I have run a GWAS and used PRSice (https://www.prsice.info/) to calculate polygenic risk scores on the data collected from the GWAS. I need to check whether alcohol dependence can predict gambling disorder, through the PRS. However I am having trouble with how exactly to do that. I have a GWAS on alcohol disorder from the one population and a GWAS on gambling and alcohol disorder from the other population, then I calculated PRS for the three GWAS datasets, but how do I use the one to predict in the other? Through the literature it was suggested to use linear mixed models, which I have done but I still feel as if I am doing it wrong as I only did the model on the one dataset and not the two combined.
Before doing anything else, you should split your dataset into training and test groups, and [this is important] don't touch the test dataset until you're fully confident that your approach is correct: no post-test modification.
A split that's considered acceptable in Computer Science is a 10%/90% split, i.e. use 10% of the data for training / algorithm generation and the remaining 90% for testing. This will give you good confidence that the algorithm works.
I personally think it's a good idea to do population sub-sampling (i.e. further subsample that 10%) to determine an informative marker set prior to any risk calculations. What you should be looking for are markers that are consistently linked with the trait of interest (i.e. in your case alcohol dependence) in multiple sub-sampled populations. I go into a lot of detail about how to do this here [bearing in mind it's an old pre-print, and doesn't do the 10/90 split I've recommended above].
After you're happy with the marker set, calculate the risk scores only using that set (hopefully PRSice can do this), then carry that risk score [only] through to test against the dependent trait of interest in the training dataset (i.e. in your case gambling disorder). If your dependent trait is a binary trait, this could be done using ROC analysis (as in my preprint) to calculate area under the curve. Or use linear mixed models, whatever works for you.
Make any changes you think you need to improve the test result (e.g. changing the composition of the marker set).
After convincing yourself that the approach is correct, do the same risk score calculation (using the same set of markers) on the test set, find out how well it predicts the dependent trait, and report on the results. Don't change anything.