Error models for immunoassays

Ann Clin Biochem 2008;45:481-485
© 2008 Association for Clinical Biochemistry



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Original Articles

William A Sadler

Department of Nuclear Medicine, Christchurch Hospital, Private Bag 4710, Christchurch, New Zealand

Corresponding author: William A Sadler. Email: bill.sadler{at}

Background: For nearly 20 years, we and others have used a three-parameterpower function as a direct estimation error model for immunoassays.The main application is imprecision profile plots (after translatingfrom variance to coefficient of variation) but other uses includeweighting functions for regression analysis and variance stabilizingtransformations. Although generally successful, the intrinsicmonotonicity of the function means that it fails to describesmall but distinct increases in variance that occasionally occurnear the assay detection limit.

Methods: A systematic comparison of five variance functions was undertaken,using randomly drawn samples from a large body of real immunoassaydata.

Results: Variance function accuracy (hence imprecision profile accuracy)can be markedly improved, particularly near the assay detectionlimit, by employing a pair of complementary three-parameterpower functions, together with a constrained four-parameterfunction, which provides for a variance turning point.

Conclusions: A set of rules, based on an objective goodness-of-fit statistic,can be used to automate presentation of the most appropriatefunction for any particular data-set. Flexibility is easilyincorporated into the selection rules and is actually highlydesirable to encourage ongoing evaluation with a wider varietyof data. A Win32 computer program that performs the variancefunction estimation and plotting is freely available.

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