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Assessment of agreement under nonstandard conditions using regression models for mean and variance. (English) Zbl 1091.62112

Summary: The total deviation index of L. Lin [Stat. Med. 19, 255–270 (2000)] and L. Lin et al. [J. Am. Stat. Assoc. 97, 257–270 (2002; Zbl 1073.62583)] 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 points 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J99 Linear inference, regression
65C05 Monte Carlo methods

Citations:

Zbl 1073.62583

Software:

SemiPar; R
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Full Text: DOI

References:

[1] Bland, Statistical methods for assessing agreement between two methods of clinical measurement, Lancet 1 pp 307– (1986) · doi:10.1016/S0140-6736(86)90837-8
[2] Bland, Measuring agreement in method comparison studies, Statistical Methods in Medical Research 8 pp 135– (1999) · doi:10.1191/096228099673819272
[3] Carroll, Transformation and Weighting in Regression (1988) · doi:10.1007/978-1-4899-2873-3
[4] Choudhary, Advances in Ranking and Selection, Multiple Comparisons, and Reliability pp 215– (2004)
[5] Efron, An Introduction to the Bootstrap (1993) · doi:10.1007/978-1-4899-4541-9
[6] Guttman, Encyclopedia of Statistical Sciences 9 pp 272– (1988)
[7] Hawkins, Diagnostics for conformity of paired quantitative measurements, Statistics in Medicine 21 pp 1913– (2002) · doi:10.1002/sim.1013
[8] Lehmann, Elements of Large Sample Theory (1998)
[9] Lin, A concordance correlation coefficient to evaluate reproducibility, Biometrics 45 pp 255– (1989) · Zbl 0715.62114 · doi:10.2307/2532051
[10] Lin, Total deviation index for measuring individual agreement with applications in laboratory performance and bioequivalence, Statistics in Medicine 19 pp 255– (2000) · doi:10.1002/(SICI)1097-0258(20000130)19:2<255::AID-SIM293>3.0.CO;2-8
[11] Lin, Statistical methods in assessing agreement: Models, issues, and tools, Journal of the American Statistical Association 97 pp 257– (2002) · Zbl 1073.62583 · doi:10.1198/016214502753479392
[12] Loader, Local Regression and Likelihood (1999)
[13] Pinheiro, Mixed-Effects Models in S and S-PLUS (2000) · Zbl 0953.62065 · doi:10.1007/978-1-4419-0318-1
[14] R Development Core Team, R: A Language and Environment for Statistical Computing (2004)
[15] Ruppert, Semiparametric Regression (2003) · Zbl 1038.62042 · doi:10.1017/CBO9780511755453
[16] Sun, Multiple comparisons of a large number of parameters, Biometrical Journal 43 pp 627– (2001) · Zbl 0978.62059 · doi:10.1002/1521-4036(200109)43:5<627::AID-BIMJ627>3.0.CO;2-F
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