(M1030-01-02) Scaled Net Analyte Signal Distance (SND) - A Leverage-Based In-Model Diagnostic for Iterative Optimization Technology (IOT) Algorithm

Purpose: Implementing a process analytical technology (PAT) model allows non-destructive, rapid determination of blend and content uniformity for intermediate and final product quality checks in the drug product manufacturing process. However, spectroscopy-based traditional PAT models like the partial least squares (PLS) regression model require calibration data with reference values for successful model deployment. Recently, an alternative approach called iterative optimization technology (IOT) has been explored as a calibration-free approach in early product development of solid oral dosage forms. Model diagnostics are essential metrics to enhance confidence in model performance and identify potential outlier samples. This work proposed an in-model diagnostic tool to detect the non-representative samples in IOT model.

Methods: A model formulation containing theophylline monohydrate (THY) as active pharmaceutical ingredient (API), lactose monohydrate (LAC), and microcrystalline cellulose (MCC) as excipients was used for this study. A full-factorial PLS calibration mixture design with three concentration levels of THY (25, 30, 35% w/w) and three LAC to MCC ratios (LAC:MCC) (1:2, 1:1, and 2:1) was utilized. Five test points of two different groups were used in the study. One group of the test sample was standard test samples with variation in chemical compositions, while the other test sample group contained either a chemical contaminant or physical variation in the sample. The study design is illustrated in figure 1. All powder components were blended in a V-blender at 15 rpm for 10 minutes. Samples were then transferred into a small-scale feed-frame simulator, and NIR spectra of the samples in the range of 900-1700 nm were collected using MicroNIR PAT-U (VIAVI Solutions Inc., Scottsdale, Arizona, USA). Pure component spectral data were collected in a small, inverted container. Details on the sample preparation method can be found elsewhere.^[1] Data analysis was facilitated using MATLAB (R2023a, MathWorks, USA).

Results: Model diagnostics are useful tools for identifying outliers and non-representative samples. Diagnostics like Hotelling’s T² and Q-residual measure the in-model and out-of-model variance of samples in the PLS model.^[2]  Pure component models, such as IOT, have an out-of-model diagnostic called SSR (squared spectral residual), which runs parallel to the Q-residual of PLS.^[3] A few in-model diagnostics were proposed for IOT, namely M metric, and NAS-T to distinguish outliers from normal samples.^[1,4] M metric is more relevant for the extended form of IOT, also called EIOT, which utilizes calibration samples to estimate pure component shapes. NAS-T, more relevant for the calibration-free IOT approach, determines the angle between the net analyte signals (NAS) of the pure component spectrum and the mixture spectrum of a component. However, unlike Hotelling’s T², NAS-T is not a leverage-based metric, making it harder to interpret. To develop an easily interpretable in-model diagnostic, the authors introduce a net analyte signal (NAS) based metric called scaled NAS distance (SND).  Net analyte signal (NAS) is the part of the signal that exclusively represents the analyte of interest and is orthogonal to all other signals in the mixture spectrum.^[5] The NAS vector for both pure component and mixture spectra of a component can be calculated using the following equations. Theoretically, the ratio of NAS vectors of the mixture and pure component should range between 0 and 1. The absolute distance between the target blend NAS ratio and the mixture NAS ratio is defined as SND. These calculations of NAS and SND are demonstrated in figure 2. When plotted in Q-residual vs Hotelling’s T², samples with chemical contaminants like caffeine (CAF) and talc demonstrated higher in-model variance compared to the calibration sample for the PLS model. The same trend has been observed when they are plotted in relative SSR vs SND plot for the IOT model. Samples with higher SND values can be identifying as non-representative samples in IOT model. The red dashed lines in figure 3(A) represent 95% confidence interval. Since SND scale represents the leverage of the relative concentration of API, a suitable theoretical range can be utilized for SND axis in the absence of a sample population, especially during the early drug product development phases.

Conclusion: The new proposed diagnostic, SND, was able to capture the in-model variance in the IOT model in a leverage-based system. When plotted against relative SSR, SND for samples with high deviation of THY concentration, and the ones with chemical contamination showed higher SND values. Overall, SND demonstrated easy interpretation and promising results for outlier detection for IOT algorithm.

References: 1. Rish, A. J., Velez-Silva, N. L., Henson, S., Hasan, M. N., Drennen, J. K., & Anderson, C. A. (2023). Diagnostic development using net analyte signal for pure component modeling approaches. Chemometrics and Intelligent Laboratory Systems, 243, 105007.
2. EMA, Guideline on the use of near infrared spectroscopy by the pharmaceutical industry and the data requirements for new submissions and variations, EMEA/CHMP/CVMP/QWP/17760/2009 Rev1, (2014).
3. Shi, Z., Hermiller, J., & Muñoz, S. G. (2019). Estimation of mass‐based composition in powder mixtures using Extended Iterative Optimization Technology (EIOT). AIChE Journal, 65(1), 87-98.
4. Muñoz, S. G., & Torres, E. H. (2020). Supervised extended iterative optimization technology for estimation of powder compositions in pharmaceutical applications: method and lifecycle management. Industrial & Engineering Chemistry Research, 59(21), 10072-10081.
5. Ferré, J., & Faber, N. K. M. (2003). Net analyte signal calculation for multivariate calibration. Chemometrics and Intelligent Laboratory Systems, 69(1-2), 123-136.

Mixture design points for the formulation

(A) Calculation of NAS vector for pure component and mixture spectra, (B) Illustration of NAS vector relative to other signals,[5] (C) Calculation for SND, (D) Variable legends.

(A) Q-residual vs Hotelling’s T2 distribution for PLS model with 2 latent variables. Spectra were preprocessed with SavGol (5 Points, 2nd order, 2nd derivative + mean centering). (B) Relative SSR vs SND distribution for the IOT model. Spectra were preprocessed with SavGol (5 Points, 2nd order, 2nd derivative).