Hyperbolic confidence bands of errors-in-variables regression lines applied to method comparison studies

Abstract

This paper focuses on the confidence bands of errors-in-variables regression lines applied to method comparison studies. When comparing two measurement methods, the goal is to ’proof’ that they are equivalent. Without analytical bias, they must provide the same results on average notwithstanding the errors of measurement. The results should not be far from the identity line Y = X (slope (b) equal to 1 and intercept (a) equal to 0). A joint-CI is ideally used to test this joint hypothesis and the measurement errors in both axes must be taken into account. DR (Deming Regression) and BLS (Bivariate Least Square regression) regressions provide consistent estimated lines (confounded under homoscedasticity). Their joint-CI with a shape of ellipse in a (b;a) plane already exist in the literature. However, this paper proposes to transform these joint-CI into hyperbolic confidence bands for the line in the (X;Y) plane which are easier to display and interpret. Four methodologies are proposed based on previous papers and their properties and advantages are discussed. The proposed confidence bands are mathematically identical to the ellipses but a detailed comparison is provided with simulations and real data.When the error variances are known, the coverage probabilities are very close to each other but the joint-CI computed with the maximum likelihood (ML) or the method of moments provide slightly better coverage probabilities. Under unknown and heteroscedastic error variances, the ML coverage probabilities drop drastically while the BLS provide better coverage probabilities.