# Towards more reliable prostate cancer detection:
Incorporating clinical data and uncertainty in MRI deep
learning

Kamilia Taguelmimt, Gustavo Andrade-Miranda, Hussein Harb, Tran Trung

Thanh, Hong-Phuong Dang, Bernard Malavaud, Julien Bert

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► To cite this version:

Kamilia Taguelmimt, Gustavo Andrade-Miranda, Hussein Harb, Tran Trung Thanh, Hong-Phuong Dang, et al.. Towards more reliable prostate cancer detection: Incorporating clinical data and uncertainty in MRI deep learning. Computers in Biology and Medicine, 2025, 194, pp.110440. 10.1016/j.compbiomed.2025.110440. hal-05113377v2

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# Towards more reliable prostate cancer detection: Incorporating clinical data and uncertainty in MRI deep learning

Kamilia Taguelmimt<sup>a,†</sup>,*, Gustavo Andrade-Miranda<sup>a,d †</sup>, Hussein Harb<sup>a</sup>, Tran Trung Thanh<sup>a,c †</sup>, Hong-Phuong Dang<sup>b</sup>, Bernard Malavaud<sup>c</sup>, Julien Bert<sup>a †</sup>

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## ARTICLE INFO

### Keywords:

- Prostate cancer

- Biparametric MRI

- Bimodal deep learning

- TabNet

- Uncertainty estimation

## ABSTRACT

Prostate cancer (PCa) is one of the most common cancers among men, and artificial intelligence (AI) is emerging as a promising tool to enhance its diagnosis. This work proposes a classification approach for PCa cases using deep learning techniques. We conducted a comparison between unimodal models based either on biparametric magnetic resonance imaging (bpMRI) or clinical data (such as prostate-specific antigen levels, prostate volume, and age). We also introduced a bimodal model that simultaneously integrates imaging and clinical data to address the limitations of unimodal approaches. Furthermore, we propose a framework that not only detects the presence of PCa but also evaluates the uncertainty associated with the predictions. This approach makes it possible to identify highly confident predictions and distinguish them from those characterized by uncertainty, thereby enhancing the reliability and applicability of automated medical decisions in clinical practice. The results show that the bimodal model significantly improves performance, with an area under the curve (AUC) reaching 0.82 ± 0.03, a sensitivity of 0.73 ± 0.04, while maintaining high specificity. Uncertainty analysis revealed that the bimodal model produces more confident predictions, with an uncertainty accuracy of 0.85, surpassing the imaging-only model (which is 0.71). This increase in reliability is crucial in a clinical context, where precise and dependable diagnostic decisions are essential for patient care. The integration of clinical data with imaging data in a bimodal model not only improves diagnostic performance but also strengthens the reliability of predictions, making this approach particularly suitable for clinical use.

## 1. Introduction

Prostate cancer (PCa) ranks as the most prevalent cancer among men in 112 countries, accounting for 15% of cancer cases. The global incidence is projected to increase from 1.4 million cases in 2020 to 2.9 million by 2040 [1]. PCa screening is designed to facilitate early detection, thereby improving treatment outcomes and survival rates. Prostate-specific antigen (PSA) testing remains a cornerstone of preliminary diagnosis; however, its limited specificity often results in a high rate of unnecessary biopsies [2].

To overcome these limitations, multiparametric MRI (mpMRI) has emerged as a key modality for reducing unnecessary medical interventions. The mpMRI combines multiple imaging sequences, T2-weighted imaging (T2 W), apparent diffusion coefficient (ADC) mapping, diffusion-weighted imaging (DWI), and dynamic contrast-enhanced MRI, offering a detailed visual evaluation of cancer risk [3]. Detected lesions are then classified using the Prostate Imaging Reporting and Data System (PI-RADS), a standardized framework aimed at enhancing diagnostic accuracy and consistency [4–6].

Despite the advances offered by mpMRI, manual image interpretation remains time-intensive and prone to variability, underscoring the need for computer-aided diagnostic (CAD) systems enhanced by artificial intelligence (AI) [7–11]. In recent years, deep learning models (DL) have been increasingly employed to improve the diagnostic accuracy and efficiency of PCa detection [12–15]. However, many of these models adopt a unimodal approach, relying solely on mpMRI data [16].

This singular focus neglects the integration of clinical data, which plays a critical role in routine PCa screening. For instance, standard clinical workflows begin with PSA testing, often supplemented by

<footnote><sup>a</sup> LaTIM, UMR1101, INSERM, University of Brest, Brest, France</footnote>

<footnote><sup>b</sup> IETR - UMR CNRS 6164, CentraleSupélec, Cesson-Sévigné, France</footnote>

<footnote><sup>c</sup> Toulouse Oncopole University Cancer Institute, Toulouse, France</footnote>

<footnote><sup>d</sup> IMT Mines Alès, Alès, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: kamilia.taguelmimt@univ-brest.fr (K. Taguelmimt).</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Distributions of PSA Levels (unit: ng/mL), Prostate Volume (unit: mL), Age and PSA density (PSAD) (unit: ng/mL²) based on data from the PICAI dataset [18] highlighting overlap between benign and malignant prostate cancer cases. This figure illustrates the distribution of PSA levels, prostate volume, and age among patients with benign (gray) and malignant (green) prostate cancer. Each panel reveals substantial overlap between the two groups, underscoring the complexity and challenge of relying solely on these individual metrics for accurate prostate cancer diagnosis.</figcaption></figure>

additional parameters such as patient age and prostate volume. These clinical factors inform physicians' decisions regarding further imaging or biopsy procedures, suggesting that their incorporation into AI models may enhance diagnostic performance [17].

The complexity of integrating clinical data into PCa diagnosis is illustrated in Fig. 1, highlighting the substantial overlap in PSA levels, age, and prostate volume between patients with benign and malignant tumors. This overlap demonstrates that no single factor is a definitive indicator of malignancy. Instead, it underscores the importance of evaluating these factors collectively, as their combined assessment is crucial for achieving accurate diagnostic outcomes.

We hypothesize that integrating diverse information sources through multimodal AI models could significantly enhance diagnostic accuracy and reduce uncertainty for PCa detection [19–21]. This work systematically examines the comparative advantages of bimodal DL models over their unimodal counterparts. By integrating clinical data with imaging information, the bimodal models effectively leverage the complementary strengths of these modalities, addressing the inherent challenges of data heterogeneity and providing a more comprehensive understanding of PCa. Additionally, we build upon this by introducing uncertainty estimation, a crucial aspect in clinical decision-making. Our approach not only detects the presence of PCa but also quantifies the uncertainty associated with its predictions. This approach enables a second classification, distinguishing certain predictions from uncertain ones, thereby enhancing the applicability of DL-based medical decisions in real clinical settings.

Our objective is to establish a multimodal framework that not only improves detection performance but also serves as a foundation for more precise and personalized patient care approaches, while reducing the radiologist's workload by focusing their attention only on patients for whom the automatic diagnosis is uncertain.

