Assessment of Agreement under Nonstandard Conditions Using Regression Models for Mean and Variance

• Published in: Biometrics 2006-03, Vol.62 (1), p.288-296
• Main Authors: Choudhary, Pankaj K, Tony Ng, Hon Keung
• Format: Article
• Language: English
• Subjects: Approximation; Biometrics; biometry; Bootstrap; Consultant's Forum; Covariance matrices; Critical points; Cyclosporins; Distribution; Likelihood Functions; Limits of agreement; Linear regression; Matched-Pair Analysis; Maximum likelihood estimation; Measurement techniques; Method comparison; Mixed model; Modeling; Models, Statistical; Penalized spline; probability; Regression Analysis; Sample Size; Simultaneous tolerance band; Statistical Distributions; Statistical methods; statistical models; Statistical variance; Total deviation index; variance
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.1541-0420.2005.00422.x

The total deviation index of Lin (2000, Statistics in Medicine19, 255–270) and Lin et al. (2002, Journal of the American Statistical Association97, 257–270) is an intuitive approach for the assessment of agreement between two methods of measurement. It assumes that the differences of the paired measurements are a random sample from a normal distribution and works essentially by constructing a probability content tolerance interval for this distribution. We generalize this approach to the case when differences may not have identical distributions—a common scenario in applications. In particular, we use the regression approach to model the mean and the variance of differences as functions of observed values of the average of the paired measurements, and describe two methods based on asymptotic theory of maximum likelihood estimators for constructing a simultaneous probability content tolerance band. The first method uses bootstrap to approximate the critical point and the second method is an analytical approximation. Simulation shows that the first method works well for sample sizes as small as 30 and the second method is preferable for large sample sizes. We also extend the methodology for the case when the mean function is modeled using penalized splines via a mixed model representation. Two real data applications are presented.