A heteroscedastic Bayesian model for method comparison data

When implementing newly proposed methods on measurements taken from a human body in clinical trials, the researchers carefully consider whether the measurements have the maximum accuracy. Further, they verified the validity of the new method before being implemented in society. Method comparison evaluates the agreement between two continuous variables to determine whether those measurements agree on enough to interchange the methods. Special consideration of our work is a variation of the measurements with the magnitude of the measurement. We propose a method to evaluate the agreement of two methods when those are heteroscedastic using Bayesian inference since this method offers a more accurate, flexible, clear, and direct inference model using all available information. A simulation study was carried out to verify the characteristics and accuracy of the proposed model using different settings with different sample sizes. A gold particle dataset was analyzed to examine the practical viewpoint of the proposed model. This study shows that the coverage probabilities of all parameters are greater than 0.95. Moreover, all parameters have relatively low error values, and the simulation study implies the proposed model deals with the higher heteroscedasticity data with higher accuracy than others. In each setting, the model performs best when the sample size is 500.