Meta-analysis is becoming an increasingly popular and powerful tool to integrate findings across studies and OMIC dimensions. But there is the danger that hidden dependencies between putatively "independent" studies can cause inflation of type I error, due to reinforcement of the evidence from false-positive findings. We present here a simple method for conducting meta-analyses that automatically estimates the degree of any such non independence between OMIC scans and corrects the inference for it, retaining the proper type I error structure. The method does not require the original data from the source studies, but operates only on summary analysis results from these in OMIC scans. The method is applicable in a wide variety of situations including combining GWAS and or sequencing scan results across studies with dependencies due to overlapping subjects, as well as to scans of correlated traits, in a meta-analysis scan for pleiotropic genetic effects. The method correctly detects which scans are actually independent in which case it yields the traditional metaanalysis, so it may safely be used in all cases, when there is even a suspicion of correlation amongst scans.