## 4 Discussion  
The objective of the present study was to examine the process of reducing the required sample size of a clinical study by generating novel data through the utilization of a variational autoencoder [11]. Conducting a clinical trial with a large sample size can be extremely  
Figure 8: Probability of accepting equivalence between the test and reference groups for several ratios (1, 1.10, 1.25, 1.50) of the average test (T)/reference (R) performance. The comparisons were made separately for the original (**a**), subsampled (**b**), and generated datasets by the variational autoencoder (**c**). In all cases, the “softplus” activation function was used for the hidden layers and two levels of variability (coefficient of variation, CV) were used: 10% and 20%. expensive and time-consuming [1; 2; 3; 4]. The recruitment, enrollment, and follow-up of a large number of participants require significant financial and logistical resources. Also, in some cases, using a large sample size might expose a larger number of participants to potential risks associated with the experimental intervention. The enrollment of many participants in a clinical trial can extend its duration, thus increasing the chances of there being external factors that influence the results and potentially affecting the study's validity. In addition, with a large number of participants, there is a higher likelihood of attrition and dropout during the course of the trial [1; 2; 3; 4]. In this context, over the last few years, efforts have been made to conduct in silico clinical trials and/or virtually increase the sample size in order to face off all the previously mentioned drawbacks. Data augmentation techniques, such as the introduced VAE method, involve generating additional data points based on existing data. These methods can increase the effective sample size and improve the robustness of the analysis. In order to accomplish this task, datasets were generated for two groups of volunteers (test vs. reference) using a normal distribution, while the conditions of an equivalence clinical trial were simulated. The most important factors affecting the outcome of a clinical trial refer to the mean difference between the two interventions (i.e., the relationships between the average T and R values), the variability of the measured endpoint (i.e., the coefficient of variation), and the sample size (i.e., the proportion of the \"subsampled\" population with regard to the original dataset). The impact of all these factors on the efficiency and robustness of the VAE methods was explored using a wide range of values. The desired situation would be one where the performance of the generated datasets is better than the one observed from the subsampled population. In other words, it would be desirable for the generated dataset to show equivalence when this truly exists (namely, when it is proven from the analysis of the original dataset) and to show non-equivalence when this is also shown from the original dataset. Any discrepancy with the original dataset indicates a deficiency in the analysis dataset. In order to investigate the efficiency of the VAE method, the performance of the VAE-generated datasets was compared with that of the original as well as with that of the subsampled dataset. In all cases, the performance of the VAE-generated data was found to be superior to any subsampled group and similar to the original (large) dataset (Figures 6-8). It is noteworthy that for high variabilities (Figure 7c), the performance of the VAE method became even better than with the original dataset. The R group was assumed to have a mean endpoint value of 100, while several endpoint means were utilized for the T group; the T means were set at 100, 110, 125, and 150 in order to express identical performance (i.e., 100%) and a 10%, 25%, and 50% discrepancy, respectively. The aforementioned data were produced using varying coefficients of variation, specifically, 10%, 20%, and 40%.