The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification Algorithm

Hepatitis C is an infectious disease which is caused by the Hepatitis C virus (HCV) and the virus primarily affects the liver. Based on the publicly available dataset used in this paper the idea is to develop a mathematical equation that could be used to detect HCV patients with high accuracy based on the enzymes, proteins, and biomarker values contained in a patient’s blood sample using genetic programming symbolic classification (GPSC) algorithm. Not only that, but the idea was also to obtain a mathematical equation that could detect the progress of the disease i.e., Hepatitis C, Fibrosis, and Cirrhosis using the GPSC algorithm. Since the original dataset was imbalanced (a large number of healthy patients versus a small number of Hepatitis C/Fibrosis/Cirrhosis patients) the dataset was balanced using random oversampling, SMOTE, ADSYN, and Borderline SMOTE methods. The symbolic expressions (mathematical equations) were obtained using the GPSC algorithm using a rigorous process of 5-fold cross-validation with a random hyperparameter search method which had to be developed for this problem. To evaluate each symbolic expression generated with GPSC the mean and standard deviation values of accuracy (ACC), the area under the receiver operating characteristic curve ($AUC$), precision, recall, and F1-score were obtained. In a simple binary case (healthy vs. Hepatitis C patients) the best case was achieved with a dataset balanced with the Borderline SMOTE method. The results are $\overline{ACC}\pm SD\left(ACC\right)$, $\overline{AUC}\pm SD\left(AUC\right)$, $\overline{Precision}\pm SD\left(Precision\right)$, $\overline{Recall}\pm SD\left(Recall\right)$, and $\overline{F1-score}\pm SD(F1-score)$ equal to $0.99\pm 5.8\times {10}^{-3}$, $0.99\pm 5.4\times {10}^{-3}$, $0.998\pm 1.3\times {10}^{-3}$, $0.98\pm 1.19\times {10}^{-3}$, and $0.99\pm 5.39\times {10}^{-3}$, respectively. For the multiclass problem, OneVsRestClassifer was used in combination with GPSC 5-fold cross-validation and random hyperparameter search, and the best case was achieved with a dataset balanced with the Borderline SMOTE method. To evaluate symbolic expressions obtained in this case previous evaluation metric methods were used however for $AUC$, $Precision$, $Recall$, and $F1-score$ the macro values were computed since this method calculates metrics for each label, and find their unweighted mean value. In multiclass case the $\overline{ACC}\pm SD\left(ACC\right)$, ${\overline{AUC}}_{macro}\pm SD\left(AUC\right)$, ${\overline{Precision}}_{macro}\pm SD\left(Precision\right)$, ${\overline{Recall}}_{macro}\pm SD\left(Recall\right)$, and ${\overline{F1-score}}_{macro}\pm SD(F1-score)$ are equal to $0.934\pm 9\times {10}^{-3}$, $0.987\pm 1.8\times {10}^{-3}$, $0.942\pm 6.9\times {10}^{-3}$, $0.934\pm 7.84\times {10}^{-3}$ and $0.932\pm 8.4\times {10}^{-3}$, respectively. For the best binary and multi-class cases, the symbolic expressions are shown and evaluated on the original dataset.