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Perspectives in modeling and model validation during analytical quality by design chromatographic method evaluation: a case study

Perspectives in modeling and model validation during analytical quality by design chromatographic... Design of experiments (DOE)-based analytical quality by design (AQbD) method evaluation, development, and validation is gaining momentum and has the potential to create robust chromatographic methods through deeper understanding and control of variability. In this paper, a case study is used to explore the pros, cons, and pitfalls of using various chromatographic responses as modeling targets during a DOE-based AQbD approach. The case study involves evaluation of a reverse phase gradient HPLC method by a modified circumscribed central composite (CCC) response surface DOE. Solid models were produced for most responses and their validation was assessed with graphical and numeric statistics as well as chromatographic mechanistic understanding. The five most relevant responses with valid models were selected for multiple responses method optimization and the final optimized method was chosen based on the Method Operable Design Region (MODR). The final method has a much larger MODR than the original method and is thus more robust. This study showcases how to use AQbD to gain deep method understanding and make informed decisions on method suitability. Discoveries and discussions in this case study may contribute to continuous improvement of AQbD chromatography practices in the pharmaceutical industry. Keywords: AQbD, DOE, MODR, Statistical model validation, Scientific model validation, Multiple responses optimization Introduction previously approved drugs both challenging and costly. Drug development using a quality by design (QbD) ap- The International Council for Harmonization of Tech- proach is an essential part of the Pharmaceutical cGMP nical Requirements for Pharmaceuticals for Human Use Initiative for the twenty-first century (FDA Pharmaceut- (ICH) embraced this initiative and began issuing QbD ical cGMPs For The 21st Century — A Risk-Based Ap- relevant quality guidelines in 2005. The final versions of proach. 2004) established by the FDA. This initiative ICH Q8–Q12 [(ICH Q8 (R2) 2009) (ICH Q9 2005) (ICH seeks to address unmet patient needs, unsustainable rise Q10 2008) (ICH Q11 2012) (ICH Q12 2019)] have been of healthcare costs, and the reluctance to adopt new adopted by all ICH members. The in-progress version of technology in pharmaceutical development and manu- ICH Q14 (ICH Q14 2018) will offer AQbD guidelines facturing. These issues were the result of old regulations for analytical procedures and promote the use of QbD that are very rigid and made continuous improvement of principles to achieve a greater understanding and con- trol of testing methods and reduction of result * Correspondence: yongzhi.dong@thermofisher.com variability. Thermo Fisher Scientific Inc., Durham, NC, USA © The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Dong et al. AAPS Open (2021) 7:3 Page 2 of 14 Product development using a QbD approach empha- an approved MODR does not impact the results and of- sizes understanding of product and process variability, as fers an advantage for continuous improvement without well as control of process variability. It relies on analyt- submission of supplemental regulatory documentation. ical methods to measure, understand, and control the Establishment of the MODR is facilitated by multivariate critical quality attributes (CQA) of raw materials and in- design of experiments (DOE) (Volta e Sousa et al. 2021). termediates to optimize critical process parameters and Typically, three types of DOE may be involved in AQbD. realize the Quality Target Product Profile (ICH Q8 (R2) The screening DOE further consolidates the potential 2009). Nevertheless, part of the variability reported by critical method parameters determined from the risk as- an analytical test can originate from the variability of the sessment. The optimization DOE builds mathematical analytical measurement itself. This can be seen from Eq. models and selects the appropriate critical method par- 1. ameter settings to reach to the target mean responses. Finally, the robustness DOE further narrows down the 2 2 2 σ ¼ σ þ σ ð1Þ critical method parameter settings to establish the reported product measurement MODR, within which the target mean responses are The reported variability is the sum of intrinsic product consistently realized. Based on this AQbD framework, it variability and extrinsic analytical measurement variabil- is very clear DOE models are essential to understanding ity (NIST/SEMATECH e-Handbook of statistical and controlling method variability to build robustness methods 2012a, 2012b, 2012c, 2012d). The measurement into analytical methods. Although there have been ex- variability can be minimized by applying QbD principles, tensive case studies published regarding AQbD (Gran- concepts, and tools during method development to as- geia et al. 2020), systematic and in-depth discussion of sure the quality and reliability of the analytical method the fundamental AQbD modeling is still largely unex- can meet the target measurement uncertainty (TMU) plored. Methodical evaluation of the pros, cons, and pit- (EURACHEM/CITAC 2015). High-quality analytical falls of using various chromatographic responses as data truthfully reveal product CQAs and thus enables modeling targets is even more rare (Debrus et al. 2013) robust, informed decisions regarding drug development, (Orlandini et al. 2013) (Bezerraa et al. 2019). The pur- manufacturing, and quality control. pose of this case study is to investigate relevant topics ICH Q14 introduces the AQbD concepts, using a ra- such as data analysis and modeling principles, statistical tional, systematic, and holistic approach to build quality and scientific validation of DOE models, method robust- into analytical methods. The Method Operable Design ness evaluation and optimization by Monte Carlo simu- Region (MODR) (Borman et al. 2007) is a multidimen- lation (Chatterjee S 2012), multiple responses method sional space based on the critical method parameters optimization (Leardi 2009), and MODR establishment. and settings that provide suitable method performance. Discoveries and discussions in this case study may con- This approach begins with a predefined analytical target tribute to continuous improvement of chromatographic profile (ATP) (Schweitzer et al. 2010), which defines the AQbD practices in the pharmaceutical industry. method’s intended purpose and commands analytical technique selection and all other method development Methods/experimental activities. This involves understanding of the method Materials and methods and control of the method variability based on sound C111229929-C, a third-generation novel synthetic science and risk management. It is generally agreed tetracycline-class antibiotic currently under phase 1 clin- upon that systematic AQbD method development ical trial was provided by KBP Biosciences. A reverse should include the following six consecutive steps (Tang phase HPLC purity and impurities method was also pro- 2011): vided for evaluation and optimization using AQbD. The method was developed using a one factor at a time 1. ATP determination (OFAT) approach and used a Waters XBridge C18 col- 2. Analytical technique selection umn (4.6 × 150 mm, 3.5 μm) and a UV detector. Mobile 3. Method risk assessment phase A was composed of ammonium acetate/ethylene- 4. MODR establishment diaminetetraacetic acid (EDTA) buffer at pH 8.8 and 5. Method control strategy mobile phase B was composed of 70:30 (v/v) aceto- 6. Continuous method improvement through a life nitrile/EDTA buffer at pH 8.5. Existing data from forced cycle approach degradation and 24-month stability studies demon- strated that the method was capable of separating all six A multivariate MODR allows freedom to make specified impurities/degradants with ≥ 1.5 resolution. method changes and maintain the method validation A 1.0 mg/mL C111229929-C solution was prepared by (Chatterjee S 2012). Changing method conditions within dissolving the aged C111229929-C stability sample into Dong et al. AAPS Open (2021) 7:3 Page 3 of 14 10 mM HCl in methanol and used as the method evalu-  Good coverage of the design space by including the ation sample. An agilent 1290 UPLC equipped with a interior design points DAD detector was used. In-house 18.2 MΩ Milli-Q  Low predictive variances of the design points Water was used for solution preparations. All other re-  Low model term coefficient estimation errors agents were of ACS equivalent or higher grade. Waters Empower® 3 was used as the Chromatographic Data Sys- The design also allows for implementation of a se- tem. Fusion QbD v 9.9.0 software was used for DOE de- quential approach, where trials from previously con- sign, data analysis, modeling, Monte Carlo simulation, ducted factorial experiments can be augmented to form multiple responses mean, and robustness optimization. the CCC design. When there is little understanding Empower® 3 and Fusion QbD were fully integrated and about the method and critical