# Generative Neural Networks for Addressing the Bioequivalence of Highly Variable Drugs
## 3 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & \multicolumn{2}{c}{**\% Similarity**} \\ \hline
**CVw** & **Augmentation Scale** & **N** & **Original vs. Sample** & **Original vs. Synthetic** \\ \hline \multirow{6}{*}{30\%} & \multirow{3}{*}{2\(\times\)} & 60 & 94.2\% & 97.4\% \\ \cline{3-5}  & & 40 & 87.4\% & 94.0\% \\ \cline{3-5}  & & 24 & 82.4\% & 92.4\% \\ \cline{3-5}  & & 60 & 94.2\% & 96.8\% \\ \cline{3-5}  & & 40 & 87.4\% & 93.4\% \\ \cline{3-5}  & & 24 & 82.4\% & 91.6\% \\ \hline \multirow{6}{*}{50\%} & \multirow{3}{*}{2\(\times\)} & 60 & 96.4\% & 92.0\% \\ \cline{3-5}  & & 40 & 93.0\% & 89.4\% \\ \cline{3-5}  & & 24 & 86.0\% & 85.4\% \\ \cline{3-5}  & & 60 & 96.4\% & 90.4\% \\ \cline{3-5}  & & 40 & 93.0\% & 85.4\% \\ \cline{3-5}  & & 24 & 86.0\% & 81.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
Figure 5: Percent BE acceptance gain across three variability levels (15%, 30%, and 50%) and three sample sizes of the original dataset (24, 40, and 60). The acceptance gain refers to the difference in statistical power between the synthetic data and the original (or sample) data. The error bars represent the standard error calculated from 1000 Monte Carlo trials performed under each condition. For all different executed scenarios, the generated distributions were better resembling the original, rather than the sample compared to the original distribution based on the statistical tests that were carried out. The tests were important to validate data distribution overlap and consisted of visual inspection (histograms for the original, sample and synthetic data) and calculation of Szymkiewicz-Simpson and Bhattacharyya distances for all datasets. To make all the estimations, three different original datasets were generated, referring to (1) N = 24, CVw = 15%, (2) N = 40, CVw = 30%, and (3) N = 60, CVw = 50%. The chosen values have been selected to be in line with the results of Figures 3-5. Figure 5 provides a visual overview of the distributions of the original, sample, and synthetic data. The Szymkiewicz-Simpson coefficient measures the overlap between two probability distributions and the closer the value to 1 then there is a better similarity. The Bhattacharyya distance measures the distance between two probability distributions and the closer the value to 0, then the more identical the distributions are. For the purpose of this analysis, \"distribution overlap\" refers to the comparison between the Test and Reference distributions, which differ by an average of 10%, across several scenarios. The statistical criteria indicated that in all cases, the synthetic distribution maintained the same (or even superior) discriminatory power compared to the original data and significantly outperformed the sample data. Table 1 demonstrated the results of the different statistical tests. Overall, three distinct conditions were studied: low sample size/low variability (Panel A), medium sample size/moderately high variability (Panel B), and large sample size/high variability (Panel C). In Panel A, the statistical criteria demonstrated that the synthetic data had better discriminatory power than the original data (and much better than the sample data). In Panel B, where the distributions begin to spread out, the discriminatory power decreases across all datasets, though the synthetic data continue to deliver strong performance. Finally, in Panel C, where data are highly dispersed due to very high variability, the discriminatory power between the T and R distributions is, as expected, further reduced--but the synthetic data still exhibit the best performance. The implementation of WGANs in real BE data, showed that in both studied drugs, the generated data either provided the same results as the original dataset (hydrochlorothiazzide) or outperformed the original dataset (atorvastatin). The study with hydrochlorothiazzide performed on 72 subjects and the CVw for the Cmax value was 29.2% [27].