Batch effects are pervasive in biomedical studies. One approach to address the batch effects is repeatedly measuring a subset of samples in each batch. These remeasured samples are used to estimate and correct the batch effects. However, rigorous statistical methods for batch-effect correction with remeasured samples are severely underdeveloped. Here we developed a framework for batch-effect correction using remeasured samples in highly confounded case-control studies. We provided theoretical analyses of the proposed procedure, evaluated its power characteristics and provided a power calculation tool to aid in the study design. We found that the number of samples that need to be remeasured depends strongly on the between-batch correlation. When the correlation is high, remeasuring a small subset of samples is possible to rescue most of the power.