Iteratively Adjusted Surrogate Variable Analysis (IA-SVA) is a statistical framework to uncover hidden sources of variation even when these sources are correlated. IA-SVA provides a flexible methodology to i) identify a hidden factor for unwanted heterogeneity while adjusting for all known factors; ii) test the significance of the putative hidden factor for explaining the unmodeled variation in the data; and iii), if significant, use the estimated factor as an additional known factor in the next iteration to uncover further hidden factors.