Statistical Techniques in Predicting Thermal Stability

In developing new pharmaceutical products it is often necessary to predict degradation rates at marketing temperatures from data collected on accelerated degradation taken at elevated temperatures. A technique for predicting degradation rate based on the Arrhenius equation was presented by Garrett in 1956. While his method is characterized by ease of computation involved (necessary due to scarcity of computer facilities at that time), it violates a number of assumptions upon which leastsquares analysis is based, and hence inferences made from the results can be misleading. This report presents a method based on weighted least-squares analysis which can easily be adapted for computer analysis. Comparisons are made with the method suggested by Garrett to illustrate differences in technique and the effect the basic assumptions have upon the results obtained by the two methods. A statistical test is presented for determining the applicability of the Arrhenius relation to the data at hand. Finally, the technique is illustrated by application to chloramphenicol.