method parameters, such validated. as when developing a new method from scratch, direct A method risk assessment was performed through re- application of an optimizing CCC design is generally not view of the literature and existing validation and stability recommended. However, there was sufficient previous data to establish priorities for method inputs and re- knowledge regarding this specific method, justifying the sponses. Based on the risk assessment, four method pa- direct approach. rameters with the highest risk priority numbers were selected as critical method parameters. Method evalu- DOE data analysis and modeling principles ation and optimization was performed by a modified cir- DOE software is one of the most important tools to fa- cumscribed central composite (CCC) response surface cilitate efficient and effective AQbD chromatographic DOE design with five levels per parameter, for a total of method development, validation, and transfer. Fusion 30 runs. The modifications were the extra duplicate rep- QbD software was employed for DOE design and data lications at three factorial points. In addition to triplicate analysis. Mathematical modeling of the physicochemical replications at the center point, the modified design had chromatographic separation process is essential for DOE a total of nine replicates. See Table 1 for the detailed de- to develop robust chromatographic methods through sign matrix. A full quadratic model for the four-factor three phases: chemistry screening, mean optimization, five-level CCC design has a total of fourteen potential and robustness optimization. The primary method pa- terms. They include four main linear terms (A, B, C, D), 2 2 2 2 rameters affecting separation (e.g., column packing, mo- four quadratic terms (A ,B ,C ,D ), and six two-way bile phase pH, mobile phase organic modifier) are interaction terms (A*B, A*C, A*D, B*C, B*D, and C*D). statistically determined with models during chemistry Pre-runs executed at selected star (extreme) points screening. The secondary method parameters affecting verified that all expected analytes eluted within the 35 separation (e.g., column temperature, flow rate, gradient min run time. This mitigated the risk of any non-eluting slope settings) are optimized during mean optimization peaks during the full DOE study, as a single unusable using models to identify the method most capable of run may raise questions regarding the validity of the en- reaching all selected method response goals on average. tire study. Based on the pre-runs, the concentration of During robustness optimization, robustness models for the stock EDTA solution was decreased four-fold to selected method responses are created with Monte Carlo mitigate inaccurate in-line mixing of mobile phase B simulation and used to further optimize method param- caused by low volumes of a high concentration stock. eters such that all method responses consistently reach The final ranges and levels for each of the four selected their goals, as reflected by a process capability value of ≥ method parameters are also listed in Table 1. 1.33, which is the established standard for a robust Each unique DOE run in Table 1 is a different method. process (NIST/SEMATECH e-Handbook of statistical As there were 25 unique running conditions, there were methods 2012a, 2012b, 2012c, 2012d). 25 different methods in this DOE study. The G- Models are critical to the AQbD approach and must Efficiency and the average predicted variance (NIST/ be validated both statistically and scientifically. Statistical SEMATECH e-Handbook of statistical methods 2012a, validation is performed using various statistical tests 2012b, 2012c, 2012d) (Myers and Montgomery 1995)of such as residual randomness and normality (NIST/ the design were 86.8% and 10.6%, respectively, meeting SEMATECH e-Handbook of statistical methods 2012a, their respective design goals of ≥ 50% and ≤ 25%. Some 2012b, 2012c, 2012d), regression R-squared, adjusted re- of the major advantages of this modified CCC design in- gression R-squared, and prediction R-squared. Scientific clude the following: validation is achieved by checking the terms in a statis- tical model against the relevant established scientific Established quadratic effects principles, which is described as mechanistic under- Robust models that minimize effects of potential standing in the relevant literature (ICH Q8 (R2) 2009). missing data Dong et al. AAPS Open (2021) 7:3 Page 4 of 14 Table 1 The experimental matrix of the modified CCC design Run No. (A) Pump flow rate (B) Final strong (C) Oven (D) EDTA additive Predicted response (mL/min) solvent (%) temperature (°C) concentration (mM) variance (%) 1 0.9 35.0 26.0 0.50 16.67 2 0.8 33.0 28.0 0.45 10.80 3 1.0 33.0 28.0 0.45 10.87 4 0.8 37.0 28.0 0.45 10.87 5 1.0 37.0 28.0 0.45 16.67 6 0.8 33.0 28.0 0.55 16.85 7 1.0 33.0 28.0 0.55 17.02 8 0.8 37.0 28.0 0.55 17.02 9 1.0 37.0 28.0 0.55 17.21 10 0.8 33.0 28.0 0.45 10.80 11 1.0 33.0 28.0 0.45 10.87 12 0.8 37.0 28.0 0.45 10.87 13 0.7 35.0 30.0 0.50 16.91 14 1.1 35.0 30.0 0.50 17.14 15 0.9 31.0 30.0 0.50 16.91 16 0.9 39.0 30.0 0.50 17.14 17 0.9 35.0 30.0 0.40 16.67 18 0.9 35.0 30.0 0.60 17.41 19 0.9 35.0 30.0 0.50 10.00 20 0.9 35.0 30.0 0.50 10.00 21 0.9 35.0 30.0 0.50 10.00 22 0.8 33.0 32.0 0.45 16.85 23 1.0 33.0 32.0 0.45 17.02 24 0.8 37.0 32.0 0.45 17.02 25 1.0 37.0 32.0 0.45 17.21 26 0.8 33.0 32.0 0.55 17.32 27 1.0 33.0 32.0 0.55 16.16 28 0.8 37.0 32.0 0.55 16.16 29 1.0 37.0 32.0 0.55 16.16 30 0.9 35.0 34.0 0.50 17.41 Parameter 0.7–1.1 33–37 26–34 0.4–0.6 ranges a b c d Each run is labeled with the type of design point: , star points; , factorial points; , triplicate replications at the center point (the nominal conditions); and , model robustness points by run 10, 11, and 12, which are the duplicate replications of the factorial points by run 2, 3, and 4, respectively Fusion uses data transformation analysis to decide understanding of how a method response, such as reso- whether data transformation is necessary before model- lution, is affected by critical method parameters. ing, and then uses analysis of variance (ANOVA) and re- Since Fusion relies on models for chemistry screening, gression to generate method response models. ANOVA mean optimization, and robustness optimization, it is provides objective and statistical rationale for each con- critical to holistically evaluate each method response secutive modeling decision. Model residual plots are model from all relevant model regression statistics to as- fundamental tools for validating the final method re- sure model validity before multiple method response sponse models. When a model fits the DOE data well, optimization. Inappropriate models will lead to poor the response residuals should be distributed randomly prediction and non-robust methods. This paper will de- without any defined structure, and normally. A valid scribe the holistic evaluation approach used to develop a method response model provides the deepest robust chromatographic method with Fusion QbD. Dong et al. AAPS Open (2021) 7:3 Page 5 of 14 Results many terms are used in the model or the sample size is Representative chromatogram under nominal conditions too small. Careful planning and pre-runs executed at select star points allowed for successful execution of the DOE with Model Term Ranking Pareto Charts for scientific all expected peaks eluting within the running time for all validation of DOE models the 30 runs. A representative chromatogram at the nom- DOE models are calculated from standardized variable inal conditions is shown in Fig. 1. The API peak level settings. Scientific validation of a DOE model (C1112299299-C) and the Epimer peak (C112299299-C- through mechanistic understanding can be challenging epimer) can be seen, as well as seven minor impurity when data transformation before modeling ostensibly in- peaks, among which impurity 2 and impurity 3 elute at verts the positive and negative nature of the model term 8.90 and 10.51 min, respectively. The inset shows the effect. To overcome this challenge, Model Term Ranking full-scale chromatogram. Pareto Charts that provide the detailed effects of each term in a model were employed. See Fig. 2 for details. The chart presents all terms of a model in descending Results for statistical validation of the DOE models order (left to right) based on the absolute magnitude of ANOVA and regression data analysis revealed many their effects. The primary y-axis (model term effect) DOE models for various peak responses. The major nu- gives the absolute magnitude of individual model terms, meric regression statistics of the peak response models while the secondary y-axis (cumulative percentage) gives are summarized in Table 2. the cumulative relative percentage effects of all model MSR (mean square regression), MSR adjusted, and terms. Blue bars correspond to terms with a positive ef- MS-LOF (mean square lack of fit) are major numeric fect, while gray bars correspond to those with a negative statistics for validating a DOE model. A model is statisti- effect. The Model Term Ranking Pareto Charts for all cally significant when the MSR ≥ the MSR significance models are summarized in Fig. 2, except the two “cus- threshold, which is the 0.0500 probability value for stat- tomer” peak area models with a single term and the two istical significance. The lack of fit of a model is not sta- C models. pk tistically significant when the MS-LOF ≤ the MS-LOF significance threshold, which is also the 0.0500 probabil- Discussion ity value for statistical significance. The MSR adjusted AQbD relies on models for efficient and effective chem- statistic is the MSR adjusted with the number of terms istry screening, mean optimization, and robustness in the model to assure a new term improves the model optimization of chromatographic methods. It is critical fit more than expected by chance alone. For a valid to “validate” the models both statistically and scientific- model, the MSR adjusted is always smaller than the ally, as inappropriate models may lead to impractical MSR and the difference is usually very small, unless too methods. As such, this section will discuss statistical and Fig. 1 A representative chromatogram under nominal conditions Dong et al. AAPS Open (2021) 7:3 Page 6 of 14 Table 2 Major model regression statistics of various chromatographic responses Response MSR MSR adjusted MSR threshold MS-LOF MS-LOF threshold API area (default) 0.9913 0.9906 0.0022 0.0006 0.0041 Epimer area (default) 0.9902 0.9895 0.0024 0.0008 0.0026 API area (customer) 0.8191 0.8124 0.0282 0.0081 0.0026 Epimer area (customer) 0.8481 0.8425 0.0237 0.0068 0.0017 API plate count 0.9101 0.8906 0.0516 0.0206 0.0716 API RT (min) 0.9988 0.9984 0.0009 0.0003 0.0028 Epimer RT (min) 0.9986 0.9982 0.0009 0.0004 0.0014 Impurity 2 RT (min) 0.9988 0.9986 0.0006 0.0002 0.0014 Impurity 3 RT (min) 0.9983 0.9979 0.0011 0.0004 0.0022 # of peaks 0.8582 0.8356 0.0626 0.0250 0.0613 # of peaks with ≥ 1.5 — resolution 0.7928 0.7889 0.0711 0.0275 0.0400 API plate count C 0.9949 0.9924 0.0059 N/A N/A pk # of peaks with ≥ 1.5 — resolution C 0.9999 0.9999 0.0001 N/A N/A pk scientific validation of the DOE models. After the than their respective MSR threshold, which ranged models were fully validated for all selected individual from 0.0006 to 0.0711, indicating that all models were method responses, the method MODR was substantiated statistically significant and explained the correspond- by balancing and compromising among the most im- ing chromatographic response data. The MSR ad- portant method responses. justed values were all smaller than their respective MSR values, and the differences between the two was Statistical validation of the DOE models always very small (the largest difference was 0.0195 As showninTable 2, the MSR values ranged from for the API plate count model), indicating that there 0.7928 to 0.9999. All MSR values were much higher was no overfitting for the models. There was slight Fig. 2 Model Term Ranking Pareto Charts. Top row from left to right: API area (default), Epimer area (default), API plate count. Middle row from left to right: API RT, Epimer RT, Impurity 2 RT. Bottom row from left to right: impurity 3 RT, # of peaks, # of peaks with ≥ 1.5 — resolution Dong et al. AAPS Open (2021) 7:3 Page 7 of 14 lack of fit for the two customer models due to very Scientific validation of the DOE models low pure errors, and the MS-LOF cannot be calcu- With all models statistically validated, the discussions lated for the two C model because the Monte Carlo below will focus on scientific validation of the models by pk simulation gives essentially zero pure error. Other mechanistic understanding. than that, the MS-LOF ≤ the MS-LOF significance threshold for all other models, indicating the lack of Peak area models for API and Epimer peaks fit was not statistically significant. Peak areas and peak heights have been used for chroma- In addition to the above numeric statistical valid- tographic quantification. However, peak area was chosen ation, various model residual plots were employed for as the preferred approach as it is less sensitive to peak graphical statistical model validation. The parameter– distortions such as broadening, fronting, and tailing, residual plots and the run number-residual plots for which can cause significant variation in analyte quantita- all models showed no defined structure, indicating tion. To use peak area to reliably quantify the analyte random residual distribution. The normal probability within the MODR of a robust chromatographic method, plots showed all residual points lay in a nearly the peak area must remain stable with consistent analyte straight line for each single model, indicating normal injections. residual distribution for all models. The randomly Peak area models can be critical to the method devel- and normally distributed residuals provided the pri- opment and validation with multivariate DOE approach. mary graphical statistical validation of the DOE Solid peak area models were revealed for the API and models. See Fig. 3 for representative residuals plots Epimer peaks in this study. See the “API (default)” and for the “# of Peaks” model. “Epimer (default)” rows in Table 2 for the detailed model Fig. 3 Representative residuals plot for the “# of Peaks” model. Upper: run no – residuals plot; lower: residues normal probability plot Dong et al. AAPS Open (2021) 7:3 Page 8 of 14 regression statistics. See Fig. 2 for the Model Term uncertainty in determining peak start and end points. In Ranking Pareto Charts. See Eqs. 2 and 3 below for the this DOE study, the API and Epimer peaks were consist- detailed models. ently well-resolved (resolution ≥ 2.0) and were also sig- nificantly higher than the limit of quantitation, API Peak Area ¼þ23; 438; 293:01−2; 672; 900:45ðÞ A contributing to the strong peak area models. In contrast, þ 268; 590:01ðÞ A no appropriate peak area models could be developed for other impurity peaks as they were either not properly re- ð2Þ solved or were too close to the limit of quantitation. For Epimer Peak Area ¼þ270; 051:96−30; 896:51ðÞ A peaks with resolution ≤ 1.0 there will likely never be an þ 4; 332:26ðÞ A area model with reliable predictivity as the peak area cannot be consistently and accurately measured. ð3Þ The importance of a mechanistic understanding of the Although a full quadratic model for the four-factor DOE models for AQbD has been extensively discussed. five-level CCC design has a total of fourteen potential The API and Epimer peak area models were very similar terms, multivariate regression analyses revealed that only in that they both contained a strong negative first order two of the fourteen terms are statistically significant for flow rate term and a weak positive second order flow both the API and Epimer peak area models. In addition, rate term. the flow rate term and flow rate squared-terms are iden- The strong negative first order term can be explained tical for the two models, indicating the other three pa- by the exposure time of the analyte molecules to the de- rameters (final percentage strong solvent, oven tector. The UV detector used in the LC method is non- temperature, and EDTA concentration) have no signifi- destructive and concentration sensitive. Analyte mole- cant effect on peak area for both peaks. cules send signals to the detector when exposed to UV Oven temperature and EDTA concentration have neg- light while flowing through the fixed length detecting ligible effect on peak area and thus were not significant window in a band. As the molecules are not degraded by terms in the peak area models. The percentage of strong the UV light, the slower the flow rate, the longer the an- solvent was also not a significant term in the peak area alyte molecules are exposed to the UV light, allowing for models even though it did appear to influence peak increased signal to the detector and thus increased ana- height almost as much as flow rate, but not the peak lyte peak area. Simple direct linear regression of the peak area, as seen in Fig. 4. It was hypothesized that the two area against inverse flow rate confirmed both the API flow rate terms in the model consisted of a strong nega- and Epimer peak areas were proportional to the inverse tive first order term and a weak positive second order flow rate, with R values ≥ 0.99 (data not included). term, but more investigation was needed. As there was no obvious mechanistic explanation of Peak purity and peak integration are the primary fac- the weak positive second order term in the models, more tors affecting peak area. Partial or total peak overlap investigation was needed. Multivariate DOE customer (resolution < 1.5) due to analyte co-elution can impact models were pursued. The acquired customer models, the peak purity resulting in inaccurate integration of listed in Eqs. 4 and 5, used inverse flow rate “1/A” in both peaks. Peak integration may also be affected by un- place of the flow rate “A” for all pertinent terms among stable baseline and/or peak fronting and tailing due to the fourteen terms. The major model regression Fig. 4 Effects of final percentage of strong solvent and flow rate on the API peak area and peak height: run 15 (black) = 31%/0.9 mL/min; run 11 (red) = 33%/1.0 mL/min; run 19 (blue) = 35%/0.9 mL/min; run 9 (green) = 37%/1.0 mL/min; run 16 (purple) = 39%/0.9 mL/min Dong et al. AAPS Open (2021) 7:3 Page 9 of 14 