General approach to handling nonuniform variance in assay calibration

A general method for handling nonuniform variance in data from assay calibrations is discussed. Calibration data from the analysis of ibuprofen and aspirin by high-performance liquid chromatography was analysed by the traditional least squares method; nonuniform error variance was found to be significant. Weighted least squares analysis overcomes the problem of nonuniform variance but relies on good estimates of the error variance. The method of extended least squares, a maximum likelihood method, is described which incorporates handling of the weighting in the regression analysis. The extended least squares method produces accurate and precise estimates of the parameters of the calibration and allows precise estimates of the variance of future predictions, provided that a sufficient number of calibrators are used.