## 5 Evaluation of Explainability  
Despite the growing body of literature on different XAI methods, and the rising interest in the topics of interpretability, explainability, and transparency, there is still limited research on the field of formal evaluations and measurements for these issues [111]. Most studies just employ XAI techniques without providing any kind of quantitative evaluation or appraisal of whether the produced explanations are appropriate.  
Developing formal metrics and a more systematic evaluation of different methods can be difficult because of the variety of the available techniques and the lack of consensus on the definition of interpretability [112]. Moreover, contrary to usual performance metrics, there is no ground-truth when evaluating explanations of a black-box model [27, 112]. However, this is a foundational work of great importance, as such evaluation metrics would help towards not only assessing the quality of explanations and somehow measuring if the goal of interpretability is met, but also to compare between techniques and help standardise the different approaches, making it easier to select the most appropriate method for each case [113].  
In short, there is a need for more robust metrics, standards, and methodologies that help data scientists and engineers to integrate interpretability in medical AI applications in a more detailed, verified, consistent, and comparable way, along the whole methodology, design, and algorithmic development process [114]. Nevertheless, in the few studies available on this topic, there are some common aspects that establish a starting point for further development, and there are some metrics, such as the robustness, consistency, comprehensibility, and importance of explanations.  
A good and useful explanation for an AI model is one that is in accordance with human intuition and easy to understand [115]. To evaluate this, some qualitative and quantitative intuitions have already been proposed.  
* On the one hand, qualitative intuitions include notions about the cognitive form, complexity, and structure of the explanation. For example, what are the basic units that compose the explanation and how many are there (more units mean more complexity), how are they related (rules or hierarchies might be more interpretable for humans), if any uncertainty measure is provided or not, and so on [111].
* On the other hand, quantitative intuitions are easier to formally measure and include, for example, notions like identity (for identical instances, explanations should be the same), stability (instances from the same class should have comparable explanations) or separability (distinct instances should have distinct explanations) [115, 116]. The metrics based on these intuitions mathematically measure the similarity between explanations and instances as well as the agreement between the explainer and the black-box model.  
Other options to evaluate XAI techniques include factors such as the time needed to output an explanation or the ability to detect bias in the data [115].  
Another interesting strategy is to quantify the overlap between human intuitions (such as expert annotations) and the explanations obtained [117, 118], or using human ratings by experts on the topic [119, 120, 121, 113].  
There are also different options regarding the context in which these various metrics can be used. The evaluation of an XAI system can be made either in the context of the final target task with the help of domain experts, in simpler tasks, or using formal definitions [111]. Depending on the specific characteristics of the problem and available resources, different approaches and metrics can be chosen.