Analytical and Bioanalytical Chemistry

, Volume 405, Issue 14, pp 4835–4848 | Cite as

Comparative study of some robust statistical methods: weighted, parametric, and nonparametric linear regression of HPLC convoluted peak responses using internal standard method in drug bioavailability studies

  • Mohamed A. KoranyEmail author
  • Hadir M. Maher
  • Shereen M. Galal
  • Marwa A. A. Ragab
Research Paper


This manuscript discusses the application and the comparison between three statistical regression methods for handling data: parametric, nonparametric, and weighted regression (WR). These data were obtained from different chemometric methods applied to the high-performance liquid chromatography response data using the internal standard method. This was performed on a model drug Acyclovir which was analyzed in human plasma with the use of ganciclovir as internal standard. In vivo study was also performed. Derivative treatment of chromatographic response ratio data was followed by convolution of the resulting derivative curves using 8-points sin x i polynomials (discrete Fourier functions). This work studies and also compares the application of WR method and Theil's method, a nonparametric regression (NPR) method with the least squares parametric regression (LSPR) method, which is considered the de facto standard method used for regression. When the assumption of homoscedasticity is not met for analytical data, a simple and effective way to counteract the great influence of the high concentrations on the fitted regression line is to use WR method. WR was found to be superior to the method of LSPR as the former assumes that the y-direction error in the calibration curve will increase as x increases. Theil's NPR method was also found to be superior to the method of LSPR as the former assumes that errors could occur in both x- and y-directions and that might not be normally distributed. Most of the results showed a significant improvement in the precision and accuracy on applying WR and NPR methods relative to LSPR.


Comparison between RSD (percent) and E r (percent) calculated for Acyclovir, for area, D 1, and D 1/FF in the internal standard methods, using the three types of regression models: parametric, nonparametric, and weighted


Weighted regression method Nonparametric regression Chemometrics HPLC Fourier transform Bioavailability 



The authors are thankful to Pharaonia Pharmaceuticals (Alexandria, Egypt) for supplying the raw materials.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mohamed A. Korany
    • 1
    Email author
  • Hadir M. Maher
    • 1
  • Shereen M. Galal
    • 1
  • Marwa A. A. Ragab
    • 1
  1. 1.Department of Pharmaceutical Analytical Chemistry, Faculty of PharmacyUniversity of AlexandriaAlexandriaEgypt

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