In this context, our main contributions are as follows:

**Comprehensive Evaluation of Unimodal Models:** We perform a comprehensive assessment of unimodal deep learning models that use either imaging data or clinical information independently. This analysis isolates the modalities to provide valuable insights into the strengths and limitations of unimodal approaches.

**Fusion of Imaging and Clinical Data in a Bimodal Network:** We design and evaluate two architectures to effectively fuse 3D MRI data with clinical information. These architectures integrate the feature extraction capabilities of CNNs with the tabular processing strengths of networks such as TabNet [22] and Multi-layer Perceptron (MLP). Furthermore, we introduce a multi-head attention fusion mechanism to enable a direct comparison with the conventional feature concatenation strategy.

**Evaluation of Bimodal vs. Unimodal Models:** We systematically compare the performance of bimodal models with that of unimodal models using well-established state-of-the-art classification metrics, such as AUC, sensitivity, specificity, and accuracy.

**Reliability Assessment Using Model Uncertainty Techniques:** An often overlooked aspect of diagnostic modeling is the estimation of uncertainty to evaluate the reliability of predictions. To address this

limitation, we compute a range of measures, including predictive entropy and confidence metrics. In addition, we conduct an ablation study focused on clinical uncertainty to assess the contribution of each clinical variable within the bimodal model.

Lastly, we leverage Grad-CAM visualizations to gain insights into the factors that influence the model's predictions, enabling a clearer understanding of how decisions are derived.

## 2. Related work

The widespread use of PSA for the early detection of prostate cancer has led to many unnecessary biopsies and diagnoses of indolent cancers [23]. To reduce these interventions, PSA density evaluation can help guide biopsy decisions and lower morbidity. However, its use is not yet recommended in clinical guidelines due to contradictory initial evidence [24].

It is also important to note that PSA is prostate-specific but not cancer-specific, as benign conditions such as prostatitis or benign prostatic hyperplasia can also elevate PSA levels [2]. Although PSA screening has not conclusively been shown to reduce prostate cancer-specific mortality, clinicians are encouraged to discuss its potential risks and benefits with patients before recommending a biopsy [25].

The integration of machine learning techniques, such as artificial neural networks (ANN), has shown promising results in improving the interpretation of PSA levels, thereby more accurately predicting the risk of prostate cancer [26]. For instance, an ANN model combining PSA, free PSA, PSA density, patient age, prostate volume, and digital rectal exam results has demonstrated a good predictive ability for high-quality biopsy outcomes [27–29]. Other studies have also highlighted the effectiveness of ANNs in assessing prostate cancer throughout patients' medical history, saving up to 17% of unnecessary biopsies [30–32].

Machine learning techniques like support vector machines (SVM), logistic regression (LR), and random forests (RF) have shown strong performance in predicting prostate cancer, often outperforming traditional PSA-based approaches. A retrospective study reported that these methods achieved an area under the curve (AUC) of 0.918, indicating high predictive accuracy and net clinical benefits [33]. Moreover, machine learning methods have shown superior performance in terms of sensitivity and specificity compared to conventional PSA-based parameters [34]. These findings underscore the potential of machine learning to improve prostate cancer detection beyond standard approaches based on PSA thresholds [35].

In parallel, prostate magnetic resonance imaging (MRI) plays a crucial role in detecting clinically significant prostate cancer. However, this technique is time-consuming and suffers from a shortage of qualified clinical personnel. To overcome these challenges, studies have shown the feasibility of automatic PCa detection through deep learning on MRIs.

Revolutionary advances in deep learning have led to significant improvements in prostate lesion classification. For example, Liu et al. developed XmasNet, a deep learning architecture based on convolutional neural networks (CNN), using 3D MRI data to achieve an AUC
of 0.84 [36]. Yoo et al. introduced an automated CNN-based model to detect clinically significant PCa from axial DWI images, achieving an AUC of 0.87 [37]. Cao et al. proposed FocalNet, a multi-class CNN that detects PCa lesions and predicts their aggressiveness using the Gleason score, with an AUC of 0.81 [38]. Aldoj et al. focused on binary classification of prostate cancer using different combinations of MRI sequences and a 3D CNN, achieving an AUC of 0.84 for the combination of T2-weighted MRI, ADC, and DWI [39].

Mehrtash et al. developed a CNN model for PCa detection using multiparametric MRI, incorporating zonal information, with an AUC of 0.80 [40]. Lapa et al. developed a deep neural network architecture to classify clinically significant PCa on MRI, using a conditional random field recurrent neural network approach (CRF-RNN), thus improving classification performance compared to previous methods studied [41].

Recent approaches based on zonal segmentation and one-step PCa aggressiveness classification have emerged. For instance, Vente et al. uses a 2D U-Net architecture to analyze MRIs, simultaneously detecting and classifying lesions while incorporating zonal information at various levels of the network to enhance performance [42]. Similarly, Pellicer et al. developed a fully automated CNN-based system that processes patient MRIs to segment the prostate, localizes PCa lesions, and predicts their Gleason score group, achieving an AUC of 0.85 [43]. Incorporating zonal information proves essential for improving detection, a methodology supported by other studies endorsing this approach. For example, Duran et al. proposed an integrated architecture using CNNs with an attention mechanism to segment both the prostate and PCa lesions into multiple classes. Their network consists of two branches: the first performs prostate segmentation, while the second uses this zonal information as an attention gate for lesion detection and grading, thereby enhancing overall performance [44].

Finally, Saha et al. proposed a 3D CNN-based detection model that incorporates key elements such as attention mechanisms to automatically localize prostate cancer in biparametric MRI [45]. These studies collectively demonstrate that leveraging spatial information can significantly enhance detection accuracy and overall model performance [46-48]. However, while training models on datasets with zonal lesion annotations has yielded promising results, obtaining such detailed annotations or segmentation masks for 3D medical images remains a challenging and time-consuming task.

Currently, deep learning-based data fusion methods have garnered considerable attention in cancer research. These datasets originate from diverse sources and exhibit significant heterogeneity in terms of data types, formats, and quality, posing substantial challenges for accurate cancer diagnosis, treatment planning, and prognosis assessment. Data fusion has emerged as an effective strategy to address this heterogeneity and enhance the value of the integrated information. By combining cancer-related data from multiple modalities, diagnostic accuracy can be improved, and a deeper understanding of cancer biology can be achieved [49-51].

For instance, in patients with serum PSA levels of 4 to 10 ng/mL, the combination of PSA with MRI findings has been shown to provide a higher net benefit in diagnosing clinically significant prostate cancer [52]. Moreover, integrating clinical parameters and imaging (MP-MRI) for advanced prostate cancer risk modeling enables more accurate patient-specific risk stratification, potentially reducing the number of unnecessary biopsies [53,54].

Although significant progress has been made in diagnosing PCa, current methods often overlook uncertainty. Accurately quantifying uncertainty is critical for improving diagnostic confidence and ensuring patient safety. In recent years, uncertainty quantification in deep learning has been successfully applied in several areas of medical image classification [55,56], including the detection of oral [57], breast [58], and skin cancers [59]. However, its specific application to prostate cancer remains an area of in-depth research yet to be explored.

