Definitions of common evaluation metrics for uncertainty quantification

This appendix provides the mathematical definitions of the most frequently used metrics and evaluation criteria summarized in table 2. These metrics are grouped by the corresponding evaluation methods.

### A.1. Coverage metrics

Coverage metrics evaluate whether the true outcomes lie within the predicted uncertainty intervals at the expected frequency. For a target confidence level (1 − α), the empirical coverage probability $\hat{C}$ (also referred to as PICP (Pearce et al 2018)) is defined as:

$$ \hat{C} = \frac{1}{N} \sum_{i=1}^{N} \mathbb{I}[y_i \in [\hat{y}_{i,\text{lower}}, \hat{y}_{i,\text{upper}}]], \quad (1) $$

where $y_i$ is the ground-truth value and $[\hat{y}_{i,\text{lower}}, \hat{y}_{i,\text{upper}}]$ is the predicted (1 − α) confidence interval. Here, N denotes the total number of samples, and $\mathbb{I}[\cdot]$ is the indicator function, which equals 1 if the condition inside the brackets is true and 0 otherwise. A well-calibrated model should satisfy $\hat{C} \approx (1 - \alpha)$.
## A.2. Predictive entropy

Predictive entropy measures the informativeness or dispersion of the model's predictive density function for a given observation $x$. It quantifies the total uncertainty in the predicted variable $y$ based on the probability distribution $p(y|x)$. The general definition is:

$$H[y|x] = - \int_{\mathcal{Y}} p(y|x) \log p(y|x) dy, \qquad (2)$$

where $p(y|x)$ denotes the probability density function for continuous outputs (Parzen 1962) or the probability mass function for discrete outputs (Stewart 2009), and $\mathcal{Y}$ is the set of possible outcomes of $y$.

In practice, for classification problems with $C$ classes, the integral reduces to a discrete sum:

$$H[y|x] = - \sum_{c=1}^{C} p(y=c|x) \log p(y=c|x), \qquad (3)$$

where $p(y=c|x)$ represents the predicted probability of class $c$. Here, higher entropy values indicate greater predictive uncertainty, while lower values correspond to more confident or peaked predictions.

## A.3. Calibration metrics

Calibration assesses the alignment between predicted confidence and empirical accuracy, indicating how well the model's probability estimates correspond to true correctness frequencies. A perfectly calibrated model would satisfy $acc(B_m) = conf(B_m)$ for all confidence bins $B_m$.

The most widely used metrics are the Expected Calibration Error (ECE) and the Maximum Calibration Error (MCE) (Guo et al 2017). Let the range of predicted confidences $[0, 1]$ be partitioned into $M$ disjoint bins $\{B_1, B_2, \dots, B_M\}$. For each bin $B_m$, let $acc(B_m)$ denote the empirical accuracy (fraction of correctly predicted samples) and $conf(B_m)$ the average predicted confidence of all samples within the bin. Then, the metrics are defined as:

$$ECE = \sum_{m=1}^{M} \frac{|B_m|}{N} |acc(B_m) - conf(B_m)|, \qquad (4)$$

and

$$MCE = \max_{m} |acc(B_m) - conf(B_m)|, \qquad (5)$$

where $N$ is the total number of evaluated samples and $|B_m|$ is the number of samples in bin $B_m$.

Several extensions of ECE have been proposed for dense prediction and regression tasks, including the Classwise ECE (CW-ECE), Thresholded ECE (T-ECE) for voxel-wise segmentation (Mehrtash et al 2020), and the Expected Uncertainty Calibration Error (UCE) for continuous predictions (Laves et al 2020). Reliability diagrams are often plotted alongside these metrics to visually assess calibration behaviour (Minderer et al 2021).

## A.4. Scoring functions

$$PCC = \frac{\sum_{i=1}^{N} (u_i - \bar{u}) (e_i - \bar{e})}{\sqrt{\sum_{i=1}^{N} (u_i - \bar{u})^2} \sqrt{\sum_{i=1}^{N} (e_i - \bar{e})^2}}, \qquad (6)$$

where $u_i$ represents the estimated uncertainty (e.g. variance or entropy) and $e_i$ the absolute prediction error for sample $i$, while $\bar{u}$ and $\bar{e}$ denote their respective means across all samples. A high positive correlation indicates that predicted uncertainty effectively tracks the model's error; however, correlation alone does not guarantee well-calibrated or clinically reliable uncertainty estimates.

Scoring functions evaluate the quality of probabilistic predictions by jointly capturing both accuracy and calibration. They quantify how well the predicted probability distribution aligns with observed outcomes across samples.

The Brier Score measures the mean squared difference between predicted probabilities and observed outcomes:

$$Brier = \frac{1}{N} \sum_{i=1}^{N} (p_i - y_i)^2, \qquad (7)$$
where $p_i$ denotes the predicted probability of the positive class for sample i, $y_i \in \{0, 1\}$ is the corresponding ground-truth label, and N is the total number of evaluated samples. Lower Brier scores indicate better-calibrated and more accurate predictions (Laves et al 2020, Mehrtash et al 2020).

The negative log-likelihood (NLL) penalizes overconfident or incorrect predictions by evaluating the log-probability of the true label under the predicted distribution:

$$ \text{NLL} = -\frac{1}{N} \sum_{i=1}^{N} \log p(y_i|x_i). \qquad (8) $$

where $p(y_i|x_i)$ is the probability assigned by the model to the true label $y_i$. A lower NLL implies better probabilistic calibration and confidence alignment.

Finally, the linear correlation between predicted uncertainty and actual error is often quantified using the Pearson correlation coefficient (PCC) (Cohen et al 2009):

$$ \text{PCC} = \frac{\sum_{i=1}^{N} (u_i - \bar{u})(e_i - \bar{e})}{\sqrt{\sum_{i=1}^{N} (u_i - \bar{u})^2 \sum_{i=1}^{N} (e_i - \bar{e})^2}}, \qquad (9) $$

where $u_i$ represents the estimated uncertainty and $e_i$ the absolute prediction error for an individual sample point i, while $\bar{u}$ and $\bar{e}$ denote their respective means across all samples. A high positive correlation indicates that uncertainty effectively predicts model error.

### A.5. Misclassification and OOD detection

Uncertainty-based discriminative metrics are used to evaluate whether predicted uncertainty values can distinguish correctly classified samples from erroneous or OOD cases. The most common quantitative measure is the receiver operating characteristic area under the curve (ROC-AUC), which quantifies the discriminative power of uncertainty estimates with respect to ground-truth correctness:

$$ \text{ROC-AUC} = \int_{0}^{1} \text{TPR}(f) \, \text{dFPR}(f), \qquad (10) $$

where TPR(f) and FPR(f) denote the true positive rate and false positive rate, respectively, computed for varying uncertainty thresholds f. Higher AUC values indicate that the model's uncertainty estimates more effectively separate unreliable predictions (e.g. misclassified or OOD samples) from reliable ones. In practice, this metric is widely adopted for evaluating uncertainty-aware models in OOD detection, misclassification identification, and selective prediction tasks (Yang et al 2024).

## ORCID iDs

Cédric Hémon ID 0009-0003-6669-5108

Blanche Texier ID 0009-0000-9961-4958

Jean-Claude Nunes ID 0000-0001-6560-1518

Anaïs Barateau ID 0009-0003-2158-3241

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