The Basis Function Regression in pharmaceutical analysis: Theory and example of application

The BFR (Basis Function Regression) is an interesting alternative to common techniques (such as PCR or PLS) in chemometrics. It is based on projecting the spectral information onto some number of equally spaced spline bases, than obtaining integrals of resulted curves. Existing references show that in certain cases it can reduce almost twice the RMSEP values. As this technique is not so popular in chemometrics nor applied in pharmaceutical analysis, it is desirable to present its theoretical considerations and implementation (with example MATLAB/Octave code). As an illustrative example we present the chemometric model for content recognition of a tablet (12 possible compounds in binary or ternary combinations) from the UV spectrum of its methanolic extract. The BFR technique gave lowest prediction error and the estimators obtained have more meritorical meaning than in case of PCR, PLS and other techniques used for comparison. In our opinion this technique should be considered in any chemometric approach as it often shows better performance.