## 2 Materials and Methods
### Strategy of the Analysis  
In clinical trials, determining an appropriate sample size is crucial for accurately assessing the effectiveness and safety of treatments (e.g., a new medicine against the existing reference treatment). Hypotheses related to the study drug are formulated based on primary endpoints and are evaluated using statistical tests within an explicitly defined clinical design to ensure accurate and reliable results (Figure 1). It is essential to clearly state these assumptions when calculating sample size, as each hypothesis requires specific sample size considerations to achieve desired statistical assurance (e.g., at most 5% false positive and 20% false negative) [4; 29]. To demonstrate the suitability of the WGAN-based approach, a new methodological procedure needs to be established and applied. The purpose of this work is to present a novel concept for reducing the sample size needed for clinical trials by using an appropriate ANN like WGANs. Specifically, the research idea involves the following steps (Figure 2):  
1. Create an entire population (\"the original dataset\"). 2. Take a subset (the \"sample\") of the population and conduct a clinical study using only this limited number of participants. 3. Combine the \"sample\" information and the WGANs to create virtual subjects, namely, the \"generated\" dataset, thus increasing statistical power. The aim is to achieve high statistical power while avoiding an increase in the false positive rate. In essence, the purpose is to draw conclusions from a small sample in a clinical trial that mirror those that would be drawn from the entire population. Since achieving this through classical statistical methods is unfeasible, a generative AI algorithm, specifically  
Figure 1: Visual representation of the existing clinical trial process. WGANs, is used to address this issue. To demonstrate the applicability of the new approach, it is important to show that the performance of the combination small sample/WGANs that leads to the \"generated\" dataset closely resembles that of the entire population (i.e., the \"original\" dataset), and notably exceeds the performance of the \"sample\" dataset (Figure 2). It should be underlined that performance pertains to the statistical power of the study and type I error, not safety considerations. This study compares the performance of the WGAN-\"generated\" dataset against that of the entire population (i.e., the \"original\") and the \"sample\" datasets. Ideally, the \"generated\" dataset performance should align closely with that of the \"original\", indicating that the desired statistical properties can be achieved using only a small sample of actual subjects. If this approach is shown to hold, then it offers numerous benefits including cost-effectiveness, earlier trial completion, and simplification of complexities. To demonstrate the usefulness of WGANs, an in silico experimental approach was implemented in this study. Below is a brief overview of the procedure, which was performed in a Jupyter Lab environment with Python:  
1. Monte Carlo simulations were used to virtually create 10,000 patients, which refer to the entire population, namely the \"original\" dataset. To simulate the conditions of two interventions (e.g., two different medicines), two distributions were created with 10,000 patients each. 2. Each distribution had a mean of the hypothetical endpoint equal to 100 units. Also, several between-subject variability values were used for the random generation of the populations: 10%, 20%, 50%, and 70%. 3. Two distributions were created, referring to the Test (T) and Reference (R) treatment. In addition, several T/R ratios among the means of the distributions were examined. 4. The T and R values were preprocessed via standard scaling. 5. To obtain the \"sample\", we mimic the process used in real-world scenarios, namely, random sampling from the \"original\" dataset.