# 3. Methodology

This section introduces our unimodal approaches, beginning with the processing of clinical data focused on key variables such as PSA levels, prostate volume, and age. These variables are analyzed using neural network architectures—namely MLP and TabNet. We then delve into bpMRI image analysis, employing a state-of-the-art 3D CNN for efficient feature extraction. Finally, we present our proposed bimodal fusion model, which integrates clinical and imaging modalities using two fusion strategies: simple concatenation and an attention-based mechanism leveraging multi-head attention. We also detail the methodology employed for predictive uncertainty estimation and conduct an ablation study to evaluate the individual contribution of each clinical variable within the bimodal framework.

## 3.1. Unimodal models

### 3.1.1. Clinical data-based models

To develop the clinical data models, we incorporate variables such as patient age, PSA level, and prostate volume. Two distinct architectures are evaluated, as described below.

Multilayer Perceptron (MLP) is an artificial neural network model composed of at least three layers: an input layer, one or more hidden layers, and an output layer. Neurons in the hidden layers typically use nonlinear activation functions, allowing the network to learn and model complex relationships within the data [60].

TabNet: Attentive Interpretable Tabular Learning is a deep learning architecture optimized for tabular data, offering unique advantages for both performance and interpretability. Unlike many models, it processes raw tabular data directly, minimizing the need for extensive preprocessing and enabling seamless integration into end-to-end learning workflows. TabNet's architecture includes a feature transformer, an attentive transformer, and a feature masking mechanism, with a split block that allocates processed representations to the next decision step and the overall output.

Its sequential attention mechanism enhances performance by dynamically selecting the most relevant features for each instance. This mechanism not only improves predictive accuracy but also provides interpretability at both local and global levels. Local interpretability is achieved by visualizing the importance of features for individual predictions, while global interpretability quantifies the overall contribution of each feature [22].

### 3.1.2. Image-based models

#### Backbone CNN architecture

ResNet (Residual Network) is designed to address the vanishing gradient problem, which is prevalent in deep networks. The key innovation of ResNet is the introduction of residual connections. These connections allow the signal to bypass one or more layers, which helps in maintaining the flow of gradients during backpropagation. This capability makes ResNet particularly effective for large and complex datasets, such as MRI images, where deep networks are necessary to capture intricate patterns. In our experiments, we implemented several variants of ResNet, including: ResNet18, ResNet50 [61]. In addition to the standard ResNet models, we also utilized SE-ResNet, a variant that integrates Squeeze-and-Excitation (SE) blocks into the ResNet architecture [62].

DenseNet, or Densely Connected Convolutional Network, further improves upon the efficiency of convolutional networks by connecting each layer to every other layer downstream. This architecture ensures that each layer receives additional information from all preceding layers, which significantly enhances information flow and feature reuse. As a result, DenseNet models are more parameter-efficient and exhibit improved performance on image classification tasks. We employed the following DenseNet variants in our study: DenseNet121 and DenseNet201 [63].
<figure><img src="image_6.png" /><figcaption>Fig. 2. This diagram illustrates the integration of clinical data and bpMRI imaging in a bimodal diagnostic model. First, bpMRI images and the segmentation mask are combined as multi-channel inputs, and features are extracted using CNN architectures. In parallel, clinical data (age, PSA level, prostate volume) are processed using models such as TabNet/MLP. The descriptors derived from these two streams are then merged and fed into dense layers for final csPCa classification. The inference process relies on Monte Carlo Dropout, which enables uncertainty estimation by generating an approximate posterior distribution. The model’s final prediction corresponds to the mean of the outputs from multiple stochastic forward passes. The standard deviation of these predictions reflects the model’s variability, while entropy are used to quantify the uncertainty associated with each prediction.</figcaption></figure>

## 3.2. Bimodal models

The bimodal model synergistically leverages clinical data and bpMRI images to provide a more comprehensive and accurate diagnosis of prostate cancer. As illustrated in Fig. 2, the process starts by incorporating the prostate segmentation mask into the MRI images as an input, helping the model focus on the region of interest and thereby improve diagnostic precision [45].

The images are passed through a CNN for feature extraction. CNN architecture was used as the ‘backbone’ for this feature extraction due to its strong performance and compactness. There are two main branches:

### 3.2.1. Fusion with clinical data

Alongside the image feature extraction, clinical data (age, PSA level, and prostate volume) are processed using either MLP or TabNet. These models analyze and prioritize the clinical parameters based on their relevance to prostate cancer prediction.

Once features from the imaging and clinical branches are extracted, they are combined to form a unified representation. In the baseline model, this fusion is achieved through simple concatenation, followed by dense layers that perform the final classification—distinguishing between benign and csPCa (malignant) cases. To further enhance feature integration, we also propose an alternative fusion strategy, termed AttentionFusion. Instead of simple concatenation, this approach leverages a multi-head attention mechanism to dynamically weight the contributions of clinical and imaging features. This enables the model to adaptively prioritize relevant information from each modality depending on the context, potentially leading to more robust and context-aware decision-making [64].

## 3.3. Uncertainty estimation

Bayesian deep learning offers an innovative approach by emphasizing uncertainty, addressing a crucial question: “How reliable is the prediction generated by our neural network?”. However, traditional Bayesian networks have been hindered in their deployment due to

the challenges associated with the spatial and temporal complexity of the training phase. This complexity arises from the fact that weights and neuron outputs are represented not as scalars, but as probability distributions characterized by means and standard deviations [65].

Initially challenging to implement due to storage space and computation time requirements during training, an approximation of these networks, called MC Dropout, seamlessly reintroduces Bayesian deep learning. Thus, it becomes possible to associate a confidence level with each neural network. This approach, known as Monte Carlo Dropout and developed by Gal and Ghahramani [66], takes its name from the “Monte Carlo” concept, which refers to a family of algorithms that make predictions through random processes, and “Dropout”, inspired by biology, where certain weights are randomly set to zero during training.

This technique leverages dropout during test phases, generating multiple outputs from a single input. By using these outputs, it becomes feasible to calculate means and standard deviations. Thus, results comparable to those of classical Bayesian networks are obtained, while preserving the traditional training of the network. This method offers the advantage of requiring no major modifications during network training, while also providing robustness and computational efficiency, making it an attractive solution for practical implementation, as demonstrated in previous works [55,67].

# 4. Experiments

## 4.1. Datasets

The PICAI (Prostate Imaging Cancer AI) [18] dataset is an essential resource for research in artificial intelligence applied to prostate cancer diagnosis. It includes 1500 cases from 1476 patients, collected across 11 centers using seven different MRI scanner models. Among these cases, 1075 are benign or correspond to indolent cancers, while 425 cases present clinically significant cancer (csPCa) with an ISUP score ≥2 [68]. For this study, we utilized the subset of 1295 cases with human expert annotations available in the dataset.

