"Correlation does not imply causation, but a lack of correlation does suggest (not prove, but suggest) a lack of causation." I don't think it's any stronger on

"Correlation does not imply causation, but a lack of correlation does suggest (not prove, but suggest) a lack of causation." I don't think it's any stronger one way or the other. Correlation does not imply causation; it may suggest it, but there may be confounders. And lack of correlation does not imply lack of causation, because there may be confounders that mask results that would suggest causation. Showing causation is hard and usually takes careful design of experiment with very good controls to eliminate any potential confounders, something that is not present in retrospective studies.