Beware the correlation coefficient

The correlation coefficient is a well known statistical index widely used in medical literature. However, the correlation coefficient needs careful handling, since an inappropriate use leads to misleading results. In this paper we discuss a tricky situation which can arise when the correlation coefficient is used to quantify the strength of the association between two variables when one of the two (the target) is not directly measurable and a proxy is used instead. The correlation with the proxy is generally different from the correlation with the target. Although it is not possible to calculate the correlation coefficient with the target from the correlation with the proxy, a simple method for calculating an admissibility interval for the correlation with the target is presented. In spite of one might expect, it is possible that, in some circumstances, a positive correlation could be negative, i.e. a positive correlation coefficient with the proxy could be found even if the correlation with the target is zero or even negative.