The patients included in this database have a median age of 66 years (IQR: 61–70 years), a median PSA level of 8.5 ng/mL (IQR: 6–13
ng/mL), and a median prostate volume of 57 mL (IQR: 40–80 mL). Among the 1295 cases annotated by human experts, only 220 positive cases contain annotations of csPCa lesions, representing approximately 17% of the annotations. These annotations were performed by a team of 10 investigators or a radiology resident, under the supervision of three expert radiologists, using the ITK-SNAP v3.80 software.

The annotations provided in this dataset are particularly valuable for developing and evaluating AI models, as they include delineations of clinically significant lesions as well as prostate zone boundaries. Prostate gland segmentation masks were generated using a deep learning pipeline based on an ensemble of five nnU-Net models [69], trained via 5-fold cross-validation. This approach achieved a Dice similarity coefficient of (0.8968 ± 0.0547).

## 4.2. Experimental protocol

The MRI images underwent several preprocessing steps, including alignment, cropping, resampling to 144 × 144 × 32 voxels, with a voxel spacing of (0.5, 0.5, 3) mm, and Min–Max normalization between 0 and 1. The T2 W, DWI, and ADC sequences, along with the segmentation masks, were combined into a single multichannel image (see Fig. 2).

The dataset consisted of 1295 cases, including 220 positive cases and 1075 benign or indolent cancer cases. The data was split into 20% for testing and 80% for training and validation, using a 5-fold cross-validation strategy to improve generalization. Data augmentation techniques were applied on the fly during training, incorporating random rotations, horizontal and vertical flips, Gaussian noise, and scaling transformations, ensuring diverse and realistic variations of the input data.

All model architectures were implemented using the PyTorch framework. Training was conducted with a batch size of 32, and model weights were optimized using the Adam optimizer with an initial learning rate of 1 × 10⁻⁴. To prevent overfitting, we employed an early stopping strategy based on validation performance.

To address class imbalance, we used the Focal Loss function [70], following recommendations from the PICAI challenge guidelines [18]. The focusing parameter gamma was set to the default value of 1.0, and the weighting factor alpha was automatically computed as the inverse of the class distribution within each training fold.

Training was carried out using two NVIDIA A6000 GPUs (48 GB each) and one TITAN RTX (24 GB). To support uncertainty estimation, we tested various dropout rates for Monte Carlo Dropout (MCD), ranging from 0.1 to 0.9 in increments of 0.1.

## 4.3. Model evaluation

In this section, we present a detailed analysis of our model's performance using two evaluations. The first evaluation is based on traditional metrics for assessing classification models, enabling the quantification of overall performance. The second evaluation focuses on estimating the model's uncertainty—a critical aspect in high-stakes domains such as medical diagnosis. By identifying predictions with high uncertainty, this approach enables radiologists to prioritize their attention on those cases where automated decision-making is less confident [71].

### 4.3.1. Evaluations metrics

To evaluate the classification performance, we employed traditional metrics such as accuracy, sensitivity, specificity, and area under the curve (AUC). These metrics provide a comprehensive understanding of the model's effectiveness in PCa classification tasks.

### 4.3.2. Predictive uncertainty evaluation

By performing a large number of iterations K, we can estimate the model's uncertainty for each prediction by enabling dropout at each iteration. This generates a distribution of K predictions for a given test MRI image. To obtain the final prediction, we calculate the mean of the K predictions, which corresponds to the posterior mean of the class. Mathematically, this can be represented by the following equation:

$$ \mu_p = \frac{1}{K} \sum_{k=1}^{K} P_k \quad (1) $$

In this equation, $\mu_p$ represents the posterior mean of the class, $P_k$ represents the prediction at iteration $k$, and K represents the total number of iterations. In addition to the mean, we also calculate the standard deviation of this prediction distribution. Mathematically, the standard deviation can be calculated using the following equation:

$$ \sigma_p = \sqrt{\frac{1}{K} \sum_{k=1}^{K} (P_k - \mu_p)^2} \quad (2) $$

In this equation, $\sigma_p$ represents the prediction uncertainty. If the standard deviation is high, it means that the predictions vary significantly from one iteration to another, indicating high uncertainty in the final prediction.

Predictive Entropy (PE) can then be calculated to assess the overall uncertainty of the prediction. Mathematically, predictive entropy is calculated as follows:

$$ PE = - \sum_{c} \mu_{p}(c) \log(\mu_{p}(c)) \quad (3) $$

In this equation, $\mu_p(c)$ represents the predictive mean for class c. The value of predictive entropy quantifies the model's uncertainty. Lower predictive entropy indicates greater confidence in predictions, while higher predictive entropy indicates greater uncertainty.

To assess the overall reliability of the model's predictions, we adopt an approach similar to a confusion matrix, aiming to objectively evaluate uncertain predictions. Additionally, we propose a second classification, which is the objective classification of predictions [56,58]. Predictions are first categorized as either correct or incorrect by comparing them with the ground truth labels. Then, using a threshold ranging from 0 to 1 based on predictive entropy, predictions are further classified as certain or uncertain. This leads to four possible groups:

* Correct and certain indicating true certainty (TC).

* Incorrect and uncertain indicating true uncertainty (TU).

* Correct and uncertain indicating false uncertainty (FU).

* Incorrect and certain indicating false certainty (FC).

TC and TU results are considered the most desirable, corresponding to TN (true negatives) and TP (true positives) results in the traditional confusion matrix. On the other hand, FU is a positive result where an uncertain prediction is actually correct, while FC is the least desirable, indicating an incorrect prediction made with confidence (see Fig. 3). Based on these results, four quantitative performance metrics are defined to objectively assess the quality of the predictive uncertainty estimates, as follows:

Uncertainty Sensitivity ($U_{Sen}$) is calculated as the number of incorrect and uncertain predictions divided by the total number of incorrect predictions

$$ U_{Sen} = TU / (TU + FC) \quad (4) $$

where ($U_{Sen}$) corresponds to the sensitivity or true positive rate of the traditional confusion matrix. This metric quantifies the model's ability to express its confidence in misclassified samples.

Uncertainty Specificity ($U_{Spe}$) is calculated as the number of correct and certain predictions (TC) divided by the total number of correct predictions.

$$ U_{Spe} = TC / (TC + FU) \quad (5) $$
<figure><img src="image_7.png" /><figcaption>Fig. 3. Uncertainty confusion matrix illustrating the relationship between model confidence (columns) and prediction correctness (rows). The matrix is divided into four quadrants: True Certainty (TC), False Uncertainty (FU), False Certainty (FC), and True Uncertainty (TU).</figcaption></figure>

$(U_{Spe})$ is similar to the specificity metric used in classification.

Uncertainty Precision ($U_{Pre}$) is calculated as the number of incorrect and uncertain predictions divided by the total number of uncertain predictions.

$$U_{Pre} = TU/(TU + FU) \qquad (6)$$

$(U_{Pre})$ shares the same concept of precision as used in traditional binary classification.

