1. Department of Mathematics and Statistics, Texas Tech University, Broadway and Boston, Lubbock, TX 79409-1042, USA.
Background: A method comparison study is a topic of considerable interest in health and biomedical-related fields. The use of this study is to compare a new method with a standard established method. There are two typical steps in method comparison studies, namely modeling the data set and using the fitted model to analyze method comparison data.
Methods: As a usual practice to model method comparison data, many recommend a mixed-effects model which assumes constant error variance (homoscedasticity) and normality of error terms. However, these assumptions are generally violated in practice. Thus, in this study, our main goal is to propose a copula based model to deal with non-replicated method comparison data. Moreover, a simulation procedure is carried out to validate the proposed model by means of different copula models.
Results: Results indicate that the Normal and Gumbel copulas give more accurate results in terms of bias, mean-squared error and coverage probability values of estimators. Further it is confirmed that the accuracy of model increases with the Kendall tau (τ) correlation between methods and the number of observations. Furthermore, the proposed methodology is illustrated by analyzing finger and arm systolic blood pressure data. Besides the Total Deviation Index (TDI) and Concordance Correlation Coefficient (CCC) values are used to check the agreement between the two methods.
Conclusion: The proposed model based on the Copula method can be used to model the method comparison data with balanced and unbalanced data designs.
Keywords: Method comparison, Concordance Correlation, Copula theory, Mixed-effects model, Total Deviation Index