A scientific and statistical analysis of accelerated aging for pharmaceuticals. Part 1: accuracy of fitting methods

Abstract

Three competing mathematical fitting models (a point-by-point estimation method, a linear fit method, and an isoconversion method) of chemical stability (related substance growth) when using high temperature data to predict room temperature shelf-life were employed in a detailed comparison. In each case, complex degradant formation behavior was analyzed by both exponential and linear forms of the Arrhenius equation. A hypothetical reaction was used where a drug (A) degrades to a primary degradant (B), which in turn degrades to a secondary degradation product (C). Calculated data with the fitting models were compared with the projected room-temperature shelf-lives of B and C, using one to four time points (in addition to the origin) for each of three accelerated temperatures. Isoconversion methods were found to provide more accurate estimates of shelf-life at ambient conditions. Of the methods for estimating isoconversion, bracketing the specification limit at each condition produced the best estimates and was considerably more accurate than when extrapolation was required. Good estimates of isoconversion produced similar shelf-life estimates fitting either linear or nonlinear forms of the Arrhenius equation, whereas poor isoconversion estimates favored one method or the other depending on which condition was most in error.

Keywords: Arrhenius fitting; accelerated stability; chemical stability; in silico modeling; isoconversion; kinetics; mathematical model; shelf-life; stability.