## 3 Decision-Making Modeling in Clinical Issues
### Classification Quality Measures  
Decision models can return results in binary form (e.g., positive/negative patient) or multiclass form (e.g., degree of disease on an n-point scale). To assess the quality of the model, it is necessary to have test data that were not used during the training process and have labels assigned by medical specialists. The test data are then evaluated by the decision model and compared with the labels of specialists, determining a confusion matrix consisting of case counts:  
* true positives (TP)--classified positively by both the model and specialists;
* false positives (FP)--classified positively by the model but negatively by specialists;
* false negatives (FN)--classified negatively by the model but positively by specialists;
* true negatives (TN)--classified negatively by both the model and specialists. The quality measures of binary decision models, such as the sensitivity (Formula (1)), specificity (Formula (2)), positive predicted value (PPV, Formula (3)), and negative predicted value (NPV, Formula (4)), are used to evaluate clinical models. The evaluation of clinical models can also be enriched with measures used in decision modelling in general, such as the accuracy (Acc, Formula (5)), balanced accuracy (BA, Formula (6)), F1-score (F1, Formula (7)), and area under the ROC curve (AUC) (Formula (8), Figure 6). \[sensitivity=\frac{TP}{TP+FN} \tag{1}\]  
\[specificity=\frac{TN}{TN+FP} \tag{2}\]  
\[PPV=\frac{TP}{TP+FP} \tag{3}\]  
\[NPV=\frac{TN}{TN+FN} \tag{4}\]  
\[Acc=\frac{TP+TN}{TP+FP+TN+FN} \tag{5}\]  
Figure 6: Diagram showing the ROC curve. The AUC is under the ROC. \[BA=\frac{sensitivity+specificity}{2} \tag{6}\]  
\[F1=\frac{2 TP}{2 TP+FP+FN} \tag{7}\]  
\[AUC=\int_{0}^{1}sensitivity(FPR^{-1}(t))dt \tag{8}\]  
where FPR (false positive ratio) denotes the percentage of FPs among ground truth negatives:  
\[FPR=\frac{FP}{FP+TN} \tag{9}\]  
The quality measures for multiclass decision models can be generalised by averaging the scores for each class \((i,j)\) of all decision classes \((K)\) using a one-versus-all approach [114] (Formulas (10)-(12) and (14)-(16)). The exception is the AUC, which requires the consideration of every pair of classes (Formula (17)). \[specificity=\frac{TN}{TN+FP} \tag{2}\]0  
\[specificity=\frac{TN}{TN+FP} \tag{2}\]1  
\[specificity=\frac{TN}{TN+FP} \tag{2}\]2  
\[specificity=\frac{TN}{TN+FP} \tag{2}\]3  
\[specificity=\frac{TN}{TN+FP} \tag{2}\]4  
\[specificity=\frac{TN}{TN+FP} \tag{2}\]5  
\[specificity=\frac{TN}{TN+FP} \tag{2}\]6  
\[specificity=\frac{TN}{TN+FP} \tag{2}\]7  
Multiclass decisions regarding the degree of advancement of pathological changes can be binarised at a later stage, e.g., to determine the validity of clinical procedures or a specific group of symptoms and threats [115; 116; 117; 118]. The condition for the correctness of such a process is the maintenance of a linear order concerning the decision classes and the corresponding degree of advancement in changes. Correctly understanding the meaning of these measures is crucial in interpreting the results of decision model evaluations. Sensitivity indicates how effectively a model can identify positive cases. Specificity determines how many of the positive cases detected are correct. PPV and NPV are the percentages of objects classified as truly positive or genuinely negative, respectively, among all positive or negative objects. Accuracy is the percentage of all objects that receive a correct decision. When the number of objects within the decision classes (positive/negative or for each grade of a given disease) varies, a more reliable measure is BA, which determines the average accuracy within each decision class. An excellent alternative to BA is the F1-score, which also determines the quality of the model within the decision classes. The final AUC is the area under the ROC curve (Figure 6). The larger the graph area that it covers, the larger the field value under it will be.