Uncertainty Accuracy ($U_{Acc}$) is calculated similarly to classifier accuracy, taking into account the number of diagonal results compared to the total number of results. A reliable model will exhibit high ($U_{Acc}$).

$$U_{Acc} = (TU + TC)/(TU + TC + FU + FC) \qquad (7)$$

## 4.4. Model explainability

Concerning the model's explainability, we conducted an in-depth analysis to understand how the model arrives at its predictions. Specifically, we employ the gradient-weighted class activation mapping (Grad-CAM) technique [72], which highlights the most influential regions in the input data. By visualizing the areas the model focuses on during decision-making, the Grad-CAM approach provides valuable insights into its reasoning process, thereby enhancing interpretability.

# 5. Results and discussion

In this section, we present the results of the classification performance, uncertainty quantification, and analysis of confident predictions and radiologist workload reduction, along with the findings from the explainability evaluation.

## 5.1. Classification performance

Table 1 presents the performance metrics of several models — clinical-based, imaging-based, and bimodal — applied to the classification of clinically significant prostate cancer (csPCa). These models incorporate clinical data (age, prostate volume, PSA value), imaging data, or a combination of both. The evaluated metrics include AUC, sensitivity, specificity, and accuracy, each reported with its mean, standard deviation, and corresponding confidence interval (CI).

In the clinical-only section, where models are trained solely on clinical data (age, PSA, and prostate volume), both TabNet and MLP exhibit comparable overall performance, with AUC values ranging from 0.72 to 0.77. The TabNet model achieves an average sensitivity of 0.72 and a specificity around 0.68, with accuracy values ranging from 0.63 to 0.78, suggesting a moderate but relatively stable predictive capacity. The clinical MLP model shows greater variability in sensitivity (0.69 ± 0.07) and specificity (0.72 ± 0.06). These findings suggest that

<figure><img src="image_8.png" /><figcaption>Fig. 4. Distribution of AUC values for different approaches in csPCa classification. The figure compares the performance of models trained on clinical data alone, and those trained using a bimodal approach (combining clinical and imaging data). The bimodal models, demonstrate a higher distribution of AUC values, highlighting the effectiveness of integrating clinical and imaging data.</figcaption></figure>

while clinical data alone enable acceptable prediction, there remains considerable room for improvement.

In the imaging section, the models evaluated for classifying clinically significant prostate cancer in MRI images include DenseNet201, ResNet50, SE-ResNet101, DenseNet121, and Res-Net18. DenseNet201 demonstrates stable performance across different folds, with an average AUC of around 0.77, indicating a moderate ability to distinguish between benign cases and csPCa. The sensitivity ranges from 0.52 to 0.84, reflecting some variability in the model's ability to correctly detect malignant cases, while the specificity averages around 0.72. DenseNet121 exhibits consistent results with an average AUC of 0.77. Sensitivity varies, with some folds showing values as high as 0.82, while specificity is relatively constant, ranging from 0.65 to 0.77, and accuracy follows a similar trend, generally around 0.72. ResNet50 shows an AUC similar to DenseNet, with values around 0.76 to 0.80, indicating good discrimination between classes. ResNet50's sensitivity is relatively high in some folds, reaching up to 0.77, demonstrating reliable malignant case identification, although lower sensitivity in other folds suggests performance variability. The specificity averages around 0.74. SE-ResNet101 offers a slightly higher AUC, reaching up to 0.83, with average AUC is 0.79, indicating better performance in classifying. The sensitivity of SE-ResNet101 varies from 0.52 to 0.80, showing effective malignant case identification in certain folds, with specificity reaching up to 0.83, highlighting the model's ability to avoid false positives with an average of 0.76 and a mean accuracy of 0.74. ResNet18 shows an AUC similar to other models, an average of around 0.78. ResNet18's sensitivity is notably high in some folds, reaching 0.89, but this performance sometimes results in lower specificity, suggesting a trade-off between detecting malignant cases and reducing false positives. Average accuracy 0.68, reflecting an overall acceptable but less consistent performance compared to some of the other evaluated models.

In the bimodal section, models combine clinical data with MRI images, relying on a DenseNet121 architecture for visual feature extraction. While SE-ResNet101 achieved a slightly higher AUC in the unimodal imaging experiments, DenseNet121 was selected for the bimodal pipeline due to its more favorable trade-off between model complexity and performance. Bimodal models based on simple concatenation (Bimodal TabNet, Bimodal MLP) show mean AUC values ranging from 0.80 to 0.81, with sensitivities reaching up to 0.85 ± 0.07 in the case of Bimodal TabNet. However, this high sensitivity is sometimes accompanied by lower specificity (e.g., 0.66 ± 0.07), reflecting a tendency toward broad detection at the cost of potential false positives. Accuracy in these models typically falls within a stable range, around 0.69 to 0.73, confirming an overall gain compared to unimodal approaches.

On the other hand, the bimodal model with attention-based fusion achieves the best overall performance, with a mean AUC of 0.82 ± 0.03, a mean accuracy of 0.73 ± 0.03, and a well-balanced trade-off between sensitivity (0.73) and specificity (0.73). The analysis of the results is
<caption>**Table 1**</caption>

Performance metrics for different models applied to prostate MRI classification using clinical data (age, prostate volume, PSA value), imaging data, and a combination of both (bimodal approach). The metrics include AUC, Sensitivity, Specificity, and Accuracy, with corresponding (CI).

<table><caption>**Table 2**</caption><thead><tr><th>Category</th><th>Model</th><th>AUC (CI)</th><th>Sensitivity (CI)</th><th>Specificity (CI)</th><th>Accuracy (CI)</th></tr></thead><tbody><tr><td rowspan="2">Clinical</td><td>TabNet</td><td>0.75 ± 0.02 (0.73, 0.77)</td><td>0.72 ± 0.05 (0.66, 0.78)</td><td>0.68 ± 0.06 (0.61, 0.76)</td><td>0.69 ± 0.04 (0.63, 0.74)</td></tr><tr><td>MLP</td><td>0.76 ± 0.01 (0.75, 0.77)</td><td>0.69 ± 0.07 (0.60, 0.78)</td><td>0.72 ± 0.06 (0.64, 0.79)</td><td>0.71 ± 0.04 (0.66, 0.76)</td></tr><tr><td rowspan="5">Imaging</td><td>DenseNet121</td><td>0.77 ± 0.02 (0.68, 0.85)</td><td>0.68 ± 0.09 (0.56, 0.79)</td><td>0.72 ± 0.05 (0.67, 0.78)</td><td>0.72 ± 0.02 (0.69, 0.75)</td></tr><tr><td>DenseNet201</td><td>0.77 ± 0.02 (0.75, 0.80)</td><td>0.66 ± 0.12 (0.51, 0.81)</td><td>0.72 ± 0.06 (0.64, 0.80)</td><td>0.71 ± 0.04 (0.66, 0.76)</td></tr><tr><td>ResNet50</td><td>0.78 ± 0.02 (0.76, 0.81)</td><td>0.67 ± 0.09 (0.56, 0.78)</td><td>0.74 ± 0.05 (0.68, 0.80)</td><td>0.73 ± 0.03 (0.69, 0.76)</td></tr><tr><td>SEResNet101</td><td>0.79 ± 0.03 (0.75, 0.82)</td><td>0.67 ± 0.11 (0.53, 0.81)</td><td>0.76 ± 0.05 (0.69, 0.82)</td><td>0.74 ± 0.02 (0.71, 0.77)</td></tr><tr><td>ResNet18</td><td>0.78 ± 0.01 (0.77, 0.79)</td><td>0.76 ± 0.14 (0.59, 0.93)</td><td>0.66 ± 0.08 (0.56, 0.76)</td><td>0.68 ± 0.05 (0.62, 0.74)</td></tr><tr><td rowspan="3">Bimodal</td><td>TabNet</td><td>0.81 ± 0.02 (0.75, 0.79)</td><td>0.85 ± 0.07 (0.76, 0.93)</td><td>0.66 ± 0.07 (0.57, 0.75)</td><td>0.69 ± 0.05 (0.63, 0.75)</td></tr><tr><td>MLP</td><td>0.80 ± 0.03 (0.76, 0.84)</td><td>0.74 ± 0.15 (0.55, 0.92)</td><td>0.70 ± 0.08 (0.60, 0.79)</td><td>0.70 ± 0.04 (0.65, 0.75)</td></tr><tr><td>AttentionFusion</td><td>0.82 ± 0.03 (0.78, 0.85)</td><td>0.73 ± 0.04 (0.68, 0.77)</td><td>0.73 ± 0.03 (0.69, 0.76)</td><td>0.73 ± 0.03 (0.69, 0.76)</td></tr></tbody></table>

