Statistically accurate estimation of hormone concentrations and associated uncertainties: methodology, validation, and applications

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Abstract
We describe a data reduction procedure to assign statistically accurate estimates of unknown hormone concentrations, with associated uncertainties, based on experimental uncertainties in sample replicates and the fitted calibration curve. Three mathematical calibration curve functions are considered. The one providing optimal statistical characterization of reference calibrators is chosen for unknown evaluation. Experimental error is addressed by assigning and propagating uncertainty estimates for each measured response (including zero-dose responses) by an empirically determined discrete uncertainty profile and by propagating calibration curve uncertainty. Discrete uncertainty profiles account for both response precision (replicability) and accuracy (deviation from predicted calibration curves) without relying on assumed theoretical response variance–assay response relations. The validity of assigning variable response weighting by this procedure was assessed by Monte Carlo simulations based on chemiluminescence growth hormone calibration curves. Much-improved accuracy and estimated precision are achieved for unknown hormone concentrations, particularly extremely low concentrations, by using this variable response weighting procedure.