Latent structure modeling underlying theophylline tablet formulations using a Bayesian network based on a self-organizing map clustering.

The "quality by design" concept in pharmaceutical formulation development requires the establishment of a science-based rationale and design space. In this article, we integrate thin-plate spline (TPS) interpolation, Kohonen's self-organizing map (SOM) and a Bayesian network (BN) to visualize the latent structure underlying causal factors and pharmaceutical responses. As a model pharmaceutical product, theophylline tablets were prepared using a standard formulation. We measured the tensile strength and disintegration time as response variables and the compressibility, cohesion and dispersibility of the pretableting blend as latent variables. We predicted these variables quantitatively using nonlinear TPS, generated a large amount of data on pretableting blends and tablets and clustered these data into several clusters using a SOM. Our results show that we are able to predict the experimental values of the latent and response variables with a high degree of accuracy and are able to classify the tablet data into several distinct clusters. In addition, to visualize the latent structure between the causal and latent factors and the response variables, we applied a BN method to the SOM clustering results. We found that despite having inserted latent variables between the causal factors and response variables, their relation is equivalent to the results for the SOM clustering, and thus we are able to explain the underlying latent structure. Consequently, this technique provides a better understanding of the relationships between causal factors and pharmaceutical responses in theophylline tablet formulation.