Ablation study comparing bimodal and unimodal imaging models: Uncertainty metrics, certain prediction performance (Threshold = 0.6), and inference time.

<table><thead><tr><th>Metrics</th><th>B<sub>PSA</sub></th><th>B<sub>PSA+Vol</sub></th><th>B<sub>PSA+Vol+Age</sub></th><th>I<sub>Model</sub></th></tr></thead><tbody><tr><td><strong>Uncertainty Metrics</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>U<sub>Sen</sub></td><td>0.95</td><td>0.92</td><td>0.73</td><td>0.93</td></tr><tr><td>U<sub>Spe</sub></td><td>0.41</td><td>0.62</td><td>0.90</td><td>0.61</td></tr><tr><td>U<sub>Pre</sub></td><td>0.46</td><td>0.42</td><td>0.73</td><td>0.50</td></tr><tr><td>U<sub>Acc</sub></td><td>0.60</td><td>0.69</td><td>0.85</td><td>0.71</td></tr><tr><td><strong>Certain Predictions</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Accuracy</td><td>0.93</td><td>0.96</td><td>0.90</td><td>0.96</td></tr><tr><td>AUC</td><td>0.91</td><td>0.50</td><td>0.84</td><td>0.58</td></tr><tr><td>Sensitivity</td><td>0.89</td><td>0.00</td><td>0.75</td><td>0.17</td></tr><tr><td>Specificity</td><td>0.94</td><td>1.00</td><td>0.92</td><td>1.00</td></tr><tr><td><strong>Inference Time</strong></td><td>23.46s</td><td>23.50s</td><td>23.48s</td><td>22.13s</td></tr></tbody></table>

further supported by Fig. 4, which illustrates the distributions of AUC scores across the different approaches. This figure clearly shows that bimodal models consistently outperform unimodal models.

In particular, TabNet in bimodal mode stands out with a mean AUC of 0.81 ± 0.02, notably higher than both the clinical TabNet model (0.75±0.02) and the imaging-based model (0.77±0.02). These differences are highly significant, with *p*-value of 0.0003 (vs. clinical) and 0.0043 (vs. imaging). Additionally, significant improvements are also observed in sensitivity (*p*-value around 0.013 in both comparisons), reflecting a notable enhancement in the detection of clinically significant prostate cancer (csPCa).

The bimodal MLP model also shows improved AUC performance compared to its unimodal counterparts: 0.80±0.03 vs. 0.76±0.01 (clinical MLP) and 0.77 ± 0.02 (imaging only). However, the corresponding *p*-value (0.0693 and 0.1362) remain above the conventional significance threshold, indicating that although an improvement trend is present, it is not statistically confirmed. This aligns with the greater variability observed in sensitivity for this model (±0.15).

The Bimodal (AttentionFusion) model achieves the highest overall performance, with a mean AUC of 0.82 ± 0.03, significantly outperforming both the clinical (*p*-value = 0.0023) and imaging-only models (*p*-value = 0.0125). While *p*-values for the other metrics do not show clearly established differences, the gain in discriminative power remains statistically robust, highlighting the advantage of combining clinical and imaging modalities. Fig. 5 presents a triangular heatmap matrix of *p*-values, illustrating the statistical significance of pairwise AUC comparisons across all unimodal and bimodal models.

## 5.2. Uncertainty estimation results

We evaluate the impact on model reliability and uncertainty when clinical data are added to image-based information. Specifically, we compare a model based solely on images with a model that combines

<caption>**Fig. 5.** Heatmap of Pairwise Statistical Significance for AUC Comparisons. This figure visualizes *p*-values from paired *t*-tests comparing the AUC scores of different unimodal and bimodal strategies. The lower triangle displays the results, where lighter (white) colors indicate statistically significant differences (*p* < 0.05). Diagonal elements (in black) represent self-comparisons (*p* = 1). Rows and columns are ordered identically to facilitate direct comparison between methods.</caption>

images and clinical data, in order to determine whether this integration improves reliability and reduces uncertainties.

The model employed in this part of the study is the Bimodal Attention Fusion architecture, which demonstrated the best performance across our previous experiments. To assess predictive uncertainty, we employed the Monte Carlo Dropout technique with *K* = 30 iterations. Various dropout rates were evaluated (see Fig. 7) to determine the optimal configuration. A dropout rate of 0.4 was selected, as it achieved the highest performance with an AUC of 85%. The predictive uncertainty was estimated using the (PE) as defined by the equations referenced in Eqs. (1), (2), and (3).

