Immunoassays are primary diagnostic and research tools throughout the medical and life sciences. The common approach to the processing of immunoassay data involves estimation of the calibration curve followed by inversion of the calibration function to read off the concentration estimates. This approach, however, does not lend itself easily to acceptable estimation of confidence limits on the estimated concentrations. Such estimates must account for uncertainty in the calibration curve as well as uncertainty in the target measurement. Even point estimates can be problematic: because of the non-linearity of calibration curves and error heteroscedasticity, the neglect of components of measurement error can produce significant bias.