Application of nonlinear fitting and selection of the most fitted equation by AIC in stability test of pharmaceutical ingredients

We proposed a method for objectively selecting the most fitted rate equation among candidate rate equations based on chemical kinetics by both nonlinear regression analysis and Akaike's information criterion (AIC), to express the decrease of pharmaceutical ingredient as an appropriate equation. Pseudo-zero, first, and second-order rate equations were prepared as candidates beforehand, and AIC was introduced for selecting the most fitted rate equation among the candidates. We compared the proposed method to the Weibull method that expressed any decrease patterns as a single equation.

We quantified the contents of thiamine nitrate (VB1) and taurine after storage for one, three, and six months under 40°C-75% relative humidity by high-pressure liquid chromatography. Decrease patterns of each sample were most fitted to one of the candidate rate equations, that is, pseudo-zero, first, and second-order rate equations, respectively, and the degree of fit in the most fitted equation was superior to that of the Weibull method, except for the pseudo-first-order rate equation.

Moreover, we confirmed that the proposed method was considerably precise for estimating the stability of pharmaceuticals by comparing estimated residual rates and confidence intervals to experimental data.