L-STATISTICS OF ABSOLUTE DIFFERENCES FOR QUANTIFYING THE AGREEMENT BETWEEN TWO VARIABLES
Open Access
- Author:
- Tashakor, Elahe
- Graduate Program:
- Biostatistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 28, 2019
- Committee Members:
- Vernon Michael Chinchilli, Dissertation Advisor/Co-Advisor
Vernon Michael Chinchilli, Committee Chair/Co-Chair
Tonya Sharp King, Committee Member
Ming Wang, Committee Member
David Spencer Phelps, Outside Member - Keywords:
- Agreement
Concordance correlation coefficient
L-statistics
Robust estimation - Abstract:
- In many clinical studies, Lin’s (1989) concordance correlation coefficient (CCC) is a popular measure of agreement for continuous outcomes. Most commonly, it is used under the assumption that data are normally distributed. However, in many practical applications, data are often skewed and/or thick-tailed. King and Chinchilli (2001b) proposed robust estimation methods of alternative CCC indices, and we propose an approach that extends the existing methods of robust estimators by focusing on functionals that yield robust L-statistics. We then extend the application of this class of estimators to a multivariate situation, possibly repeated measurements, based on a matrix norm that possesses the properties needed to characterize the level of agreement between two p × 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 a Frobenius norm function and compared it to a matrix-based concordance correlation coefficient (MCCC) developed by Hiriote and Chinchilli (2011). The results of simulation studies confirmed that when encountering thick-tailed or skewed data, the robust approach for estimating the CCC between two variables is a more accurate approach than Lin’s CCC in the univariate case and the MCCC in the multivariate case. Finally, we provide data examples to illustrate the methodology.