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I currently have data from several studies, with each having different sample sizes and possibly different set-ups. There is a common binary variable of interest across all studies that I would like to predict. Suppose I have $5$ studies, $s \in \{1, \ldots, 5\}$, with each study having a $Y_s$ vector of binary outcomes, and an $X_s$ matrix of predictors in the columns and observations by row. One idea I have is to train a classifier method on each of the data pairs across the $5$ studies:

$$ (Y_1, X_1), \ldots, (Y_5, X_5) $$

Then somehow aggregate them. What becomes complicated is how I should think about the training/testing set breakdowns. In other words, should I break the sets according to study and if so, how can I combine them later?

I am wondering generally if such frameworks exist for machine learning methods across many studies. Thanks.

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