Weighting functions and parameter resolvability for oxygenation data subject to error in the independent variable

Parameter resolvability and bias has been investigated for weighted nonlinear regression of data where the independent variable is subject to instrumental uncertainty. The specific example of cooperative oxygenation of hemoglobin was studied, where fractional saturation is determined spectrophotometrically and the oxygen activity is measured with a Clark polarographic electrode. For this system the instrumental uncertainty in the oxygen electrode was measured directly and the influence of the uncertainties on resolution of oxygen binding parameters was determined by Monte Carlo simulations. Four weighting functions were tested for their ability to minimize parameter uncertainty and bias: (1) uniform weighting; (2) "propagated weighting" whereby uncertainties in the independent variable are propagated into and added to uncertainties of the dependent variable; (3) Hill plot transform, or "end weighting"; and (4) maximum likelihood analysis, where deviations between fitting function and data are minimized as weighted horizontal and vertical distance vectors. Results of the Monte Carlo simulations favor the use of either uniform weighting, propagated weighting, or maximum likelihood weighting methods. Use of the Hill transform as a weighting function produced poorer parameter resolvability and inaccurate representation of the data in general. Bias error was negligible for all weighting functions.