Conducting correlation analysis: important limitations and pitfalls

The correlation coefficient is a statistical measure often used in studies to show an association between variables or to look at the agreement between two methods. In this paper, we will discuss not only the basics of the correlation coefficient, such as its assumptions and how it is interpreted, but also important limitations when using the correlation coefficient, such as its assumption of a linear association and its sensitivity to the range of observations. We will also discuss why the coefficient is invalid when used to assess agreement of two methods aiming to measure a certain value, and discuss better alternatives, such as the intraclass coefficient and Bland-Altman's limits of agreement. The concepts discussed in this paper are supported with examples from literature in the field of nephrology.