statistics of the customer models are summarized in the Deemter equation (van Deemter et al. 1956), which “API (customer)” and “Epimer (customer)” rows in Table states that flow rate directly affects column plate height 2. Both customer models contain a single inverse flow and thus plate count. However, the missing flow rate rate term, confirming the negative effect of flow rate on term can be rationalized by the LC column that was peak area for both peaks. The customer models in Eqs. 4 used. According to the Van Deemter equation, plate and 5 provide more intuitive understanding of the flow height for the 150 × 4.6 mm, 3.5 μm column will remain rate effects on peak area than the “default” models in flat at a minimum level within the 0.7–1.1 mL/min flow Eqs. 2 and 3. The weak positive second order flow rate rate range used in this DOE study (Altiero 2018). As term in Eqs. 2 and 3 contributes less than 15% effect to plate count is inversely proportional to the plate height, the peak area and is very challenging to explain mechan- it will also remain flat at a maximal level within the 0.7– istically. This kind of model term replacing technique 1.1 mL/min flow rate range. may be of general value when using DOE to explore and The most dominating parameter in the API plate discover new scientific theory, including new chromato- count model was the final percentage of strong solvent. graphic theory. Its two terms B and B provided more than 60% positive Additionally, the peak area models in Eqs. 2–5 re- effects to the plate count response (see the Model Term vealed that the pump flow rate must be very consistent Ranking Pareto Chart in Fig. 2) and could be easily ex- among all injections during a quantitative chromato- plained by the inverse relationship between plate count graphic sequence. Currently, the best-in-industry flow and peak width when the gradient slope is increased. rate precision for a binary UPLC pump is “< 0.05% RSD or < 0.01 min SD” (Thermo Fisher Scientific, Vanquish Retention time models Pump Specification. 2021). Retention time (RT) and peak width are the primary at- tributes for a chromatographic peak. They are used to API Peak Area ¼þ21; 403; 748:42 calculate secondary attributes such as resolution, plate þ 100; 731:30ðÞ ðÞ 1=A ð4Þ count, and tailing. These peak attributes together define the overall quality of separation and subsequently quan- Epimer Peak Area ¼þ247; 286:48 tification of the analytes. RT is determined using all data þ 1; 173:90ðÞ ðÞ 1=A ð5Þ points on a peak and is thus a more reliable measurand than peak width, which uses only some data points on a peak. As such, peak width cannot provide the same level API peak plate count model of RT accuracy, especially for minor peaks, due to uncer- Column plate count is potentially useful in DOE model- tainty in the determination of peak start, end, and ing as it is a key parameter used in all modes of chroma- height. Consequently, RT is the most reliably measured tography for measuring and controlling column peak attribute. efficiency to assure separation of the analytes. The equa- The reliability of the RT measurement was confirmed tion for plate count (N) is shown below. It is calculated in this DOE study. As listed in Table 2, well-fitted RT using peak retention time (t ) and peak width at half models were acquired for the major API and Epimer height (w ) to mitigate any baseline effects and provide 1/2 peaks as well as the minor impurity 2 and impurity 3 a more reliable response for modeling-based QbD chro- peaks. The retention time models are listed in Eqs. 7–10 matographic method development. (note: reciprocal square for the Epimer and impurity 2, ðÞ t r and reciprocal for impurity 3 retention time data trans- N ¼ 5:54 formation before modeling inverted the positive and 1=2 negative nature of the model term effect in Eqs. 8–10, The peak plate count model for the API peak can be see the Model Term Ranking Pareto Charts in Fig. 2 for seen in Eq. 6. It was developed by reducing the fourteen the actual effect). The four models shared three com- terms. The major model quality attributes are summa- mon terms: flow rate, final percentage of strong solvent, rized in Table 2. and the square of final percentage of strong solvent. These three terms contributed more than 90% of the ef- API Peak Plate Count ¼þ19; 991:86 fect in all four RT models. Furthermore, in all four þ3; 322:41ðÞ B −767:71ðÞ D models the flow rate and final percentage of strong solv- 2 2 ent terms consistently produced a negative effect on RT, þ720:10ðÞ B −741:62ðÞ C −664:70ðÞ CD whereas the square of the final percentage of strong ð6Þ solvent term consistently produced positive effects. The flow rate was not a critical factor in the plate While the scientific rationale for the negative effects of count model. This seemingly goes against the Van the first two terms is well-established, the rationale for Dong et al. AAPS Open (2021) 7:3 Page 10 of 14 the positive effects of the third term lies beyond the four were statistically significant for the peak number scope of this study. model and only three were statistically significant for the resolved peak number model. Additionally, it is API RT ¼ 13:37632−0:99845ðÞ A −2:05511ðÞ B notable that the two models share three common þ 0:08980ðÞ C þ 0:14804ðÞ A terms (final percentage of strong solvent (B), flow rate þ 0:33645ðÞ B þ 0:21846ðÞ AB ð7Þ (A), and oven temperature (C)) and the orders of im- pact for the three terms is maintained as (B)>(A)> −1=2 ðÞ Epimer RT ¼ 0:01520 þ 0:00176ðÞ A (C), as seen in the Model Term Ranking Pareto þ0:00149ðÞ B −0:00008ðÞ C −0:00007ðÞ B Chart. The models indicated that within the evaluated þ0:00014ðÞ AB −0:00006ðÞ AD ranges the final percentage of strong solvent and flow rate have negative effects on the overall separation, ð8Þ while column temperature has a positive effect. These −1=2 ðÞ Imp 2 RT ¼ 0:01306 þ 0:00154ðÞ A observations align well with chromatographic scien- þ 0:00165ðÞ B tific principles. þ 0:00005ðÞ D −0:00011ðÞ B þ 0:00012ðÞ AB ð9Þ −1=2 ðÞ No:of Peaks ¼þ0:028 þ 0:003ðÞ A −1 þ 0:009ðÞ B −0:002ðÞ C −0:002ðÞ D ðÞ Imp 3 RT ¼ 0:09801 þ 0:00619ðÞ A þ 0:00918ðÞ B −0:00022ðÞ C ð11Þ 2 2 þ 0:00025ðÞ D −0:00026ðÞ A −0:00072ðÞ B −1=2 ð10Þ ðÞ No:of Peaks≥1:5−USP Resolution ¼þ0:039 þ 0:005ðÞ A þ 0:015ðÞ B −0:003ðÞ C ð12Þ As RT is typically the most reliable measured peak re- sponse, therefore, it produces most reliable models. One potential shortcoming of RT modeling-based method optimization is that the resolution of two neighboring Challenges and solutions to peak resolution modeling peaks is not only affected by the retention time, but also No appropriate model was found for the API peak reso- by peak width and peak shape, such as peak fronting lution response in this study, possibly due to very high and tailing. pure experimental error (34.2%) based on the replication runs. With this elevated level of resolution measurement Peak number models error, only large effects of the experiment variables A representative analytical sample is critical for AQbD would be discernable from an analysis of the resolution to use DOE to develop a chromatographic method cap- data. There are many potential reasons for the high pure able of resolving all potential related substances. Multi- experimental error: (1) error in the resolution value de- variate DOE chromatography of a forced degradation termination in each DOE run, especially with small peak sample may contain many minor peaks, which may elute size or tailing of the reference impurity peaks; (2) the in different orders across the different runs of the study, use of different reference peaks to calculate the reso- making tracking of the individual peaks nearly impos- lution when elution order shifts between DOE runs; (3) sible. One way to solve this problem is to focus on the the column is not sufficiently re-equilibrated between number of peaks observed, instead of tracking of individ- different conditions (note: Mention of column equilibra- ual peaks. Furthermore, to avoid an impractical method tion was hypothetical in this case and only to stress the with too many partially resolved peaks, the number of importance of column conditioning during DOE in gen- peaks with ≥ 1.5 resolution could be an alternative re- eral. As Fusion QbD automatically inserts conditioning sponse for modeling. runs into the DOE sequence where needed, this was not Excellent models were acquired for both the num- found to be an issue in this case study). The respective ber of peak responses and the number of peaks with solutions to overcome these challenges are (1) when ref- ≥ 1.5 resolution in this DOE study. See Table 2 for erence materials are available, make a synthetic method- the major model statistics, Fig. 2 for the Model Term development sample composed of each analyte at con- Pareto Ranking Chart, and Eqs. 11 and 12 for the de- centrations at least ten times the limit of quantitation; tailed models (note: reciprocal square data transform- (2) keep the concentration of analytes in the synthetic ation before modeling reversed the positive and sample at distinguishably different levels so that the negative nature of the model term effect in Eqs. 11– peaks can be tracked by size; and (3) allow enough time 12; see the Model Term Ranking Pareto Charts in for the column to be sufficiently re-equilibrated between Fig. 2 for the actual effect). Of the 14 terms, only different conditions. Dong et al. AAPS Open (2021) 7:3 Page 11 of 14 Table 3 Critical method parameter settings for the optimized regulatory guidelines (FDA Guidance for industry- method analytical procedures and methods validation for drugs Variable Level setting and biologics. 