Concordance correlation coefficient under multiplicative distortion measurement errors

We study the estimation of the concordance correlation coefficient (CCC) under the multiplicative distortion measurement errors. These unobservable variables are distorted in a multiplicative fashion by an observed confounding variable. A direct estimator and a two-steps estimators of CCC are proposed under the conditional mean, the conditional absolute mean, the conditional variance, the conditional absolute logarithmic mean calibration methods. The asymptotic results of estimators and the asymptotic confidence intervals for CCC are studied under different calibration methods. Simulation studies demonstrate the performance of the proposed procedure in this paper, and a real example is analyzed to illustrate its practical usage.