Error models for immunoassays

For nearly 20 years, we and others have used a three-parameter power function as a direct estimation error model for immunoassays. The main application is imprecision profile plots (after translating from variance to coefficient of variation) but other uses include weighting functions for regression analysis and variance stabilizing transformations. Although generally successful, the intrinsic monotonicity of the function means that it fails to describe small but distinct increases in variance that occasionally occur near the assay detection limit.

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

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

A set of rules, based on an objective goodness-of-fit statistic, can be used to automate presentation of the most appropriate function for any particular data-set. Flexibility is easily incorporated into the selection rules and is actually highly desirable to encourage ongoing evaluation with a wider variety of data. A Win32 computer program that performs the variance function estimation and plotting is freely available.