2015). In this DOE study, solid C models were produced Pump flow rate (mL/min) 0.78 pk for the “API Plate Count” and “Number of Peaks ≥ 1.5 Final % strong solvent (%) 34.2 USP Resolution”. See Table 2 for the detailed model re- Oven temperature (°C) 30.8 gression statistics. EDTA concentration (mM) 0.42 Multiple responses method optimization Method robustness evaluation and optimization by Once models have been established for selected individ- Monte Carlo simulation ual method responses, overall method evaluation and The robustness of a method is a measure of its capacity optimization can be performed. This is usually substanti- to remain unaffected by small but deliberate variations ated by balancing and compromising among multiple in method parameters. It provides an indication of the method responses. Three principles must be followed in method’s reliability during normal usage. Robustness selecting method responses to be included in the final was demonstrated for critical method responses by run- optimization: (1) the selected response is critical to ning system suitability checks, in which selected method achieve the goal (see Table 4); (2) a response is included parameters were changed one factor at a time. In com- only when its model is of sufficiently high quality to parison, the AQbD approach quantifies method robust- meet the goals of validation; and (3) the total number of ness with process robustness indices, such as C and responses included should be kept to a minimum. C , through multivariate robustness DOE, in which crit- pk Following the above three principles, five method re- ical method parameters are systematically varied, simul- sponses were selected for the overall method evaluation taneously. Process robustness indices are standard and optimization. Best overall answer search identified a statistical process control matrices widely used to quan- new optimized method when the four critical method tify and evaluate process and product variations. In this parameters were set at the specific values as listed in AQbD case study, method capability indices were calcu- Table 3. The cumulative desirability for the five desired lated to compare the variability of a chromatographic method response goals reached the maximum value of method response to its specification limits. The com- 1.0. The desirability for each individual goal also reached parison is made by forming the ratio between the spread the maximum value of 1.0, as listed in Table 4. of the response specifications and the spread of the re- sponse values, as measured by six times standard devi- ation of the response. The spread of the response values Method Operable Design Region (MODR) is acquired through tens of thousands of virtual Monte The critical method parameter settings in Table 3 define Carlo simulation runs of the corresponding response a single method that can simultaneously fulfill all five model, with all critical method parameters varied around targeted method goals listed in Table 4 to the best ex- their setting points randomly and simultaneously ac- tent possible. However, the actual operational values of cording to specified distributions. A method with a the four critical parameters may drift around their set process capability of ≥ 1.33 is considered robust as it will points during routine method executions. Based on the only fail to meet the response specifications 63 times out models, contour plots for method response can be cre- of a million runs and thus is capable of providing much ated to reveal how the response value changes as the more reliable measurements for informed decisions on method parameters drift. Furthermore, overlaying the drug development, manufacturing, and quality control. contour plots of all selected method responses reveal the Due to its intrinsic advantages over the OFAT approach, MODR, as shown in Figs. 4, 5, and 6. Note that for each multivariate DOE robustness evaluation was recom- response, a single unique color is used to shade the re- mended to replace the OFAT approach in the latest gion of the graph where the response fails the criteria; Table 4 Predicted results and confidence intervals for the selected responses of the optimized method Response Goal Predicted result Desirability − 2 Sigma conf. limit + 2 Sigma conf. limit No. of peaks Maximize 8.0 1.0000 6.3 10.5 No. of peaks ≥ 1.5 — USP resolution Maximize 6.2 1.0000 4.8 9.5 Max peak 1 – USP plate count Maximize 20,313 1.0000 17,560 23,067 Max peak 1 — USP plate count — C Maximize 2.01 1.0000 1.78 2.24 pk No. of peaks ≥ 1.5 — USP resolution — C Maximize 3.59 1.0000 3.54 3.63 pk Dong et al. AAPS Open (2021) 7:3 Page 12 of 14 Fig. 5 Trellis overlay graph shows how the size of the MODR (unshaded area) changes as the four method parameters change Fig. 6 Single overlay graph shows the original as-is method at point T is not robust (pump flow rate = 0.90 mL/min; final % strong Fig. 7 Single overlay graph shows a much more robust method at solvent = 35%; oven temperature = 30 °C; EDTA concentration = point T (pump flow rate = 0.78 mL/min; final % strong solvent = 0.50 mM) 34.2%; oven temperature = 30.8 °C; EDTA concentration = 0.42 mM) Dong et al. AAPS Open (2021) 7:3 Page 13 of 14 thus, criteria for all responses are met in the unshaded Abbreviations AQbD: Analytical quality by design; DOE: Design of experiments; area. CCC: Circumscribed central composite; MODR: Method Operable Design The Trellis overlay graph in Fig. 5 reveals the MODR Region; QbD: Quality by design; ICH: The International Council for from the perspectives of all four critical method parame- Harmonization of Technical Requirements for Pharmaceuticals for Human Use; CQA: Critical quality attributes; TMU: Target measurement uncertainty; ters, among which flow rate and final percentage of ATP: Analytical target profile; ANOVA: Analysis of variance; strong solvent change continuously while oven EDTA: Ethylenediaminetetraacetic acid; MSR: Mean square regression; MS- temperature and EDTA additive concentration were LOF: Mean square lack of fit; OFAT: One factor at a time each set at three different levels. Figure 5 clearly demon- Acknowledgements strates how the size of the MODR changes with the four The authors would like to thank KBP Biosciences for reviewing and giving method parameters. The single overlay graph in Fig. 6 permission to publish this case study. They would also like to thank Thermo Fisher Scientific and S Matrix for the Fusion QbD software, Lynette Bueno shows that the original as-is method (represented by the Perez for solution preparations, Dr. Michael Goedecke for statistical review, center point T) is on the edge of failure for two method and both Barry Gujral and Francis Vazquez for their overall support. responses, number of peaks (red) and number of peaks ≥ 1.5 resolution (blue), indicating that the original method Authors’ contributions YD designed the study and performed the data analysis. ZL was the primary is not robust. Conversely, point T in the single overlay scientist that executed the study. CL, EP, AP, TT, and WW contributed ideas graph in Fig. 7 is at the center of a relatively large un- and information to the study and reviewed and approved the manuscript. shaded area, indicating that the method is much more The authors read and approved the final manuscript. robust than the original method. Funding Not applicable; authors contributed case studies based on existing company Conclusion knowledge and experience. Through the collaboration of regulatory authorities and the industry, AQbD is the new paradigm to develop ro- Availability of data and materials The datasets used and/or analyzed during the current study are available bust chromatographic methods in the pharmaceutical from the corresponding author on reasonable request. industry. It uses a systematic approach to understand and control variability and build robustness into chro- Declarations matographic methods. This ensures that analytical re- Competing interests sults are always close to the product true value and meet The authors declare that they have no competing interests. the target measurement uncertainty, thus enabling in- formed decisions on drug development, manufacturing, Received: 27 May 2021 Accepted: 29 July 2021 and quality control. Multivariate DOE modeling plays an essential role in References AQbD and has the potential to elevate chromatographic Altiero, P. Why they matter, an introduction to chromatography equations. Slide methods to a robustness level rarely achievable via the 21. https://www.agilent.com/cs/library/eseminars/public/Agilent_Webinar_ Why_They_Matter_An_Intro_Chromatography_Equations_Nov262018.pdf. traditional OFAT approach. However, as demonstrated Accessed 13 May 2021. (2018). in this case study, chromatography science was still the Bezerraa MA, , Ferreirab SLC, Novaesa CG, dos Santoset AMP, Valasquesal GS, da foundation for prioritizing method inputs and responses Mata Cerqueira UMF, et al. Simultaneous optimization of multiple responses and its application in Analytical Chemistry – a review. Talanta; 194: 941-959. for the most appropriate DOE design and modeling, and (2019). provided further scientific validation to the statistically Borman P, Chatfield M, Nethercote P, Thompson D, Truman K (2007) The validated DOE models. Once models were fully validated application of quality by design to analytical methods. Pharma.l Technol 31(12):142–152 (n.d.) for all selected individual method responses, the MODR Chatterjee S, CMC Lead for QbD, ONDQA/CDER/FDA. Design space was substantiated by balancing and compromising considerations, AAPS Annual Meeting,2012. (n.d.). among the most important method responses. Debrus B, Guillarme D, Rudaz S (2013) Improved quality-by-design compliant methodology for method development in reversed-phase liquid Developing a MODR is critical for labs that transfer in chromatography. J Pharm Biomed Anal 84:215–223 (n.d.) externally sourced chromatographic methods. In this EURACHEM / CITAC. Setting and using target uncertainty in chemical case study, method evaluation using AQbD produced measurement. 