Bootstrap Resampling Technique to Evaluate the Reliability of the Optimal Liposome Formulation: Skin Permeability and Stability Response Variables

Abstract

A nonlinear response surface method incorporating multivariate spline interpolation (RSM-S) is a useful technique for the optimization of pharmaceutical formulations, although the direct reliability of the optimal formulation must be evaluated. In this study, we demonstrated the feasibility of using the bootstrap (BS) resampling technique to evaluate the direct reliability of the optimal liposome formulation predicted by RSM-S. The formulation characteristics (X n ), including vesicle size (X 1 ), size distribution (X 2 ), zeta potential (X 3 ), elasticity (X 4 ), drug content (X 5 ), entrapment efficiency (X 6 ), release rate (X 7 ), and the penetration enhancer (PE) factors as formulation factors (Z n ), with the type of PE (Z 1 ) and content of PE (Z 2 ) were used as causal factors of the response surface analysis. The intended responses were high skin permeability (flux, Y 1 ) and high stability formulation (drug remaining, Y 2 ). Based on the dataset obtained, the simultaneous optimal solutions were estimated using RSM-S. Leave-one-out-cross-validation showed satisfying reliability of the optimal solution. Concurrently, similar BS optimal solutions were estimated from the BS dataset that was generated from the original dataset through BS resampling at frequencies of 250, 500, 750, and 1000. The analysis and simulation indicated that X 4 , X 5 , and Z 2 were the prime factors affecting Y 1 and Y 2 . These findings suggest that this approach could also be useful for evaluating the reliability of an optimal liposome formulation predicted by RSM-S and would be beneficial for the pharmaceutical development of liposomes for transdermal drug delivery.Key words bootstrap; response surface; simultaneous optimal solution; transdermal drug delivery Optimization techniques using computer-based rationales to research and develop pharmaceutical formulations have recently become attractive and interesting. A non-linear response surface method incorporating multivariate spline interpolation (RSM-S) is a powerful method for pharmaceutical optimization.1) RSM-S has shown that the complex relationships between causal factors and response variables could be simply comprehended and that the simultaneous optimal solutions obtained would be stable and reproducible.2) Several intensive studies successfully developed novel pharmaceutical formulations using RSM-S (e.g., water-in-oil-water multiple emulsion of insulin for intestinal delivery, 3) sustained release of diltiazem tablets for oral delivery 4) and ultra-deformable liposome of meloxicam for transdermal delivery 5) ). RSM-S was determined to be a promising technique for formulation optimization.3-7) Simultaneously, it is considerable to evaluate the accuracy and reliability of each optimal formulation estimated by RSM-S. The leave-one-out-cross-validation (LOOCV) method was also employed. The LOOCV method can evaluate the generalization error of a given response surface.8) Moreover, the reliability of optimal formulation estimated by certain response surface can be directly ...

Topical ketoprofen nanogel: artificial neural network optimization, clustered bootstrap validation, and in vivo activity evaluation based on longitudinal dose response modeling

“…The term ''robustness'' here describes the ability of the model to replicate the optimal solution, irrespective of prior assumptions. Resampling techniques, such as bootstrapping, can test the robustness of optimization results (Arai et al, 2007;Onuki et al, 2008;Duangjit et al, 2014). The basic idea of bootstrap is random sampling of the original dataset with replacement to generate arbitrary number of subsets belonging to the empirical distribution of the original data.…”