## 2 Materials and Methods
### Monte Carlo Simulations  
In our research, we utilized a Monte Carlo simulation approach to generate random patient data for the evaluation of our algorithm. The Monte Carlo framework used in this study is the typical one that has been extensively used in simulated bioequivalence studies [10]. The reason for utilizing a Monte Carlo simulation framework in our study was to assess the performance of the WGAN algorithm across a range of simulated patient populations, capturing the variability inherent in real-world clinical scenarios. For the generation of the 10,000 \"virtual patients\", two different normal distributions (T and R, referring to the Test and Reference treatment, respectively) were created. Each distribution had a mean endpoint value of 100 units, with the standard deviation varying according to the scenario explored. These normal distributions were created using the NumPy library. The function used to generate the distributions included three parameters: the mean of the distribution, the standard deviation, and the number of \"patients\". Our goal was to mimic real clinical trial conditions, where an unknown population is sampled randomly to apply interventions in the sample drawn. The random sample maintained the format of the original population. Subsequently, statistical analysis is performed using the information gained from the sample. In our study, we simulated the population (referred to as the \"original\" dataset) from which we extracted the \"sample\". We then progressed one step further by synthesizing virtual patients (i.e., the \"generated\" dataset). To obtain robust estimates, this process was repeated thousands of times using Monte Carlo simulations. It should be mentioned that in this manuscript the data source is the \"original data\" that come from simulations. However, in practical applications, the WGAN can easily process various formats of real-world clinical data (e.g., CSV, XLSX), making its implementation straightforward. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Activation Function**} & \multicolumn{2}{c}{**Number of Hidden Layers**} & \multicolumn{2}{c}{**Number of Neurons in Hidden Layers**} & \multirow{2}{*}{**Learning Rates**} & \multirow{2}{*}{**Epochs**} & \multirow{2}{*}{**Latent Dimensions**} & \multirow{2}{*}{**Batch Size**} \\ \cline{1-1} \cline{6-10} \multicolumn{1}{c}{**Hidden Layers**} & & & & & & & & & \\ \cline{1-1} \cline{6-10} \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & & & & & & \\ \cline{1-1} \cline{6-10} \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & & & & & & & \\ \cline{1-1} \cline{6-10} \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hyperparameter tuning of the WGANs. All data distributions were preprocessed through standard normalization (z-scores), and then a random sampling was performed. The sampling percentage was 0.5% and 1.0% of the population, which corresponds to 50 and 100 subjects, respectively. With that choice, the aim was to have a small representative \"sample\" of subjects from which the \"generated\" dataset would be created, using WGAN. This procedure was repeated for all scenarios listed in Table 2:  
Four different ratios of the T/R ratio were examined where the mean value of the R group was kept constant to 100, while the T group had a mean of 100 multiplied by specific values: 1.0, 1.05, 1.1, and 1.15. The coefficient of variation (CV), for between-subject variability, was the same for both the T and R groups, determined by the scenario. The CV values indicate variability, with 10% representing low variability and 20% medium variability, while 50% and 70% refer to high and very high variability, respectively. The statistical evaluation of the \"original\", \"sample\", and \"generated\" datasets was performed through the \(t\)-test criterion.