## 3 Results
### Quality Evaluation of Synthetic Clinical Data  
Several data quality metrics were considered to evaluate the similarity between synthetic and real data according to different IRs. As stated in Section 2.2.4, the PMFs associated with the different features were estimated as the previous step for computing these metrics. In Figure 3, the estimated PMFs associated with age, BMI, sex, and high cholesterol are depicted. The panels in the first column of the figure show the estimated PMF for those features when considering real data, and the remaining represent the PMFs estimated from synthetic data when using SMOTEN, TVAE and CTGAN. We aim to measure the similarity between the PMF of real data and that estimated with synthetic data, comparing how well the different oversampling methods can reproduce the PMF estimated using real data. Remarkably, the PMFs estimated using data generated with TVAE do not follow the probability distribution linked to the real data, showing a lack of probability values in certain categories. For instance, if we look at the age feature (see Figure 3a), in the PMF of synthetic data obtained with TVAE (third column), there are categories without samples, specifically for 16-20, 30-39 and NA. In the same manner, for the BMI feature (see Figure 3b), the categories HW, NA, OBC-II and OBC-III do not have values. Additionally, in some categories, the probability is much higher than that obtained when using real data (see the category OW in the BMI feature). We conclude that TVAE is the method that worst mimics the distribution for the four features considered. This further points out the low performance of TVAE for replicating samples of categorical data. By analyzing SMOTEN, we find similar insights that in TVAE. There are categories in the estimated PMF with zero values (see panels (a) and (b) associated with age and BMI). Regarding CTGAN, note that the PMFs estimated using the generated data are quite similar to those estimated using real data. All categories have probability values different from zero and they are similar to those estimated when considering real data. The insights drawn from these figures allow us to understand how similar the synthetic and real data are to one another in terms of  
Figure 3: Estimations of the PMFs associated with: (**a**) age; (**b**) BMI; (**c**) sex; and (**d**) high cholesterol. Estimated PMF obtained using real data (first column); SMOTEN (second column); TVAE (third column); and CTGAN (fourth column). univariate attribute fidelity, CTGAN being the oversampling approach that more precisely emulates the real distributions. The next step was to analyze the data quality metrics considering different IR values (see Figure 4). We observed that, in terms of KLD, HD, MAEP, and RSVR (panels (a), (b), (c) and (d), respectively), CTGAN showed the best results. Note that lower values in these metrics indicate more similar distribution probabilities associated with features. Regarding PCD (Figure 4e), which measures whether the correlations between features are preserved, CTGAN also reached the lowest values compared to SMOTEN and TVAE. For LCM (Figure 4f), where the lower values indicate fewer differences in the distribution between \(\mathcal{X}_{R}\) and \(\mathcal{X}_{S}\), it was SMOTEN that reached the lowest values, followed by CTGAN. Regarding RSVR (Figure 4d), CTGAN showed the lowest values, indicating that it generates fewer repeated vectors. Table 2 presents a summary of the quality metrics that analyzes: (_i_) the similarity between the features of \(\mathcal{X}_{R}\) and \(\mathcal{X}_{S}\) (KLD, HD, and MAEP) and (_ii_) the relationships between features captured (PCD and LCM). The results of RSVR are shown to identify the percentage of repeated vectors generated by the oversampling methods. Note that these metrics were obtained considering IR = 1.0 and 5 different training partitions, and we present the mean and the standard deviation (std).