Multiple estimation of concentrations in immunoassay using logistic models.

Immunoassay techniques yield estimates of concentrations of analytes based on comparison to known concentrations of a reference solution. The use of the nonlinear logistic model makes the error estimates and confidence levels approximate. When the goal of such a study is estimation of several unknowns, methods in common usage do not account for 'simultaneous' inference, i.e. the repeated use of the standard curve for estimating several concentrations. Alternative methods are described which take multiple use of the reference curve into account. Simulations using normally distributed data with variance proportional to a power of the mean compare different methods of obtaining calibration intervals and illustrate the approximate nature of all such techniques. Calibration intervals based on simple, commonly used methods do not provide the coverage promised, even for one-at-a-time estimation, and are not suited for multiple estimation and comparison.