Method comparison on confidence interval construction for the slope in a linear measurement model with heteroscedastic errors
In analytical chemistry, the evaluation on performance accuracy of an analytical method is an important issue. When an adjusted or new method (test method) is developed, the linear measurement error model is commonly used to compare it with another reference method. For this routine practice, the measurements on the reference method can be placed on the x-axis, whereas those of the test method on the y-axis, then the slope of this linear relationship indicates the agreement between them and also the performance of the test method. Under the assumption that both variables are subject to heteroscedastic measurement errors, a novel approach based on the concepts of a generalized pivotal quantity (GPQ) is proposed to construct confidence intervals for the slope. Its performance is compared with two maximum likelihood estimation (MLE)-based approaches through simulation studies. It is shown that the proposed GPQ-based approach is capable of maintaining the empirical coverage probabilities close to the nominal level and yielding reasonable expected lengths. The GPQ-based approach can be recommended in practical use because of its easy implementation and better performance than the MLE-based approaches in most simulation scenarios. Two real datasets are given to illustrate the approaches. Copyright (C) 2011 John Wiley & Sons, Ltd.
measurement error model errors-in-variables model generalized confidence interval generalized pivotal quality