Bracketing the Design Space within the Knowledge Space in Pharmaceutical Product Development

Abstract

A key element of the Quality-by-Design initiative set forth by the pharmaceutical regulatory agencies (such as the U.S. Food and Drug Administration) is the determination of the design space (DS) for a new pharmaceutical product. When the determination of the DS cannot be assisted by the use of a first-principles model, one must heavily rely on experiments. In many cases, the DS is found using experiments carried out within a domain of input combinations (e.g., raw materials properties and process operating conditions) that result from similar products already developed. This input domain is the so-called knowledge space, and the related experimentation can be very demanding, especially if the number of inputs is large. To limit the extension of the domain over which the experiments are carried out (hence, to reduce the experimental effort), a methodology is proposed that aims at segmenting the knowledge space in such a way as to identify a subspace of it (which we call the experiment space) that most likely brackets the DS. The methodology relies on the exploitation of historical databases on products that have already been developed and are similar to the new one, and is based on the inversion of a latent-variable model. The relationship between the regulatory concept of DS and the mathematical concept of null space is discussed for products characterized by one equality constraint specification, and the effect of model prediction uncertainty is accounted for. Three simulated examples are used to test the effectiveness of the proposed segmentation methodology. The segmentation results are shown to be effective, in that the designated experiment space is able to effectively bracket the DS and is much narrower than the historical knowledge space.

Probabilistic Design space determination in pharmaceutical product development: A Bayesian/latent variable approach

“…For example, Facco et al 16 build a frequentist confidence region for the model prediction of the DS and name this restricted portion of the KS as the "experiment space." For example, Facco et al 16 build a frequentist confidence region for the model prediction of the DS and name this restricted portion of the KS as the "experiment space."…”

“…For example, Facco et al 16 build a frequentist confidence region for the model prediction of the DS and name this restricted portion of the KS as the "experiment space." The practical outcome is that, whereas the experiment space proposed by Facco et al 16 cannot be considered as a model-based representation of the DS, the Bayesian DS proposed in this study can be deemed as such, given that the intrinsic probabilistic nature of model predictions is recognized. On the other side, the Bayesian DS discussed in this study can be interpreted as the portion of the KS within which the probability for the product to be on target is greater than (or equal to) an assigned threshold: the greater the probability threshold, the narrower the Bayesian DS.…”

“…Historical data for this case study were generated by Facco et al 16 based on the model of Johanson. Historical data for this case study were generated by Facco et al 16 based on the model of Johanson.…”

“…to study the robustness of the methodology, namely to analyze how numerical issues (e.g., convergence of the 16 Based on the Model of Johanson 17 and Characterization of the Input Dataset (Columns 5 and 6)) Markov chain for every Bayesian simulation) may be affected when the problem dimensionality increases. to study the robustness of the methodology, namely to analyze how numerical issues (e.g., convergence of the 16 Based on the Model of Johanson 17 and Characterization of the Input Dataset (Columns 5 and 6)) Markov chain for every Bayesian simulation) may be affected when the problem dimensionality increases.…”

“…The first one involves a model-generated historical dataset for the dry granulation of a pharmaceutical blend (taken from the work of Facco et al, 16 based on the model of Johanson). The first one involves a model-generated historical dataset for the dry granulation of a pharmaceutical blend (taken from the work of Facco et al, 16 based on the model of Johanson).…”