Identifying design spaces as linear combinations of parameter ranges for biopharmaceutical control strategies

According to ICH Q8 guidelines, a biopharmaceutical manufacturer may submit a design space (DS) definition as part of the regulatory approval application, in which case process parameter (PP) deviations within this space are not considered changes and do not trigger a regulatory post approval procedure. A DS can be described by nonlinear PP ranges, i.e., the range of one PP conditioned on specific values of another. However, independent PP ranges (linear combinations) are often preferred in biopharmaceutical manufacturing due to their operational simplicity, as mentioned in the guideline. While statistical software such as Modde supports the calculation of a DS comprised of linear combinations, their algorithms are generally based on discretizing the parameter space an approach that suffers from the curse of dimensionality as the number of PPs increases. Here, we introduce a novel method for finding linear PP combinations using a numeric optimizer to calculate the largest design space within the parameter space that results in critical quality attribute boundaries within acceptance criteria, predicted by a regression model. A precomputed approximation of tolerance intervals is used in inequality constraints to facilitate fast evaluations of this boundary using a single matrix multiplication. The correctness of the method was validated by comparing results to that of a grid-based approach and, in a simple case, to an analytically defined ground truth. In the examples investigated, the volume of the resulting DS was significantly larger than that of the grid method, with the improvement being proportional to the granularity of the grid and the number of parameters involved. Furthermore, computational time for the optimization-based approach is several orders of magnitude faster in higher dimensions. In addition, a proposed weighting scheme can be used to favor certain PPs over others and therefore enabling a more dynamic approach to DS definition and exploration. The increased PP ranges of the larger DS provide greater operational flexibility for biopharmaceutical manufacturers.