Variance weighting functions in radioimmunoassay calibration.

Software packages for radioimmunoassay calibration assume that expected counting rate is a function of ligand dose. Previous studies have indicated that variances of counting rate are also related to dose, but the structure of individual assays does not permit precise estimation of counting rate variances at individual doses. The method described here uses results from an accumulation of assays to characterize the relationship between mean and variance of counting rate, thus providing a variance weighting function for the calibration. Analysis of 140 cortisol assays, all with two replicates of each of 50 sources (9 standard doses, 3 quality control preps, and 38 unknowns), led to an asymmetric rising ogive relating variances to means of counting rates. A rectangular hyperbola provided an adequate characterization of this relationship in an accumulation of 21 testosterone assays. Relationships between mean and variance of counting rate in 19 growth hormone assays and 7 triiodothyronine assays were characterized by a straight line and a rising exponential curve, respectively. Calibration curves, such as the commonly adopted logistic ogive in relation to log dose, are fitted by weighted least squares to observed counts directly using empirical weights proportional to the reciprocal of estimated counting variance. The advantage of this method is that all observations contribute to the calibration in accordance with their merit.