Fig. 8 illustrates the distribution of predictive entropy across various model configurations, depending on the amount and type of information used—ranging from imaging alone to combinations with clinical data. Each plot distinguishes between correct predictions (in green) and incorrect predictions (in purple). The evolution of these distributions allows us to evaluate how the progressive addition of clinical variables affects uncertainty reduction. (a) *I*<sub>Model</sub> The model relying exclusively on MRI data exhibits high predictive uncertainty. Correct and incorrect predictions are largely intermixed, especially in the higher entropy region (0.6–0.7). This overlap reflects limited reliability and low confidence in the model’s outputs. (b) *B*<sub>PSA</sub>: Adding PSA to the image-based

<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Visualization of prostate MRI scans across multiple modalities (T2 W, ADC, DWI) with corresponding Grad-CAM maps. The Grad-CAM highlights the regions of the MRI scans that significantly influence the model's predictions. Warmer colors in the GC maps indicate areas where highlighting leads to a noticeable increase in prediction confidence, reflecting the model's reliance on these regions for accurate diagnosis. This analysis aids in understanding and validating the model's decision-making process by confirming its focus on clinically relevant areas.</figcaption></figure>

model does not improve confidence—quite the opposite. Entropy remains high, and incorrect predictions are still prevalent. This can be explained by the variability of PSA, which is influenced by benign conditions. When considered in isolation, PSA tends to introduce more noise than useful information, thus increasing the model's global uncertainty. (c) **B<sub>PSA+Vol</sub>**: Including prostate volume, derived from imaging, offers better contextualization of PSA values. A moderate reduction in predictive uncertainty is observed, with correct predictions increasingly concentrated in low-entropy zones. However, a significant portion of predictions still lies in high-uncertainty regions. (d) **B<sub>PSA+Vol+Age</sub>**: This complete bimodal model demonstrates the best performance in terms of confidence. Correct predictions are densely clustered in low-entropy ranges (0.0–0.3), while incorrect predictions appear mainly in the high-entropy regions. A clear separation emerges between accurate and inaccurate predictions, reflecting a marked reduction in predictive uncertainty.

After calculating the predictive entropy, the next step is to define a threshold to classify predictions as either certain or uncertain. To do this, we systematically varied the threshold from 0 to 1, which allows us to categorize the predictions into four groups: True Certainty (TC), True Uncertainty (TU), False Certainty (FC), and False Uncertainty (FU). These categories help evaluate the model's performance in terms of managing uncertainty in predictions.

**Fig. 9** illustrates the results based on different thresholds. The four subplots compare the performance metrics ($U_{Sen}$), ($U_{Spe}$), ($U_{Pre}$), and ($U_{Acc}$) between the image-only model and the bimodal model.

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Effect of different dropout rates on model performance. The plot shows the AUC values obtained for dropout rates ranging from 0.1 to 0.9, using MCD with $K = 30$ iterations.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Predictive entropy distributions for different model configurations. (a) $I_{Model}$: model based on imaging data alone. (b) $B_{PSA}$: model combining MRI with PSA only. (c) $B_{PSA+Vol}$: MRI with PSA and prostate volume. (d) $B_{PSA+Vol+Age}$: full bimodal model with MRI, PSA, volume, and age. Each histogram distinguishes correct predictions (green) from incorrect ones (purple).</figcaption></figure>

The overall analysis justifies the choice of the 0.6 threshold as the optimal cutoff to distinguish between certain and uncertain predictions. This threshold represents a good compromise between uncertainty sensitivity and specificity, as evidenced by the metric evolution curves ($U_{Sen}$, $U_{Spe}$, $U_{Pre}$, $U_{Acc}$) and the confusion matrices. It enables a better separation between confident and ambiguous predictions, significantly reducing false certainty errors. The model $B_{PSA+Vol+Age}$ achieves the best overall balance, with high uncertainty precision ($U_{Pre} = 0.73$), global accuracy ($U_{Acc} = 0.85$), and strong specificity. In contrast, the $B_{PSA}$ model shows the highest uncertainty sensitivity ($U_{Sen} = 0.95$) but suffers from low specificity, indicating that it frequently flags correct predictions as uncertain, which may reduce its clinical reliability. The image-only model ($I_{Model}$) demonstrates acceptable performance but is penalized by poor calibration of confidence estimates ($U_{Spe} = 0.61$, $U_{Pre} = 0.50$). Evaluating uncertainty metrics at the 0.6 threshold (see Table 2) allows for a precise comparison of how each modality combination influences uncertainty management. The $B_{PSA}$ model (MRI + PSA) shows very high uncertainty sensitivity ($U_{Sen} = 0.95$), meaning it effectively identifies incorrect predictions as uncertain. However, it exhibits low specificity ($U_{Spe} = 0.41$), suggesting that it also flags many correct predictions as uncertain, reflecting an inability to establish reliable confidence. This behavior is likely due to the limited specificity of PSA, which can introduce noise into the prediction. By incorporating
<figure><img src="image_13.png" /><figcaption>**Fig. 9.** Uncertainty performance metrics across various thresholds (0.1 to 0.9) for the image-only model ($I_{\text{Model}}$) and the three bimodal models ($B_{\text{PSA}}$, $B_{\text{PSA+Volum}}$, $B_{\text{PSA+Volum+Age}}$). The plots report uncertainty-based sensitivity ($U_{\text{Sen}}$), specificity ($U_{\text{Spe}}$), accuracy ($U_{\text{Acc}}$), and precision ($U_{\text{Pre}}$). A threshold of 0.6 emerges as the best compromise, balancing sensitivity and specificity while maximizing overall accuracy and precision, particularly for the $B_{\text{PSA+Volum+Age}}$ model.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Uncertainty confusion matrices for all four models ($B_{\text{PSA}}$, $B_{\text{PSA+Volum}}$, $B_{\text{PSA+Volum+Age}}$, and $I_{\text{Model}}$) across a range of uncertainty thresholds (0.1 to 0.9). Each matrix categorizes predictions into True Certainty (TC), False Certainty (FC), True Uncertainty (TU), and False Uncertainty (FU).</figcaption></figure>

prostate volume ($B_{\text{PSA+Vol}}$), we observe a notable improvement in specificity ($U_{\text{Spe}}$ = 0.62) and overall accuracy ($U_{\text{Acc}}$ = 0.69), although precision remains moderate. This improvement can be attributed to the fact that prostate volume allows for normalization of PSA (e.g., via PSA density), thereby enhancing the quality of the clinical information and stabilizing the model's confidence. The $B_{\text{PSA+Vol+Age}}$ model reaches the best overall performance, with high specificity ($U_{\text{Spe}}$ = 0.90), high precision ($U_{\text{Pre}}$ = 0.73), and the best global accuracy ($U_{\text{Acc}}$ = 0.85). The inclusion of age introduces an additional layer of context, enabling the model to better weigh PSA and volume in light of typical clinical profiles, which likely explains its superior confidence calibration. The more informative the input, the lower the uncertainty. Finally, the image-only model ($I_{\text{Model}}$) achieves high uncertainty sensitivity ($U_{\text{Sen}}$ = 0.93) but suffers from low specificity ($U_{\text{Spe}}$ = 0.61). This model tends to doubt its correct predictions, making it less reliable for confident decision-making in a clinical context.

### 5.3. Analysis of confident predictions and radiologist workload reduction

By applying a predictive entropy threshold of 0.6, we extracted the predictions considered confident by each model and assessed their classical performance metrics (accuracy, AUC, sensitivity, specificity). The results are presented in Table 2, in the part dedicated to certain predictions. In addition, we estimated their ability to reduce the radiologist's workload by computing the proportion of correctly classified cases among confident predictions (True Certain cases), representing instances that could be automatically handled without expert review.

The image-only model ($I_{\text{Model}}$) produced 117 (TC + FC) confident predictions, representing 45% of the dataset. Among these, 111 were benign cases out of the total 215 (51.6%), and only 1 was a cancer case out of the 44 positives (2.3%). Although specificity was perfect (1.00), sensitivity was low (0.17), with only one true positive. The model rarely expresses confidence when facing cancer cases, referring 43 out of 44 to the radiologist. However, since 112 of the 117 confident predictions were correct, this model could achieve a workload reduction of 43.2%.