2015. (n.d.). FDA Guidance for industry-analytical procedures and methods validation for objective data that enabled a deeper understanding of drugs and biologics. 2015. method variability, upon which a more robust method FDA pharmaceutical cGMPs for the 21st century — a risk-based approach. 2004. with a much larger MODR was proposed. The in-depth (n.d.). 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(n.d.). Orlandini S, Pinzauti S, Furlanetto S (2013) Application of quality by design to the development of analytical separation methods. Anal Bioanal Chem 2:443–450 (n.d.) Schweitzer M, Pohl M, Hanna-Brown M, Nethercote P, Borman P, Hansen P, Smith K et al (2010) Implications and opportunities for applying QbD principles to analytical measurements. Pharma. Technol 34(2):52–59 (n.d.) Tang YB, FDA/CDER/ONDQA (2011) Quality by design approaches to analytical methods -- FDA perspective. AAPS, Washington DC (n.d.) Thermo Fisher Scientific, Vanquish pump specification. 2021. https://assets. thermofisher.com/TFS-Assets/CMD/Specification-Sheets/ps-73056-vanquish- pumps-ps73056-en.pdf. Accessed May 22, 2021. (n.d.). van Deemter JJ, Zuiderweg FJ, Klinkenberg A. Longitudinal diffusion and resistance to mass transfer as causes of non ideality in chromatography. 1956. (n.d.). Volta e Sousa L, Gonçalves R, Menezes JC, Ramos A (2021) Analytical method lifecycle management in pharmaceutical industry: a review. AAPS PharmSciTech 22(3):128–141. https://doi.org/10.1208/s12249-021-01960-9 (n.d.) Publisher’sNote Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png AAPS Open Springer Journals

Perspectives in modeling and model validation during analytical quality by design chromatographic method evaluation: a case study

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Abstract

Design of experiments (DOE)-based analytical quality by design (AQbD) method evaluation, development, and validation is gaining momentum and has the potential to create robust chromatographic methods through deeper understanding and control of variability. In this paper, a case study is used to explore the pros, cons, and pitfalls of using various chromatographic responses as modeling targets during a DOE-based AQbD approach. The case study involves evaluation of a reverse phase gradient HPLC method by a modified circumscribed central composite (CCC) response surface DOE. Solid models were produced for most responses and their validation was assessed with graphical and numeric statistics as well as chromatographic mechanistic understanding. The five most relevant responses with valid models were selected for multiple responses method optimization and the final optimized method was chosen based on the Method Operable Design Region (MODR). The final method has a much larger MODR than the original method and is thus more robust. This study showcases how to use AQbD to gain deep method understanding and make informed decisions on method suitability. Discoveries and discussions in this case study may contribute to continuous improvement of AQbD chromatography practices in the pharmaceutical industry. Keywords: AQbD, DOE, MODR, Statistical model validation, Scientific model validation, Multiple responses optimization Introduction previously approved drugs both challenging and costly. Drug development using a quality by design (QbD) ap- The International Council for Harmonization of Tech- proach is an essential part of the Pharmaceutical cGMP nical Requirements for Pharmaceuticals for Human Use Initiative for the twenty-first century (FDA Pharmaceut- (ICH) embraced this initiative and began issuing QbD ical cGMPs For The 21st Century — A Risk-Based Ap- relevant quality guidelines in 2005. The final versions of proach. 2004) established by the FDA. This initiative ICH Q8–Q12 [(ICH Q8 (R2) 2009) (ICH Q9 2005) (ICH seeks to address unmet patient needs, unsustainable rise Q10 2008) (ICH Q11 2012) (ICH Q12 2019)] have been of healthcare costs, and the reluctance to adopt new adopted by all ICH members. The in-progress version of technology in pharmaceutical development and manu- ICH Q14 (ICH Q14 2018) will offer AQbD guidelines facturing. These issues were the result of old regulations for analytical procedures and promote the use of QbD that are very rigid and made continuous improvement of principles to achieve a greater understanding and con- trol of testing methods and reduction of result * Correspondence: yongzhi.dong@thermofisher.com variability. Thermo Fisher Scientific Inc., Durham, NC, USA © The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Dong et al. AAPS Open (2021) 7:3 Page 2 of 14 Product development using a QbD approach empha- an approved MODR does not impact the results and of- sizes understanding of product and process variability, as fers an advantage for continuous improvement without well as control of process variability. It relies on analyt- submission of supplemental regulatory documentation. ical methods to measure, understand, and control the Establishment of the MODR is facilitated by multivariate critical quality attributes (CQA) of raw materials and in- design of experiments (DOE) (Volta e Sousa et al. 2021). termediates to optimize critical process parameters and Typically, three types of DOE may be involved in AQbD. realize the Quality Target Product Profile (ICH Q8 (R2) The screening DOE further consolidates the potential 2009). Nevertheless, part of the variability reported by critical method parameters determined from the risk as- an analytical test can originate from the variability of the sessment. The optimization DOE builds mathematical analytical measurement itself. This can be seen from Eq. models and selects the appropriate critical method par- 1. ameter settings to reach to the target mean responses. Finally, the robustness DOE further narrows down the 2 2 2 σ ¼ σ þ σ ð1Þ critical method parameter settings to establish the reported product measurement MODR, within which the target mean responses are The reported variability is the sum of intrinsic product consistently realized. Based on this AQbD framework, it variability and extrinsic analytical measurement variabil- is very clear DOE models are essential to understanding ity (NIST/SEMATECH e-Handbook of statistical and controlling method variability to build robustness methods 2012a, 2012b, 2012c, 2012d). The measurement into analytical methods. Although there have been ex- variability can be minimized by applying QbD principles, tensive case studies published regarding AQbD (Gran- concepts, and tools during method development to as- geia et al. 2020), systematic and in-depth discussion of sure the quality and reliability of the analytical method the fundamental AQbD modeling is still largely unex- can meet the target measurement uncertainty (TMU) plored. Methodical evaluation of the pros, cons, and pit- (EURACHEM/CITAC 2015). High-quality analytical falls of using various chromatographic responses as data truthfully reveal product CQAs and thus enables modeling targets is even more rare (Debrus et al. 2013) robust, informed decisions regarding drug development, (Orlandini et al. 2013) (Bezerraa et al. 2019). The pur- manufacturing, and quality control. pose of this case study is to investigate relevant topics ICH Q14 introduces the AQbD concepts, using a ra- such as data analysis and modeling principles, statistical tional, systematic, and holistic approach to build quality and scientific validation of DOE models, method robust- into analytical methods. The Method Operable Design ness evaluation and optimization by Monte Carlo simu- Region (MODR) (Borman et al. 2007) is a multidimen- lation (Chatterjee S 2012), multiple responses method sional space based on the critical method parameters optimization (Leardi 2009), and MODR establishment. and settings that provide suitable method performance. Discoveries and discussions