Dear Igor,

it is hard to answer not having full details of what makes the patients different between the first (Prot1 and 2) and second (Prot 3 and 4) study.

From a purely technical point of view, you can put the datasets together as long as you have predictors in common between the studies and if the outcome is the same (response variable/s). Nevertheless, the nature of the difference between patients should be taken into account before merging the datasets and before even thinking of any possible analysis to perform.

You can do this by using an explicit variable that reflects such differences. For example, let's assume that your first and second study groups differ in age (first younger, second older). Pay attention, though, that if the outcome and the Prot1,2,3,4 are dependent on the factor (age in our imaginary case), it will be hard to extract much information from the data.

One way to approach this would be to create this new variable and then perform an exploratory Principal Component Analysis of the predictors (including this variable) just to have a look at the relative importance of each predictor to explain the variance of the dataset. If the relative importance of the new variable (age in our imaginary case) is overwhelming, there is not much information you can have from the dataset, except from the fact that you should do a third experiment with all 4 Prots and designed to include the factor that differed between the first two studies.

You can find more information in the following paper. In summary, federated learning is an innovative mechanism to train a united model on data from multiple parties without compromising privacy and security of those data. There are different types of federated learning including horizontal, vertical and transfer learning that you can use based on your dataset. For example, if you have same features but different samples (different patients have same disease, symptoms ...) you can use horizontal federated learning.

Article Federated Machine Learning: Concept and Applications

"... Medical data such as disease symptoms, gene sequences, medical reports are very sensitive and private, yet medical data are difficult to collect and they exist in

isolated medical centers and hospitals. The insufficiency of data sources and the lack of labels have led to an unsatisfactory performance of machine learning models, which becomes the bottleneck of current smart healthcare. We envisage that if all medical institutions are united and share their data to form a large medical dataset, then the performance of machine learning models trained on

that large medical dataset would be significantly improved. Federated learning combining with transfer learning is the main way to achieve this vision. Transfer learning could be applied to fill the missing labels thereby expanding the scale of the available data and further improving the performance of a trained model. Therefore, federated transfer learning would play a pivotal role in the development of smart healthcare and it may be able to take human health care to a whole new

level."