## 4 Results  
### Post Hoc Explanation Methods  
The findings of this paper are split into two sections. The initial section assesses if post hoc explanations enhance radiologists' ability to detect prostate lesions and investigates the \begin{table}
\begin{tabular}{l l} \hline \hline
**Method** & **Description** \\ \hline DeepLIFT & Uses a reference point to compute attribution \\ SHAP & Is a game theoretic approach used for deep learning explanations \\ Grad-CAM & Uses the gradient with respect to feature maps to compute explanations \\ Integrated Gradients & Is a proposed solution to the saturated gradient problem found in \\  & vanilla gradients \\ SmoothGrad & Is a a saliency method that was designed to be robust to noise \\ CXPlain & Uses causal models to provide deep learning explanations \\ DistDeepSHAP & Uses a reference distribution to compute Shapely values \\ BLRP & Is a Bayesian extension of layer-wise relevance propagation \\ BayLIME & Uses Bayesian regression models in the LIME framework \\ \hline \hline \end{tabular}
\end{table} 
Table 2: An overview of the methods evaluated in this work. preferred explanation technique and the reasons behind this preference. The latter section examines methods for quantifying uncertainty, a critical factor in high-risk clinical tasks, to minimize diagnostic errors and enhance the diagnostic process after evaluating explanation techniques in a similar manner. This study is among the first to explore quantification in explanation methodologies for clinical tasks. Explanation methods manifest on the image by color marking key areas. In our case, in an MRI prostate lesion image, the explanation method highlights regions of interest with a heatmap, assisting radiologists in identifying lesions. Python was employed for this analysis, utilizing libraries such as SciPy and StatsModels to perform the necessary statistical calculations and derive the results presented. The F1 score, which measures a test's accuracy by balancing precision (true positives divided by positive predictions) and recall (true positives divided by actual positives), is particularly useful for understanding the performance on imbalanced datasets:  
\[\text{F1 Score}=2\times\left(\frac{\text{Precision}\times\text{Recall}}{ \text{Precision}+\text{Recall}}\right)\]  
Sensitivity measures the proportion of actual positives that are correctly identified by the test. It is defined as follows:  
\[\text{Sensitivity}=\frac{\text{True Positives}}{\text{True Positives}+\text{False Negatives}}\]  
Accuracy measures the proportion of correctly identified instances among the total number of instances. It is defined as follows:  
\[\text{Accuracy}=\frac{\text{True Positives}+\text{True Negatives}}{\text{Total Number of Instances}}\]  
Additionally, a confidence interval \(CI\) provides a range that likely contains the true value of a population parameter with a specified confidence level (e.g., 95%), helping to understand the reliability and precision of the estimate:  
\[CI=\bar{x}\pm Z\times\frac{\sigma}{\sqrt{n}}\]  
A total of 250 responses were collected from ten radiologists, and the findings of both evaluations are reported. This part presents radiologists' lesion detection performance and compares their results with and without the use of an associated explanation technique. Additionally, the performances were divided to examine potential differences among various explanation methods, aiming to establish their effectiveness and explore their specific advantages. The outcomes of these comparisons can be found in Table 3.  
Table 3 demonstrates the varying impact of individual explanation methods on diagnostic performance performed by the radiologist in tandem with the explanation method, with some methods enhancing the performance, while others impeded it. DeepLIFT and SHAP, for instance, contribute to improved diagnoses, while SmoothGrad hampers them. Integrated Gradients and Grad-CAM also seem to influence diagnostic outcomes.