## 3 Results  
Initially, the scenarios studied referred to a 0.5% sampling rate, which corresponds to 50 patients (\"sample\") from the initial 10,000 subjects in the population (\"original\"). From this low number of subjects, the WGAN approach was used to synthetize the \"generated\" dataset which was set to have equal size with the \"original\" (that is 10,000 generated subjects). The average histograms of two different scenarios can be seen in Figure 4. These histograms were calculated by creating individual histograms for each execution of the WGANs within a certain scenario and then averaging them. In Figure 4A, a scenario with a small T/R ratio and low variability was examined. A desired performance of the WGAN is observed towards reproducing a dataset (\"generated\") with almost exactly identical distribution with the \"original\" data. Despite the fact that the \"sample\" did not appear to reflect the traits of the original population, due to the limited sample size, the generated dataset behaves similarly to the actual population. In Figure 4B, the results were consistent, even with a larger T/R ratio but the same variability. This indicates that the WGANs were able to capture the population performance from a sample that did not accurately represent the population. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test/Reference Ratios** & \begin{tabular}{c} **Coefficient of Variation** \\ **for Between-Subject Variability** \\ \end{tabular} & \
\begin{tabular}{c} **Size of the “Original”** \\ **Dataset (Population)** \\ \end{tabular} &
\begin{tabular}{c} **Size of the** \\ **“Generated” Dataset** \\ \end{tabular} \\ \hline
1.0, 1.05, 1.1, 1.15 & 10\% & 10,000 & 10,000 \\
1.0, 1.05, 1.1, 1.15 & 20\% & 10,000 & 10,000 \\
1.0, 1.05, 1.1, 1.15 & 50\% & 10,000 & 10,000 \\
1.0, 1.05, 1.1, 1.15 & 70\% & 10,000 & 10,000 \\
1.0, 1.05, 1.1, 1.15 & 10\% & 10,000 & 1000 \\
1.0, 1.05, 1.1, 1.15 & 10\% & 10,000 & 500 \\
1.0, 1.05, 1.1, 1.15 & 10\% & 10,000 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Scenarios that were examined in the Monte Carlo simulations of the clinical trials. Figure 4 shows that WGANs have the capability to synthesize virtual data with the same distribution shape. This aspect is crucial as it serves as a necessary prerequisite for the further assessment of performance among the three sets of data, namely, \"original\", \"sample\", and the WGAN-\"generated\". Thus, the analysis could proceed to investigate the similarity in the statistical outcomes between the virtual population and the original population. In this context, the concept of \"similarity\", as defined in Section 2.1, was assessed (Figure 5). It is reminded that similarity is assessed between two pairs: \"original\" vs. \"generated\" population, and \"original\" vs. \"sample\". Figure 5 clearly shows that across several different scenarios, the similarity between the \"generated\" population and the \"original\" population consistently exceeded that of the \"original\" vs. \"sample\". These findings highlight the desired ability of the AI-synthesized data to mimic the behavior of the actual population. It also highlights the potential risk of false negative errors (i.e., type II error) within the traditional way we perform the clinical trials, a risk which is eliminated by virtually increasing the sample size with WGANs. Notably, the similarity percentage remains relatively stable for the \"original\" vs. \"generated\" population comparisons (minimum percentage: 94% and maximum percentage: 100%), indicating the successful imitation of population performance by the WGANs compared with the \"original\"-\"sample pair\" (minimum percentage: 4% and maximum percentage: 100%). Apart from the similarities in the distributions, the success percentages were calculated and visualized, as illustrated in Figure 6 for the scenario of a = T/R = 1.0. The \"generated\" population exhibited higher or equal success percentages than the \"original\" and \"sample\" datasets across all different scenarios.