Correlation and agreement: overview and clarification of competing concepts and measures.
Agreement and correlation are widely-used concepts that assess the association between variables. Although similar and related, they represent completely different notions of association. Assessing agreement between variables assumes that the variables measure the same construct, while correlation of variables can be assessed for variables that measure completely different constructs. This conceptual difference requires the use of different statistical methods, and when assessing agreement or correlation, the statistical method may vary depending on the distribution of the data and the interest of the investigator. For example, the Pearson correlation, a popular measure of correlation between continuous variables, is only informative when applied to variables that have linear relationships; it may be non-informative or even misleading when applied to variables that are not linearly related. Likewise, the intraclass correlation, a popular measure of agreement between continuous variables, may not provide sufficient information for investigators if the nature of poor agreement is of interest. This report reviews the concepts of agreement and correlation and discusses differences in the application of several commonly used measures.
Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, USA.
Jinyuan
J
Liu
Department of Biostatistics & Bioinformatics, School of Public Health and Tropical Medicine, Tulane University, New Orleans, LA, USA.
Wan
W
Tang
Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, USA.
Guanqin
G
Chen
VA Cooperative Studies Program Palo Alto Coordinating Center, VA Palo Alto Health Care System, Palo Alto, CA, USA ; Department of Biomedical Data Science, Stanford University, Stanford, CA, USA.
Yin
Y
Lu
Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, USA.
Changyong
C
Feng
Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, USA.
Xin M
XM
Tu
Kendall's tau; Pearson's correlation; Spearman's rho; concordance correlation; intraclass correlation; non-linear association