Alternatives to Least Squares Linear Regression Analysis for Computation of Standard Curves for Quantitation by High Performance Liquid Chromatography: Applications to Clinical Pharmacology

Standard curves and validation points for high-performance liquid chromatography (HPLC) determination of four drugs (carbamazepine and phenytoin at therapeutic drug monitoring concentrations and deuterium labeled carbamazepine and phenytoin at tracer dose concentrations) were computed using standard least squares linear regressions analysis and six alternative regression techniques (weighted 1/x, 1/y, 1/x2, 1/y2 least squares linear, log/log least squares linear, and robust). The coefficient of determination (R2) and the coefficient of prediction (R2pred) values for standard curves and the computed values for validation points did not differ significantly among the seven methods. The lower limit of quantitation (LLQ) values obtained with all six of the alternative regression methods were significantly (P < .01) lower than the LLQ values obtained with least squares linear regression analysis. The lowest LLQ values were obtained with 1/x2 and 1/y2 weighting and were threefold to tenfold less than the values obtained with unweighted least squares linear regression analysis (P < .001). The authors conclude that alternative regression analysis techniques (especially 1/x2 and 1/y2 weighting) offer significant advantages for clinical pharmacology studies when concentration values being measured by HPLC are near the LLQ of the method determined by unweighted least squares linear regression analysis. In other situations, alternative forms of regression analysis had no significant advantages in our study.