Statistical prediction of drug stability based on nonlinear parameter estimation

The classical approach in Arrhenius prediction of drug stability uses two sequential steps of linear regression involving (a) a function of drug content versus time to obtain the rate constants (k) at several elevated temperatures and (b) the relationship of logarithm of mean k versus reciprocal temperature to predict the room temperature rate constant and hence the shelf‐life of the drug. Uncertainties in drug content determinations are often neglected in the second regression. The classical approach also provides a wide and unsymmetrical 95% confidence interval for the predicted shelf‐life. We have developed equations which allow for direct statistical prediction of shelf‐life using observed values of drug content, time, and temperature. Nonlinear regression analysis was employed to provide parameter estimates of drug shelf‐life and the energy of activation. The developed approach was shown to provide good estimates of shelf‐life with meaningful statistics of reactions over a wide range of stability and energetics, with various kinetic orders, with different levels of noise in the data, and with different types of data structure. Comparison between the nonlinear approach and the classical approach showed that the nonlinear approach provided better mean estimates of shelf‐life with much smaller and more symmetrical 95% confidence intervals than the classical approach. The method appears sufficiently robust and wide‐ranging as to be potentially applicable for the prediction of the drug stability of pharmaceutical products.