The hierarchical Bayesian modeling approach was used to select the appropriate empirical kinetics model of sustained release and to optimize the in vitro dissolution rate of the sustained-release suppository by controlling the composition of Eudragit L-100 and Eudragit S-100 in the experimental mixture. Thirteen formulations of suppositories were prepared with 2 g (10%) mixture of Eudragit ® R-100 and S-100 according to a personalized mixture experimental design. The cumulative release of active ingredient was measured at five times (20, 50, 80, 160, and 235 minutes). The best model was selected using Rsq (Adjust) and akaike information criterion for standard method and by using the weight of widely applicable information criterion (WAIC) and leave-one-out (LOO) cross-validation for the Bayesian approach. Frequentist approach gave three best model depending on the formulation. Compared to this, the Bayesian method was able to define a single model, which is the first-order model. The relative probability of this model is 0.97, 0.99 based on the WAIC, and LOO, respectively. The relationship between K 1 (Release rate constant) and the quantities of the two Eudragits is quadratic, for Eudragit_L, Q release (%) = 0.0031X 2 -0.0026 X + 0.0069 and X is the Eudragit L100 and K 1 (Rate release) = 0.41 minutes −1. The Bayesian method allowed finding the most adequate model among several models that can be generated by the standard frequentist approach.

The objective of this work is to (i) study the effect of variations in the proportions of four Macrogols on the pharmaco-technical characteristics of suppositories, (ii) define the optimal formula for a suppository with immediate effect; maximum disintegration and a minimum of hardness as defined in the European Pharmacopoeia. The lattice design mixture has been proposed as an optimization technique, the formulation factors are presented by the proportions of PEG 400 (X1), PEG 600 (X2), PEG 4000 (X3) and PEG 6000 (X4) and the response variables are (i) the disintegration time (Y1) (ii) the hardness (Y2). The second-degree empirical model was postulated to model the variations of the two response variables using the least-squares method.  The selected model explained about 67% and 84% of the variation for Y1 and Y2, respectively. All four factors had significant effects on the properties of the suppository. Interactions negatively affected both responses.  The numerical desirability method gave the following optimal formula: PEG400 (28.71334 %); PEG600 (24.23773%), PEG4000 (35.00944%) and PEG6000 (12.03949%) for a disintegration of 25.839 (+/-2.3) min and hardness =2147.321 (+/- 50) g.