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 nanoparticles (SLNs) formulations. Employed a central composite design and graphical optimization process using three steps. A design of experiments to evaluate the impact of BQ, Tween 80 (T80), polyethylene glycol (PEG), and lecithin on the formulations' response variables: Z-average (PSD), polydispersibility index (PdI), and Zeta potential (ZP). Secondly, quantified the relationship between experimental variables using the regression model coefficients. Lastly, predicted the responses and verified the models’ adequacies to ensure accurate representation and effective optimization. First-order polynomial showed poor model adequacy that required further refinement. 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 (19.4mg), T80 (25.2mg), PEG (39.2mg), and Lecithin (200mg) corresponded to PdI (0.41), PSD (250.99 nm), and ZP (-25.95 mV). Maintaining BQ concentration between 10-20% and T80 between 15-18% is vital for maximizing ZP and minimizing PdI and PSD, ensuring stable SLN formulations. The study underscores significance of precise model selection and statistical analysis in pharmaceutical formulation optimization for enhanced drug delivery systems.