Sample Size Requirements of a Pharmaceutical Material Library: A Case in Predicting Direct Compression Tablet Tensile Strength by Latent Variable Modeling

The material library is an emerging, new data-driven approach for developing pharmaceutical process models. How many materials or samples should be involved in a particular application scenario is unclear, and the impact of sample size on process modeling is worth discussing. In this work, the direct compression process was taken as the research object, and the effects of different sample sizes of material libraries on partial least squares (PLS) modeling in the prediction of tablet tensile strength were investigated. A primary material library comprising 45 materials was built. Then, material subsets containing 5 x i (i = 1, 2, 3, horizontal ellipsis , 8) materials were sampled from the primary material library. Each subset underwent sampling 1000 times to analyze variations in model fitting performance. Both hierarchical sampling and random sampling were employed and compared, with hierarchical sampling implemented with the help of the tabletability classification index d. For each subset, modeling data were organized, incorporating 18 physical properties and tableting pressure as the independent variables and tablet tensile strength as the dependent variable. A series of chemometric indicators was used to assess model performance and find important materials for model training. It was found that the minimum R2 and RMSE values reached their maximum, and the corresponding values were kept almost unchanged when the sample sizes varied from 20 to 45. When the sample size was smaller than 15, the hierarchical sampling method was more reliable in avoiding low-quality few-shot PLS models than the random sampling method. Two important materials were identified as useful for building an initial material library. Overall, this work demonstrated that as the number of materials increased, the model's reliability improved. It also highlighted the potential for effective few-shot modeling on a small material library by controlling its information richness.