A Comparative Study of Strategies for Incorporating Uncertainty in Design Space Determination for Pharmaceutical Manufacturing

A case study concerned with batch synthesis of 2,6-difluoropurine-9-tetrahydropyran (THP) is used to compare the effectiveness of different methods for determining design spaces (DSs) where process operation results in satisfactory product quality. A mechanistic model is used to map a deterministic design space (DDS) and various probabilistic design spaces (PDSs). Uncertainties in model parameters, process parameters, and final measurement errors for quality variables lead to the shrinkage of the DDS, helping to avoid undesirable process outcomes. This case study reveals that ignoring correlated effects of model parameters and ignoring model nonlinearity leads to unreliable results. By contrast, parametric bootstrapping, which accounts for nonlinearity and parameter correlation, provides reliable information about the influence of uncertain parameters on the DS. For this case study, model parameter uncertainty reduces the size of the DS by ∼5%. Incorporating uncertainty in key process parameters further reduces the size of the DS by ∼20%. Additional shrinkage of the DS by ∼12% occurs when uncertainties in final quality variables are considered. The largest rectangular region within the resulting DS is obtained using optimization. Contour plots reveal that operation at the center of this rectangular region would lead to a ∼2% reduction in yield compared with operation at other satisfactory points in the DS. This comparative analysis offers important guidance for selecting approaches for handling uncertainties when constructing DSs for pharmaceutical development. The value of integrating mechanistic modeling, robust uncertainty quantification, and optimization for reliable DS determination is illustrated.