Check this paper: Batch Effect Confounding Leads to Strong Bias in Performance Estimates Obtained by Cross-Validation (PMC4072626) that measures how bad batch effects are. Perhaps the same simulations could be used to show how to avoid them. code
The bias in the cross-validation performance estimates is not eliminated by the batch effect removal, and consequently the cross-validation performance estimates obtained after batch effect elimination are not more reliable measures of the true performance than those obtained without batch effect elimination.
Check this paper: Batch Effect Confounding Leads to Strong Bias in Performance Estimates Obtained by Cross-Validation (PMC4072626) that measures how bad batch effects are. Perhaps the same simulations could be used to show how to avoid them. code