A Bayesian design space for analytical methods based on multivariate models and predictions

The International Conference for Harmonization (ICH) has released regulatory guidelines for pharmaceutical development. In the document ICH Q8, the design space of a process is presented as the set of factor settings providing satisfactory results. However, ICH Q8 does not propose any practical methodology to define, derive, and compute design space. In parallel, in the last decades, it has been observed that the diversity and the quality of analytical methods have evolved exponentially, allowing substantial gains in selectivity and sensitivity. However, there is still a lack of a rationale toward the development of robust separation methods in a systematic way. Applying ICH Q8 to analytical methods provides a methodology for predicting a region of the space of factors in which results will be reliable. Combining design of experiments and Bayesian standard multivariate regression, an identified form of the predictive distribution of a new response vector has been identified and used, under noninformative as well as informative prior distributions of the parameters. From the responses and their predictive distribution, various critical quality attributes can be easily derived. This Bayesian framework was then extended to the multicriteria setting to estimate the predictive probability that several critical quality attributes will be jointly achieved in the future use of an analytical method. An example based on a high-performance liquid chromatography (HPLC) method is given. For this example, a constrained sampling scheme was applied to ensure the modeled responses have desirable properties.