Jornal de Biometria e Bioestatística

Comparison of Dependent Pearson and Spearman Correlation Coefficients with and without Correction for Measurement Error

Abstract

Bernard Rosner, Wei Wang, Heather Eliassen and Eileen Hibert

There already exist methods for comparing dependent Pearson correlation coefficients. However, each of the variables (X, Y) has associated random error; and a related question is after correcting for random error, which variable correlates most highly with the outcome variable Z. In this paper, we present methods for comparing dependent deattenuated correlation coefficients. This is a generalization of previous work for obtaining confidence limits for a single deattenuated correlation coefficient. In addition, we extend this work to the comparison of dependent Spearman correlation coefficients. The methods are illustrated with two examples. The first example concerns the comparison of nephrotoxicity of phenacetin and aspirin intake as measured by repeat biomarkers obtained from the same subjects. The second example is a comparison of the validity of different storage conditions for measuring HbA1c from dried blood specimens as compared to the gold standard of immediate processing. Results from using these methods indicate that phenacetin intake is more highly correlated with serum creatinine levels than aspirin intake and that short-term storage is preferable to long-term storage for assessment of HbA1c levels. We have available SAS software for comparing dependent deattenuated Pearson correlation and dependent Spearman correlations with and without deattentuation.