Multivariate Concordance Correlation Coefficient
Open Access
- Author:
- Hiriote, Sasiprapa
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- April 20, 2009
- Committee Members:
- Vernon Michael Chinchilli, Dissertation Advisor/Co-Advisor
Vernon M Chinchilli, Committee Chair/Co-Chair
Donald Richards, Committee Member
Bing Li, Committee Member
Tonya Sharp King, Committee Member
Peter Cm Molenaar, Committee Member - Keywords:
- measures of agreement
repeated measurement
concordance correlation coefficient - Abstract:
- In many clinical studies, the Lin's concordance correlation coefficient (CCC) is a common tool to assess the agreement of a continuous response measured by two raters or methods. However, the need of measures of agreement may arise for more complex situations, such as when the responses are measured on more than one occasion by each rater or method. In this work, we propose a new CCC in the presence of repeated measurements, called the multivariate concordance correlation coefficient. We constructed the multivariate CCC based on a matrix that possesses the properties needed to characterize the level of agreement between two p x 1 vectors of random variables. For ease of interpretation, we transformed this matrix to a scalar whose value is scaled to range between -1 and 1 by using three distinct functions, namely trace, highest eigenvalue, and determinant. It can be shown that the multivariate CCC reduces to Lin's CCC when p = 1. For inference, we proposed an asymptotically unbiased estimator based on U-statistics and derived its asymptotic distribution for each form of the function. The proposed estimators are proven to be asymptotically normal and their performances are evaluated via simulation studies. To obtain a confi dence interval or a test statistic, we considered a sample moment estimator of the asymptotic variance and the Z-transformation to improve the normal approximation and bound the confi dence limits. The simulation studies confi rmed that overall in terms of accuracy, precision, and the coverage probabilities, the estimator of the multivariate CCC based on the determinant function works relatively well in general cases even with small samples. However, for a skewed underlying distribution with moderate or weaker correlation between the two variables, the trace multivariate CCC is slightly more robust. Finally, We used real data from an Asthma Clinical Research Network(ACRN) study and the Penn State Young Women's Health Study for demonstration.