« DISSOLUTION
As suggested by the categories’ nomenclature, the main difference between MIM and MDM lies in the fact that, while the former can be calculated directly from the dissolution data, the latter require prior adjustment of the data to a model or equation that describes its temporal evolution. Therefore, the simplicity of calculation is the first advantage that one finds when working with MIM, such as the difference and similarity factors, f1
and f2 , and the statistical comparisons
of parameters obtained from the profiles as the area under the curve (AUC) and its related parameter, the dissolution efficiency (DE).
The f2 and f1 factors are very easy to compute and two given profiles
are considered similar if the f2 value between them is greater than or equal to 50 and the f1 less than 15 [6, 8]. It is important to note that the value of the similarity factor f2 could be different depending on which
of the two products is considered the reference for the comparison. The “classical” calculation method of the f2
factor does not reveal the
related standard deviation and thus no confidence interval could be associated with the metric. The use of the statistical bootstrap technique overcomes this major drawback: in a recent publication, Mendyk et al. presented an open source program to perform bootstrap calculations of the f2
factor, designed to help with f2 computation in cases where intra- and inter-batch variability is large (e.g. greater
than 10%). The algorithm provides possible “worst case scenarios” of f2 values, thus supporting claims about pharmaceutical equivalence [9].
On the other hand, MDM are those with the most complicated calculation. In general, no universal model is set to fit all dissolution profiles and there are no established criteria to select the proper mathematical model. Therefore, experimental data should be fitted to more than one non-linear model, (e.g. First Order, Weibull, Gompertz, Logistic equations), and after that the best-fitting equation must be chosen on a statistical basis: R2
, AIC (Akaike Information Criterion)
and/or lack of fit analysis. Once the mathematical method is selected, the equation’s parameters of each tablet, of each product, should be recorded and compared using appropriate multivariate statistical methods (e.g. Hotelling’s T2 others) [10,11].
test, regions of similarity method, among
Finally, the ASM treat the percent dissolved as a random variable to perform the analysis of variance, considering the formulation a single class variable (one way ANOVA) or both the formulation and the time as class variables (two way ANOVA), under the null hypothesis of similarity.
Although these methods are easy to calculate with
friendly software, their application is not strictly correct because the assumption of independent variables it is not fulfilled due to the correlation between the percent dissolved and the time.
Are these Methods Equally Suitable for their Application to Dissolution Profile Comparison of Multisource Drug Products?
To answer this question, the performance of MIM, MDM and ASM will be analyzed using some of the many dissolution results that we have
obtained in our laboratory over the years as examples. Without going into experimental details, the methods were applied to the comparison of dissolution profiles of oxcarbazepine 600 mg tablets (OxCBZ, 4 brands), carbamazepine 200 mg tablets (CBZ, 4 brands), acenocoumarol 4 mg tablets (ACM, 4 brands), and sodium phenytoin 100 mg capsules (PHT, 2 brands). All of the dissolution tests were conducted according to USP 34 conditions, and the following paragraphs present a summary of the main results (the interested reader can find the tables containing the complete results elsewhere [12]).
With regard to the MDM, only in the case of OxCBZ was it possible to fit the profiles of the individual brands to the same mathematical model. For the other drugs tested, fitting to a common model could not be attained, and therefore the comparison by MDM could not be performed. Furthermore, although the fitting of OxCBZ to one equation was possible, the results from the subsequent statistical comparison did not allow demonstrating similarity between any pair of OxCBZ products.
On the other hand, and their application is not strictly correct for the previously mentioned reasons, two-way and one-way ANOVA were performed to all the products. As in the case of MDM, similarity could not be established between any pair of products by these methods.
Finally, when MIM were applied, several similarities could be established, although different methods (f factors, AUC, DE) did not always yield coincident results.
At this point, two conclusions could be drawn: the fitting of dissolution data of multisource drug products to one and common model or equation (necessary step prior to profiles comparison by MDM) could not always be achieved; and both MDM and ASM are so discriminating that the differences usually found in products from different sources, although biopharmaceutically irrelevant, do not allow concluding similarity.
Hence the MIM appear to be the most suitable for assessing the equivalence in dissolution behavior between multisource drug products. However, in all cases (all drugs, all products) the results of AUC and DE comparison were not always coincident with the f indexes.
In Vitro-In Vivo Correlations as a Tool to Assess the Biorelevance of Dissolution Profile Comparison
The results discussed in the previous section assessed some main characteristics of the dissolution profile comparison methods analyzed, but their biorelevance (i.e. their ability to predict the in vivo behavior of the drug products) still remains undiscussed.
To address this matter, key remarks of a qualitative correlation between the in vitro data of some of the solid oral drug products mentioned previously and their respective in vivo data will be discussed. The in vivo profiles of the CBZ and PHT products (same brand, same batch) were previously obtained in our laboratory by administering the
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