Calibration in immunoassay with proportional errors

In immunoassay, calibration curves are used for transformation of sample responses into concentrations. The calibration curve is a linear or nonlinear regression curve fitted to a set of calibrators (standards) with known concentrations. In this report we discuss consequences of random errors in the dispensed volumes of the calibrators. Provided that these errors are the main source of intra-assay variation, a constant coefficient of variation in concentration could be expected. It is suggested that the curve parameters in this case be estimated by inverse regression (i.e. regression of X on Y ), weighted by squared calibrator concentrations. An approximate formula is derived for the standard deviation in response, given that the response follows a four-parameter logistic function