## 3 Results
For the original dataset, the probability of acceptance fell to low values (close to 20%, Figure 7a). Similarly, the subsampled dataset showed poor performance since, not only for small portions of the original data but also for large parts, the probability of acceptance remained quite low  
Figure 6: Probability of accepting equivalence between the original and the generated datasets for three levels of variability (CV): (**a**) 10%, (**b**) 20%, and (**c**) 40%. The results are shown separately for the test and reference groups, as well as the two types of activation functions (“softplus” and linear) used for the hidden layers. (Figure 7b). On the contrary, the VAE-generated (Figure 7c) dataset showed superior performance since, for all portions, the probability of acceptance was much higher than for the original and subsampled datasets. It is worth mentioning that even for low proportions (e.g., 10% or 20%), the statistical power of the VAE data was three times higher than that of the original data. For larger proportions, the probability of acceptance of the VAE-generated data reached rather high values (close to 80%), which was around four times higher than that of the original data. In Figure 7, it becomes evident that for highly variable data, the application of the VAE worked rather efficiently as a data augmentation method. In all cases, the average performance (i.e., the mean endpoint value) between the two compared groups (T vs. R) was considered to be identical. In order to investigate additional situations where the two compared groups differed, Figure 8 was constructed. In Figure 8, the mean values for the T group are 100, 110, 125, and 150, while the mean value for the R group is always 100. This means that the T group is thought to be the same (T/R = 1) or different by 10%, 25%, or 50% (T/R = 1, 1.1, 1.25, and 1.50). Also, the statistical characteristics of the original, subsampled, and generated data were investigated for a range of subsample sizes spanning from 10% to 90%. The impact of the CV on the clinical study outcomes was investigated based on two distinct values, specifically, 10% and 20%. Several iterations were used for each case, and the probability of accepting equivalence was subsequently calculated. In all cases in Figure 8, a decrease in statistical power can be observed with an increase in the T/R ratio. In particular, for the original data (Figure 8a), a high probability of acceptance (almost 100%) can be observed when the two groups (T vs. R) do not differ (T/R = 1) or differ a little (T/R = 1.1). As the discrepancy between T and R gets larger (to 25% or 50%), a dramatic decrease in statistical power is observed. A similar performance is observed for the subsampled data (Figure 8b). Again, at low T/R ratios (e.g., 1 or 1.1), there is a high probability of equivalence acceptance, whereas, as the discrepancy between T and R becomes higher, the statistical power decreases and reaches almost zero values. Also, when small portions of the original data are used (around 10% to 30%), the probability of acceptance is even lower. For the VAE-generated datasets (Figure 8c), the results obtained for low T/R ratios (1 or 1.1) show a profile similar to the one observed before for the original and subsampled data. However, a desired performance with much higher statistical power can be observed when the two groups differ by 25%. For larger  
Figure 7: Probability of accepting equivalence between the test and reference groups for the original (**a**), subsampled (**b**), and generated (**c**) datasets Three levels of variability (coefficient of variation, CV) were used: 10%, 20%, and 40%. In all cases, the “softplus” activation was used for the hidden layers, while both the test and reference groups were assumed to exhibit identical average performances. discrepancies, namely, when T/R = 1.50, as expected, the probability of acceptance falls to zero since these high discrepancies in the average performance are outside the acceptance limits of equivalence.