The analysis of ligand-binding data with experimental uncertainties in the independent variables

Abstract

The method of experimental data analysis known as least-squares requires several inherent assumptions to be met in order for the analysis to be statistically correct. In particular, it must be assumed that the experimental uncertainties exist only on the dependent variables. Least-squares is often used for applications where this assumption is not satisfied. An alternative method of data analysis circumvents the assumption that no experimental uncertainty exists in the independent variables. This method, known as maximum likelihood, will produce statistically correct results in cases where experimental uncertainty exists on both the dependent and independent variables. The method can easily be generalized to include cases where the dependent and independent variables are cross-correlated. The method can also be generalized to include non-Gaussian distributions of experimental uncertainties. The examples presented are simulated applications to ligand-binding problems. The general method is, however, applicable to a wide range of problems in biochemistry.