Analisi di stabilità: modelli d'effetti misti

Abstract

In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a stability analysis, is to determin the period of time within wich the compound conserve its initial characetris. 
At each time point an evaluation a previous trend analysis is caried out. The underlining trend is supposed to be linear or reduced to be linear following the equation C=a+b_t, where C is the level of active content. 
The determination of such trend allows the estimation of the content at varous time points, and to check if the level is greater  than a fixed value (the specification). This value represent theminimal condition the copmound must fulfill.,that is:ICH and FDA guide-lines recommend that the lower confidence limit is reported too. If such limit at a time point si greater than the specification,then at such time the specification is fulfilled.Such analysis is performed under the condition of classical regression model. 
An alternative approach is represented by the use of a mixed model in which the batch effect is regarded as a random effect. This approach appear, from a theoretical point of view, more appealing, since it does not reguest to adopt the step wise procedure seen below. The difference between batch is a variability factor whose effect the variability of the observed result. Such variability can be modelled using a suitable covariance matrix.