Variance functions and the minimum detectable concentration in assays

Abstract

Assay data are often fitted by a nonlinear heteroscedastic regression model with the standard deviation of the response typically taken to be proportional to a power θ of the mean. For many assays, how one estimates θ does not greatly affect estimates of the mean regression function. Assay analysis also involves estimation of auxiliary calibration constructs such as minimum detectable concentration. An asymptotic theory is developed to show that standard methods for estimating θ lead to estimators for minimum detectable concentration that can differ markedly in efficiency. Simulation results support the asymptotic theory.