## 2 Materials and Methods
### Strategy of the Analysis  
Classically, in clinical trials, the sample size is explicitly stated in the study protocol and, therefore, estimated before the initiation of the study. Estimation of the sample size is a complex procedure that relies on several parameters of the trials, among which the most important are measured endpoint (or endpoints), measurement scale of the endpoint, variability of the endpoint, nominal level of the type I error, maximum anticipated type II error, acceptance limits, and difference between the treatments (in the case of interventional studies). However, when the variability of the endpoint(s) is high, the type I error is set to be very low or we want to increase the statistical power of the study (i.e., decrease type II error), there is a need for a large sample size. The latter leads to the inclusion of many human participants, rather increased costs, a long duration of the study, a high possibility of dropouts, etc. There is no much we can do to limit the sample size; only in the case of bioequivalence studies, the scaled average approach has been proposed, where the acceptance limits scale as a function of the residual variability of the study [4; 5; 6]. The aim of this work is to introduce a novel idea for reducing the required sample size in clinical trials. The idea is as follows:  
1. Perform the clinical study using a limited number of volunteers;
2. Using the results from \"a\", apply in the next step a VAE in order to create virtual subjects and increase the statistical power. The ideal situation would be one where we could achieve high statistical power without increasing the false positive rate (type I error). In the following lines, the methodology and results are presented of such a method where the latter requirements are fulfilled. In order to show that VAE works efficiently, an experimental method was set up. In brief, the experimental part is outlined below:  
1. Create N virtual subjects (e.g., N = 100) using Monte Carlo simulations. This is considered the \"original\" dataset. 2. Set the average endpoint value equal to 100 units and conduct sampling assuming log-normal distribution [4]. Several levels of variability (e.g., 10%, 20%, 40%, etc.) are used for the random creation of virtual subjects. 3. Assume two treatments: Test (T) and Reference (R), as in the case of bioequivalence studies. Several levels of the T/R ratios are explored. 4. Use these virtual subjects to form a clinical trial; for the purposes of this work, a parallel clinical design was used. Half of the subjects are considered to receive one treatment (e.g., T) and the other half received the other (e.g., R). 5. Draw a random sample from the original dataset (steps \"i\" and \"ii\") to create the sub-sample. 6. Apply VAE to the sub-sample created in the previous step (i.e., \"v\"). This leads to the creation of the \"generated sample of subjects\". 7. Apply the typical statistics imposed by the regulatory authorities [5; 6]. The statistical analysis compares T vs. R separately for the \"original dataset\", \"sub-sample\", and \"VAE-generated dataset\" (or simply the \"generated dataset\"). * Record the success or failure of the study separately for the \"original dataset\", \"sub-sample\", and \"generated dataset\". * Repeat steps \"i\"-\"viii\" many times (e.g., 500) to obtain robust estimates for the percentage of acceptance (i.e., % success) of each of the three datasets. * Compare the performances obtained in step \"ix\". The set-up, validation, and fine-tuning of the VAE hyperparameters were conducted exhaustively after step \"vi\". Generally speaking, it would be preferred for the VAE-generated dataset to result in higher percentages compared to the sub-sampled dataset. It would be almost ideal if the performance of VAE-generated data were similar to that of the original dataset. Finally, it would be ideal if the performance of the VAE dataset were even better than the original data.