Evaluation of the Reliability of Nonlinear Optimal Solutions in Pharmaceuticals Using a Bootstrap Resampling Technique in Combination With Kohonen's Self‐Organizing Maps

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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...

Section: Construction Of Response Surfaces and Design Space Of 100 Mgmentioning

confidence: 99%

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confidence: 99%

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

Maeda

Suzuki

Takayama

2012

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“…[15][16][17] In addition to generating response surfaces, TPS can predict untested variables with high accuracy using reading points on the response surfaces. Taking advantage of this predictive ability, we were able to predict the characteristics of a large number of untested tablets (4096) instead of conducting experiments.…”

Section: Discussionmentioning

confidence: 99%

Self-Organizing Map Analysis Using Multivariate Data from Theophylline Tablets Predicted by a Thin-Plate Spline Interpolation

Yasuda

Onuki

Obata

et al. 2013

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The "quality by design" concept in pharmaceutical formulation development requires the establishment of a science-based rationale and a design space. We integrated thin-plate spline (TPS) interpolation and Kohonen's self-organizing map (SOM) to visualize the latent structure underlying causal factors and pharmaceutical responses. As a model pharmaceutical product, theophylline tablets were prepared based on a standard formulation. The tensile strength, disintegration time, and stability of these variables were measured as response variables. These responses were predicted quantitatively based on nonlinear TPS. A large amount of data on these tablets was generated and classified into several clusters using an SOM. The experimental values of the responses were predicted with high accuracy, and the data generated for the tablets were classified into several distinct clusters. The SOM feature map allowed us to analyze the global and local correlations between causal factors and tablet characteristics. The results of this study suggest that increasing the proportion of microcrystalline cellulose (MCC) improved the tensile strength and the stability of tensile strength of these theophylline tablets. In addition, the proportion of MCC has an optimum value for disintegration time and stability of disintegration. Increasing the proportion of magnesium stearate extended disintegration time. Increasing the compression force improved tensile strength, but degraded the stability of disintegration. This technique provides a better understanding of the relationships between causal factors and pharmaceutical responses in theophylline tablet formulations.Key words tablet formulation; simulation; multivariate analysis; physical characterization; thin-plate spline; self-organizing map Many pharmaceutical formulations are composed of several formulation factors and response variables, with complicated relationships between these causal factors and responses. In addition, the formulator's expertise and experience are essential for designing an acceptable product formulation. The empirical approach requires a prolonged development time and significant resources. The "quality by design" concept was proposed in the International Conference on Harmonization (ICH) Q8 guidance, 1) and the need to apply scientific formulation development has been recognized.2) To gain insight into pharmaceutical formulations, a quantitative visualization technique is needed to understand the relationships between the causal factors and the pharmaceutical responses.The response surface method (RSM) is widely used to visualize the relationships between causal factors and responses. However, this method is limited to the three-dimensional space and includes basic information about the relationship between only two limited factors and one response. The selforganizing map (SOM) proposed by Kohonen allows one to map multidimensional data onto a two-dimensional surface. 3)Applications of the SOM have been reported across a range of pharmaceutical and medical fiel...

“…6. 26) As mentioned above, BS datasets are generated from the original data. If the corrected data points are located near the original solution, the BS optimal solution is consistent with the global optima.…”

Section: Resamplingmentioning

confidence: 99%

Reliability Evaluation of the Design Space of the Granulation Process of Mefenamic Acid Tablets Using a Bootstrap Resampling Technique

Arai

Suzuki

Yada

et al. 2011

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The design space of the granulation process of mefenamic acid tablets, based on Box and Behnken design datasets, was described by a response surface method incorporating multivariate spline interpolation. The reliability of the optimal solutions and the acceptance ranges were evaluated by a bootstrap (BS) resampling technique. The distribution of the BS optimal solutions was almost symmetrical; however, several solutions, which were quite different from the original solution, were mixed. The reason for this problem was considered to be the mixing of the global and the local optima. Therefore, we applied self-organizing map (SOM) clustering for dividing data into several clusters and identified the cluster containing the global optima. The accuracy and reproducibility of the optimal solution in the cluster containing the optimal solution were quantitatively evaluated. In addition, the response surfaces modeled from all the BS datasets contained in the cluster were plotted into the same coordinates with the original response surface. The plots of BS optimal solutions were distributed around the original solution. Moreover, the average of all the BS response surfaces sufficiently corresponded with the original response surface. The conservative limits of the 95% confidence intervals of the acceptance ranges in three response variables could be calculated using the standard deviations of the BS response surfaces. Consequently, it was considered that a novel evaluation method based on BS resampling and SOM could be used for quantitatively evaluating the precision of the nonlinear response surface model.