On improved calibrations of unknowns in a system of quality-controlled assays

Two new estimators for calibrating unknowns from dose-response curves, in a system of quality-controlled assays, are examined. In contrast with the conventional estimator which uses only the results of the one assay in which the response of the unknown dose is measured, the new estimators also utilize the results of all other assays through the replications of the control samples in the system. The first estimator is based on maximizing the likelihood of the given system (with respect to the different dose-response parameters, the levels of the control samples and the levels of the unknowns) when response errors are normally distributed. The second estimator is a regression-like estimator obtained by subtracting from the conventional estimator its estimated regression on the deviation of the calibrated control levels in the given assay from their average values in the system. Evaluations of the reductions in bias and variance attained by the new estimators show when substantial reductions in mean square error can be expected. The new estimators are illustrated with a system of 22 hFSH radioimmunoassays.