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Deep learning shows great promise for medical image analysis but often lacks explainability, hindering its adoption in healthcare. Attribution techniques that explain model reasoning can potentially increase trust in deep learning among clinical stakeholders. In the literature, much of the research on attribution in medical imaging focuses on visual inspection rather than statistical quantitative analysis. In this paper, we proposed an image-based saliency framework to enhance the explainability of deep learning models in medical image analysis. We use adaptive path-based gradient integration, gradient-free techniques, and class activation mapping along with its derivatives to attribute predictions from brain tumor MRI and COVID-19 chest X-ray datasets made by recent deep convolutional neural network models. The proposed framework integrates qualitative and statistical quantitative assessments, employing Accuracy Information Curves (AICs) and Softmax Information Curves (SICs) to measure the effectiveness of saliency methods in retaining critical image information and their correlation with model predictions. Visual inspections indicate that methods such as ScoreCAM, XRAI, GradCAM, and GradCAM++ consistently produce focused and clinically interpretable attribution maps. These methods highlighted possible biomarkers, exposed model biases, and offered insights into the links between input features and predictions, demonstrating their ability to elucidate model reasoning on these datasets. Empirical evaluations reveal that ScoreCAM and XRAI are particularly effective in retaining relevant image regions, as reflected in their higher AUC values. However, SICs highlight variability, with instances of random saliency masks outperforming established methods, emphasizing the need for combining visual and empirical metrics for a comprehensive evaluation. The results underscore the importance of selecting appropriate saliency methods for specific medical imaging tasks and suggest that combining qualitative and quantitative approaches can enhance the transparency, trustworthiness, and clinical adoption of deep learning models in healthcare. This study advances model explainability to increase trust in deep learning among healthcare stakeholders by revealing the rationale behind predictions. Future research should refine empirical metrics for stability and reliability, include more diverse imaging modalities, and focus on improving model explainability to support clinical decision-making. [ABSTRACT FROM AUTHOR]