The $B_{\text{PSA}}$ model (image + PSA) generated 74 confident predictions, including 8 cancer cases (covering 18% of the cancer cohort) and 61

benign cases. It showed high sensitivity among confident predictions (0.89) with only one false negative, and a specificity of 0.94. Out of these 74 predictions, 69 were correct, leading to a potential workload reduction of 26.6%. Although the model performs well when confident, its limited deployment (29% of the dataset) reduces its potential clinical impact.

The $B_{\text{PSA+Vol}}$ model (image + PSA + prostate volume) provided 129 confident predictions (49% of the dataset), correctly identifying 124 benign cases. However, it did not confidently classify any of the 44 cancer cases, resulting in zero sensitivity among confident predictions. Despite its perfect specificity (1.00), the model adopts an ultra-conservative stance, handling only non-suspect cases. Its effective workload reduction, based solely on correct confident predictions, reaches 47.9%.

The $B_{\text{PSA+Vol+Age}}$ model demonstrated the best overall performance. It classified 188 cases as confident (73% of the dataset), including 21 cancer cases out of 44 (48%) and 148 benign cases out of 215 (69%). With a sensitivity of 0.75 and a specificity of 0.92 among confident predictions, the model achieved 169 correct confident classifications. This translates into a workload reduction of 65.3%, making it the only model that offers a substantial offloading of radiologist effort while reliably identifying a large number of cancer cases (see Fig. 10).

Fig. 11 presents representative examples of each prediction group defined by our uncertainty method: (TC), (FU), (FC), and (TU). For each example, we visualized the corresponding MRI scans and the probabilities associated with each class after $K = 30$ iterations. These visualizations help to better understand how the model classifies images based on its certainty and uncertainty.

A thorough analysis of the model's predictions across these four groups provides valuable insights into the reliability and limitations of the algorithm in a clinical context. The examples of True Certainty (TC) reinforce confidence in using the model for cases where it is confident in its prediction, which is essential for effective clinical use.

However, the groups of False Certainty (FC) and False Uncertainty (FU) highlight areas of risk where the model could potentially lead to errors. In particular, the cases of False Certainty (FC) are the most concerning, as they represent situations where the model could provide
<figure><img src="image_15.png" /><figcaption>**Fig. 11.** Representative examples of each prediction group as defined by our uncertainty method: True Certainty (TC), False Uncertainty (FU), False Certainty (FC), and True Uncertainty (TU). The figure displays corresponding MRI scans along with the probability distributions for each class after *K* = 30 iterations. These visualizations demonstrate how the model differentiates between certainty and uncertainty in its predictions, providing insights into the model's decision-making process and highlighting potential areas of risk in clinical application.</figcaption></figure>

false assurance of an incorrect diagnosis, a scenario that must be avoided at all costs in medicine.

Finally, the True Uncertainty (TU) group could serve as an indicator for clinicians of situations requiring special attention or additional examinations, even when the model predicts correctly.

### 5.4. Explainability

Fig. 6 illustrates examples of prostate MRI scans across multiple modalities — T2 W, ADC, and DWI — alongside the Grad-CAM maps generated for each prediction. Grad-CAM involves generating class activation maps that highlight the regions of the input image that most influence the model's output. This technique allows us to identify which areas of the image contribute most to the model's decision-making process. The heatmaps shown in the GC column represent areas of the image that, when highlighted, significantly impacted the model's confidence in its predictions. Warmer colors indicate regions of high importance, where highlighting leads to a noticeable increase in prediction confidence, while cooler colors show less significant areas. We can visually confirm that the model focuses on the regions within or

near the tumor boundaries, as expected for accurate diagnosis. The use of multiple imaging modalities in conjunction with Grad-CAM enhances our ability to validate that the model is not only making correct predictions but is also relying on clinically relevant areas of the MRI scans. This step towards explainability is crucial in medical AI, ensuring that models are trustworthy and their predictions are interpretable by clinicians.

## 6. Conclusion

Throughout this work, we explored the effectiveness of a deep learning model for prostate MRI classification, adopting a bimodal approach that combines imaging data with clinical information. The model was assessed not only based on overall performance but also with a specific focus on uncertainty management, a critical factor for real clinical deployment.

The results show that the bimodal model, which integrates MRI data with clinical variables such as age, prostate volume, and PSA level, consistently outperforms the image-only model. This approach enables better discrimination between benign cases and prostate cancer (PCa) cases.
The B<sub>PSA+Vol+Age</sub> model offers a particularly relevant trade-off: it generates a high number of confident predictions (188 cases, 73% of the dataset), including 21 cancer cases (48% of the 44 positive cases) and 148 benign cases (69% of the 215 negatives). Its sensitivity among confident predictions reaches 0.75, while specificity remains high at 0.92. These results position the model as a strong candidate for real-world clinical deployment in triage settings, where the objective is to automatically filter straightforward cases while ensuring robust diagnostic coverage. By reducing the radiologist's workload by 65.3%, this model contributes to streamlining the clinical workflow without compromising patient safety.

These findings support the idea that multimodal models enriched with clinical data (such as PSA, prostate volume, and age), when combined with explicit uncertainty management through predictive entropy, can lead to AI tools that are safer, more transparent, and better suited for deployment in clinical practice.

However, several important limitations remain. In this study, the model was trained and evaluated solely on the PICAI dataset. Although PICAI is multi-center and offers some degree of clinical variability, it does not fully capture the diversity of imaging protocols, scanner vendors, and patient populations encountered in broader clinical practice. Future work will need to prioritize external validation on independent datasets to rigorously assess the model's robustness and generalizability. Additionally, integrating further data modalities — such as blood-based biomarkers, radiomic features, or genomic information — could enhance the model's predictive power by capturing more complex biological variability. Finally, the adoption of advanced explainability techniques, such as attention-based visualizations or counterfactual reasoning, will be essential to build trust and transparency around the model's decision-making processes. Addressing these limitations will be key for the safe and effective translation of AI tools into clinical workflows.

### CRediT authorship contribution statement

**Kamilia Taguelmimt:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Formal analysis, Data curation, Conceptualization. **Gustavo Andrade-Miranda:** Writing – review & editing, Writing – original draft, Methodology, Formal analysis. **Hussein Harb:** Writing – review & editing, Software. **Tran Trung Thanh:** Writing – review & editing. **Hong-Phuong Dang:** Writing – review & editing, Supervision, Methodology. **Bernard Malavaud:** Validation, Supervision, Project administration, Funding acquisition. **Julien Bert:** Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition.

### Declaration of competing interest

The authors declare that they have no conflict of interest.

### Acknowledgments

This work was partly supported by the French State under the Future Investments Program through the DIANA project (PSPC-DIANA-2021 BPI) and by France Life Imaging (grant ANR-11-INBS-0006).

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