Design Space Construction of Multiple Dose-Strength Tablets Utilizing Bayesian Estimation Based on One Set of Design-of-Experiments

Abstract

Design spaces for multiple dose strengths of tablets were constructed using a Bayesian estimation method with one set of design of experiments (DoE) of only the highest dose-strength tablet. The lubricant blending process for theophylline tablets with dose strengths of 100, 50, and 25 mg is used as a model manufacturing process in order to construct design spaces. The DoE was conducted using various Froude numbers (X 1 ) and blending times (X 2 ) for theophylline 100-mg tablet. The response surfaces, design space, and their reliability of the compression rate of the powder mixture (Y 1 ), tablet hardness (Y 2 ), and dissolution rate (Y 3 ) of the 100-mg tablet were calculated using multivariate spline interpolation, a bootstrap resampling technique, and self-organizing map clustering. Three experiments under an optimal condition and two experiments under other conditions were performed using 50-and 25-mg tablets, respectively. The response surfaces of the highest-strength tablet were corrected to those of the lower-strength tablets by Bayesian estimation using the manufacturing data of the lower-strength tablets. Experiments under three additional sets of conditions of lower-strength tablets showed that the corrected design space made it possible to predict the quality of lower-strength tablets more precisely than the design space of the highest-strength tablet. This approach is useful for constructing design spaces of tablets with multiple strengths.Key words quality by design; design of experiments; multivariate regression; modelingThe International Conference on Harmonization (ICH) 1) has outlined Quality by Design (QbD) as a systematic approach to development that begins with predefined objectives and emphasizes product and process understanding and process control, based on sound science and quality risk management. According to the QbD principle, pharmaceutical quality should not be tested via day-to-day release testing, instead, it should be elaborated by design in advance. One of the most significant aspects in the QbD concept is the establishment of a design space based on a multidimensional combination of input formulation parameters, process parameters, or material attributes that have been shown to provide assurance of quality attributes 2) . A design of experiments (DoE) study has been effectively used in order to construct a design space.3,4) DoE is a useful method for systematically understanding the relationship between input parameters and output quality attributes. A typical design space is established as a superposition of the response surfaces for each quality attribute generated by the response surface method (RSM) using the DoE results.5-11) RSM includes statistical analyses such as multiple linear regression analysis 12) and artificial neural networks. 13,14) Takayama et al. developed RSM-S, a novel RSM that incorporates multivariate spline interpolation.15) RSM-S is an effective tool for obtaining reliable response surfaces of nonlinear phenomena and calculating optimal solutions. A boots...

Novel Method for Constructing a Large-Scale Design Space in Lubrication Process by Using Bayesian Estimation Based on the Reliability of a Scale-Up Rule

“…The large-scale acceptance areas calculated by Eqs. 7 and 8 were narrower than the previously-reported acceptance areas 25) calculated by Eqs. 5 and 6 because the small-scale knowledge was downplayed on the improved Bayesian estimation of quality attributes with discrepancy between the manufacturing scales.…”

“…This finding indicated that all the response surfaces had high estimation accuracy because no scale effect was involved. With regard to tablet hardness and dissolution rate, the renewed large-scale design space had higher prediction accuracy than the small-scale and previously-reported large-scale design spaces 25) because of the precise Bayesian estimation and correction of the discrepancy in the quality attributes between the manufacturing scales. We concluded that an accurate large-scale design space can be constructed by Bayesian estimation using the reliabilities of response surface models and scale-up rules without a large-scale DoE study, irrespective of the accuracy of the scale-up rule.…”

“…In our previous report, 25) only the standard deviation of the response surfaces calculated by the bootstrap resampling was considered as the standard deviation of the prior probability:…”

“…25) The large-scale design space was more reliable than the small-scale one, despite the small discrepancy in the pharmaceutical quality between the two manufacturing scales. However, we believed that a more reliable design space could be constructed if a precision of the scale-up rule was predicted in advance and the large-scale data was emphasized more than the small-scale design space in Bayesian estimation, when the scale-up rule was less reliable.…”