Model Adequacy in Assessing the Predictive Performance of Regression Models in Pharmaceutical Product Optimization: The Bedaquiline Solid Lipid Nanoparticle Example

This study aimed to assess the predictive performance of first- and second-order regression models in optimizing bedaquiline (BQ) solid lipid nanoparticle (SLN) formulations. A three-step central composite design and graphical optimization process was employed. A design of experiments method was used to evaluate the impact of BQ, Tween 80 (T80), polyethylene glycol (PEG), and lecithin on the formulations' response variables, including Z-average (PSD), polydispersibility index (PdI), and Zeta potential (ZP). Secondly, we quantified the relationship between experimental variables using the regression model coefficients. Lastly, we predicted the responses and verified the models' adequacies to ensure accurate representation and effective optimization. The first-order polynomial showed poor model adequacy and required further refinement due to its lack of explanatory power and significant predictors. Conversely, the second-order models provided superior fitness, sensitivity to variability, complexity, and prediction consistency. The optimized formulation achieved a desirability value of 0.9998, indicating alignment with the desired criteria. Specifically, the levels of BQ (19.4 mg), T80 (25.2 mg), PEG (39.2 mg), and lecithin (200 mg) corresponded to PdI (0.41), PSD (250.99 nm), and ZP (-25.95 mV). Maintaining a BQ concentration between 10 and 20% and T80 between 15 and 18% is vital for maximizing ZP and minimizing PdI and PSD, ensuring stable SLN formulations. This study underscores the significance of precise model selection and statistical analysis in pharmaceutical formulation optimization for enhanced drug delivery systems.