Application of kalman filter statistical technique in pharmaceutics

Abstract

Pharmaceutics experiments involving time-dependent or space-dependent observations are generally subjected to single or multiple regression analysis based on the tacit assumption that the regression coefficients are fixed and invariant through time or across space. However, this assumption is invariably not tenable, specially for this type of observations, and the coefficients do indeed vary during the experiment through time or across space. The results of the analysis which does not take this aspect into consideration may be inaccurate. For instance, the results of the standard least squares analysis applied to a multicomponent mixture experiment to determine the concentrations of individual components will be absolutely misleading in the presence of parametric variation. Kalman filter statistical technique is devised to handle such complex problems. A detailed description of the technique is presented in the context of a specific pharmaceutic experiment. For the purpose of data analysis, one has the choice of applying one of the three models, fixed parameter model (standard least squares), random coefficient model, or variable (stochastic) parameter model. The unique feature of this presentation is the introduction of the three statistical tests of validity which, upon application, can delineate the single model appropriate for the analysis of the available data. Finally, for the purpose of illustration, the numerical results of the statistical analysis of two multicomponent mixture experiments are presented and appropriately interpreted.