in this case study may con- This approach begins with a predefined analytical target tribute to continuous improvement of chromatographic profile (ATP) (Schweitzer et al. 2010), which defines the AQbD practices in the pharmaceutical industry. method’s intended purpose and commands analytical technique selection and all other method development Methods/experimental activities. This involves understanding of the method Materials and methods and control of the method variability based on sound C111229929-C, a third-generation novel synthetic science and risk management. It is generally agreed tetracycline-class antibiotic currently under phase 1 clin- upon that systematic AQbD method development ical trial was provided by KBP Biosciences. A reverse should include the following six consecutive steps (Tang phase HPLC purity and impurities method was also pro- 2011): vided for evaluation and optimization using AQbD. The method was developed using a one factor at a time 1. ATP determination (OFAT) approach and used a Waters XBridge C18 col- 2. Analytical technique selection umn (4.6 × 150 mm, 3.5 μm) and a UV detector. Mobile 3. Method risk assessment phase A was composed of ammonium acetate/ethylene- 4. MODR establishment diaminetetraacetic acid (EDTA) buffer at pH 8.8 and 5. Method control strategy mobile phase B was composed of 70:30 (v/v) aceto- 6. Continuous method improvement through a life nitrile/EDTA buffer at pH 8.5. Existing data from forced cycle approach degradation and 24-month stability studies demon- strated that the method was capable of separating all six A multivariate MODR allows freedom to make specified impurities/degradants with ≥ 1.5 resolution. method changes and maintain the method validation A 1.0 mg/mL C111229929-C solution was prepared by (Chatterjee S 2012). Changing method conditions within dissolving the aged C111229929-C stability sample into Dong et al. AAPS Open (2021) 7:3 Page 3 of 14 10 mM HCl in methanol and used as the method evalu-  Good coverage of the design space by including the ation sample. An agilent 1290 UPLC equipped with a interior design points DAD detector was used. In-house 18.2 MΩ Milli-Q  Low predictive variances of the design points Water was used for solution preparations. All other re-  Low model term coefficient estimation errors agents were of ACS equivalent or higher grade. Waters Empower® 3 was used as the Chromatographic Data Sys- The design also allows for implementation of a se- tem. Fusion QbD v 9.9.0 software was used for DOE de- quential approach, where trials from previously con- sign, data analysis, modeling, Monte Carlo simulation, ducted factorial experiments can be augmented to form multiple responses mean, and robustness optimization. the CCC design. When there is little understanding Empower® 3 and Fusion QbD were fully integrated and about the method and critical method parameters, such validated. as when developing a new method from scratch, direct A method risk assessment was performed through re- application of an optimizing CCC design is generally not view of the literature and existing validation and stability recommended. However, there was sufficient previous data to establish priorities for method inputs and re- knowledge regarding this specific method, justifying the sponses. Based on the risk assessment, four method pa- direct approach. rameters with the highest risk priority numbers were selected as critical method parameters. Method evalu- DOE data analysis and modeling principles ation and optimization was performed by a modified cir- DOE software is one of the most important tools to fa- cumscribed central composite (CCC) response surface cilitate efficient and effective AQbD chromatographic DOE design with five levels per parameter, for a total of method development, validation, and transfer. Fusion 30 runs. The modifications were the extra duplicate rep- QbD software was employed for DOE design and data lications at three factorial points. In addition to triplicate analysis. Mathematical modeling of the physicochemical replications at the center point, the modified design had chromatographic separation process is essential for DOE a total of nine replicates. See Table 1 for the detailed de- to develop robust chromatographic methods through sign matrix. A full quadratic model for the four-factor three phases: chemistry screening, mean optimization, five-level CCC design has a total of fourteen potential and robustness optimization. The primary method pa- terms. They include four main linear terms (A, B, C, D), 2 2 2 2 rameters affecting separation (e.g., column packing, mo- four quadratic terms (A ,B ,C ,D ), and six two-way bile phase pH, mobile phase organic modifier) are interaction terms (A*B, A*C, A*D, B*C, B*D, and C*D). statistically determined with models during chemistry Pre-runs executed at selected star (extreme) points screening. The secondary method parameters affecting verified that all expected analytes eluted within the 35 separation (e.g., column temperature, flow rate, gradient min run time. This mitigated the risk of any non-eluting slope settings) are optimized during mean optimization peaks during the full DOE study, as a single unusable using models to identify the method most capable of run may raise questions regarding the validity of the en- reaching all selected method response goals on average. tire study. Based on the pre-runs, the concentration of During robustness optimization, robustness models for the stock EDTA solution was decreased four-fold to selected method responses are created with Monte Carlo mitigate inaccurate in-line mixing of mobile phase B simulation and used to further optimize method param- caused by low volumes of a high concentration stock. eters such that all method responses consistently reach The final ranges and levels for each of the four selected their goals, as reflected by a process capability value of ≥ method parameters are also listed in Table 1. 1.33, which is the established standard for a robust Each unique DOE run in Table 1 is a different method. process (NIST/SEMATECH e-Handbook of statistical As there were 25 unique running conditions, there were methods 2012a, 2012b, 2012c, 2012d). 25 different methods in this DOE study. The G- Models are critical to the AQbD approach and must Efficiency and the average predicted variance (NIST/ be validated both statistically and scientifically. Statistical SEMATECH e-Handbook of statistical methods 2012a, validation is performed using various statistical tests 2012b, 2012c, 2012d) (Myers and Montgomery 1995)of such as residual randomness and normality (NIST/ the design were 86.8% and 10.6%, respectively, meeting SEMATECH e-Handbook of statistical methods 2012a, their respective design goals of ≥ 50% and ≤ 25%. Some 2012b, 2012c, 2012d), regression R-squared, adjusted re- of the major advantages of this modified CCC design in- gression R-squared, and prediction R-squared. Scientific clude the following: validation is achieved by checking the terms in a statis- tical model against the relevant established scientific Established quadratic effects principles, which is described as mechanistic under- Robust models that minimize effects of potential standing in the relevant literature (ICH Q8 (R2) 2009). missing data Dong et al. AAPS Open (2021) 7:3 Page 4 of 14 Table 1 The experimental matrix of the modified CCC design Run No. (A) Pump flow rate (B) Final strong (C) Oven (D) EDTA additive Predicted response (mL/min) solvent (%) temperature (°C) concentration (mM) variance (%) 1 0.9 35.0 26.0 0.50 16.67 2 0.8 33.0 28.0 0.45 10.80 3 1.0 33.0 28.0 0.45 10.87 4 0.8 37.0 28.0 0.45 10.87 5 1.0 37.0 28.0 0.45 16.67 6 0.8 33.0 28.0 0.55 16.85 7 1.0 33.0 28.0 0.55 17.02 8 0.8 37.0 28.0 0.55 17.02 9 1.0 37.0 28.0 0.55 17.21 10 0.8 33.0 28.0 0.45 10.80 11 1.0 33.0 28.0 0.45 10.87 12 0.8 37.0 28.0 0.45 10.87 13 0.7 35.0 30.0 0.50 16.91 14 1.1 35.0 30.0 0.50 17.14 15 0.9 31.0 30.0 0.50 16.91 16 0.9 39.0 30.0 0.50 17.14 17 0.9 35.0 30.0 0.40 16.67 18 0.9 35.0 30.0 0.60 17.41 19 0.9 35.0 30.0 0.50 10.00 20 0.9 35.0 30.0 0.50 10.00 21 0.9 35.0 30.0 0.50 10.00 22 0.8 33.0 32.0 0.45 16.85 23 1.0 33.0 32.0 0.45 17.02 24 0.8 37.0 32.0 0.45 17.02 25 1.0 37.0 32.0 0.45 17.21 26 0.8 33.0 32.0 0.55 17.32 27 1.0 33.0 32.0 0.55 16.16 28 0.8 37.0 32.0 0.55 16.16 29 1.0 37.0 32.0 0.55 16.16 30 0.9 35.0 34.0 0.50 17.41 Parameter 0.7–1.1 33–37 26–34 0.4–0.6 ranges a b c d Each run is labeled with the type of design point: , star points; , factorial points; , triplicate replications at the center point (the nominal conditions); and , model robustness points by run 10, 11, and 12, which are the duplicate replications of the factorial points by run 2, 3, and 4, respectively Fusion uses data transformation analysis to decide understanding of how a method response, such as reso- whether data transformation is necessary before model- lution, is affected by critical method parameters. ing, and then uses analysis of variance (ANOVA) and re- Since Fusion relies on models for chemistry screening, gression to generate method response models. ANOVA mean optimization, and robustness optimization, it is provides objective and statistical rationale for each con- critical to holistically evaluate each method response secutive modeling decision. Model residual plots are model from all relevant model regression statistics to as- fundamental tools for validating the final method re- sure model validity before multiple method response sponse models. When a model fits the DOE data well, optimization. Inappropriate models will lead to poor the response residuals should be distributed randomly prediction and non-robust methods. This paper will de- without any defined structure, and normally. A valid scribe the holistic evaluation approach used to develop a method response model provides the deepest robust chromatographic method with Fusion QbD. Dong et al. AAPS Open (2021) 7:3 Page 5 of 14 Results many terms are used in the model or the sample size is Representative chromatogram under nominal conditions too small. Careful planning and pre-runs executed at select star points allowed for successful execution of the DOE with Model Term Ranking Pareto Charts for scientific all expected peaks eluting within the running time for all validation of DOE models the 30 runs. A representative chromatogram at the nom- DOE models are calculated from standardized variable inal conditions is shown in Fig. 1. The API peak level settings. Scientific validation of a DOE model (C1112299299-C) and the Epimer peak (C112299299-C- through mechanistic understanding can be challenging epimer) can be seen, as well as seven minor impurity when data transformation before modeling ostensibly in- peaks, among which impurity 2 and impurity 3 elute at verts the positive and negative nature of the model term 8.90 and 10.51 min, respectively. The inset shows the effect. To overcome this challenge, Model Term Ranking full-scale chromatogram. Pareto Charts that provide the detailed effects of each term in a model were employed. See Fig. 2 for details. The chart presents all terms of a model in descending Results for statistical validation of the DOE models order (left to right) based on the absolute magnitude of ANOVA and regression data analysis revealed many their effects. The primary y-axis (model term effect) DOE models for various peak responses. The major nu- gives the absolute magnitude of individual model terms, meric regression statistics of the peak response models while the secondary y-axis (cumulative percentage) gives are summarized in Table 2. the cumulative relative percentage effects of all model MSR (mean square regression), MSR adjusted, and terms. Blue bars correspond to terms with a positive ef- MS-LOF (mean square lack of fit) are major numeric fect, while gray bars correspond to those with a negative statistics for validating a DOE model. A model is statisti- effect. The Model Term Ranking Pareto Charts for all cally significant when the MSR ≥ the MSR significance models are summarized in Fig. 2, except the two “cus- threshold, which is the 0.0500 probability value for stat- tomer” peak area models with a single term and the two istical significance. The lack of fit of a model is not sta- C models. pk tistically significant when the MS-LOF ≤ the MS-LOF significance threshold, which is also the 0.0500 probabil- Discussion ity value for statistical significance. The MSR adjusted AQbD relies on models for efficient and effective chem- statistic is the MSR adjusted with the number of terms istry screening, mean optimization, and robustness in the model to assure a new term improves the model optimization of chromatographic methods. It is critical fit more than expected by chance alone. For a valid to “validate” the models both statistically and scientific- model, the MSR adjusted is always smaller than the ally, as inappropriate models may lead to impractical MSR and the difference is usually very small, unless too methods. As such, this section will discuss statistical and Fig. 1 A representative chromatogram under nominal conditions Dong et al. AAPS Open (2021) 7:3 Page 6 of 14 Table 2 Major model regression statistics of various chromatographic responses Response MSR MSR adjusted MSR threshold MS-LOF MS-LOF threshold API area (default) 0.9913 0.9906 0.0022 0.0006 0.0041 Epimer area (default) 0.9902 0.9895 0.0024 0.0008 0.0026 API area (customer) 0.8191 0.8124 0.0282 0.0081 0.0026 Epimer area (customer) 0.8481 0.8425 0.0237 0.0068 0.0017 API plate count 0.9101 0.8906 0.0516 0.0206 0.0716 API RT (min) 0.9988 0.9984 0.0009 0.0003 0.0028 Epimer RT (min) 0.9986 0.9982 0.0009 0.0004 0.0014 Impurity 2 RT (min) 0.9988 0.9986 0.0006 0.0002 0.0014 Impurity 3 RT (min) 0.9983 0.9979 0.0011 0.0004 0.0022 # of peaks 0.8582 0.8356 0.0626 0.0250 0.0613 # of peaks with ≥ 1.5 — resolution 0.7928 0.7889 0.0711 0.0275 0.0400 API plate count C 0.9949 0.9924 0.0059 N/A N/A pk # of peaks with ≥ 1.5 — resolution C 0.9999 0.9999 0.0001 N/A N/A pk scientific validation of the DOE models. After the than their respective MSR threshold, which ranged models were fully validated for all selected individual from 0.0006 to 0.0711, indicating that all models were method responses, the method MODR was substantiated statistically significant and explained the correspond- by balancing and compromising among the most im- ing chromatographic response data. The MSR ad- portant method responses. justed values were all smaller than their respective MSR values, and the differences between the two was Statistical validation of the DOE models always very small (the largest difference was 0.0195 As showninTable 2, the MSR values ranged from for the API plate count model), indicating that there 0.7928 to 0.9999. All MSR values were much higher was no overfitting for the models. There was slight Fig. 2 Model Term Ranking Pareto Charts. Top row from left to right: API area (default), Epimer area (default), API plate count. Middle row from left to right: API RT, Epimer RT, Impurity 2 RT. Bottom row from left to right: impurity 3 RT, # of peaks, # of peaks with ≥ 1.5 — resolution Dong et al. AAPS Open (2021) 7:3 Page 7 of 14 lack of fit for the two customer models due to very Scientific validation of the DOE models low pure errors, and the MS-LOF cannot be calcu- With all models statistically validated, the discussions lated for the two C model because the Monte Carlo below will focus on scientific validation of the models by pk simulation gives essentially zero pure error. Other mechanistic understanding. than that, the MS-LOF ≤ the MS-LOF significance threshold for all other models, indicating the lack of Peak area models for API and Epimer peaks fit was not statistically significant. Peak areas and peak heights have been used for chroma- In addition to the above numeric statistical valid- tographic quantification. However, peak area was chosen ation, various model residual plots were employed for as the preferred approach as it is less sensitive to peak graphical statistical model validation. The parameter– distortions such as broadening, fronting, and tailing, residual plots and the run number-residual plots for which can cause significant variation in analyte quantita- all models showed no defined structure, indicating tion. To use peak area to reliably quantify the analyte random residual distribution. The normal probability within the MODR of a robust chromatographic method, plots showed all residual points lay in a nearly the peak area must remain stable with consistent analyte straight line for each single model, indicating normal injections. residual distribution for all models. The randomly Peak area models can be critical to the method devel- and normally distributed residuals provided the pri- opment and validation with multivariate DOE approach. mary graphical statistical validation of the DOE Solid peak area models were revealed for the API and models. See Fig. 3 for representative residuals plots Epimer peaks in this study. See the “API (default)” and for the “# of Peaks” model. “Epimer (default)” rows in Table 2 for the detailed model Fig. 3 Representative residuals plot for the “# of Peaks” model. Upper: run no – residuals plot; lower: residues normal probability plot Dong et al. AAPS Open (2021) 7:3 Page 8 of 14 regression statistics. See Fig. 2 for the Model Term uncertainty in determining peak start and end points. In Ranking Pareto Charts. See Eqs. 2 and 3 below for the this DOE study, the API and Epimer peaks were consist- detailed models. ently well-resolved (resolution ≥ 2.0) and were also sig- nificantly higher than the limit of quantitation, API Peak Area ¼þ23; 438; 293:01−2; 672; 900:45ðÞ A contributing to the strong peak area models. In contrast, þ 268; 590:01ðÞ A no appropriate peak area models could be developed for other impurity peaks as they were either not properly re- ð2Þ solved or were too close to the limit of quantitation. For Epimer Peak Area ¼þ270; 051:96−30; 896:51ðÞ A peaks with resolution ≤ 1.0 there will likely never be an þ 4; 332:26ðÞ A area model with reliable predictivity as the peak area cannot be consistently and accurately measured. ð3Þ The importance of a mechanistic understanding of the Although a full quadratic model for the four-factor DOE models for AQbD has been extensively discussed. five-level CCC design has a total of fourteen potential The API and Epimer peak area models were very similar terms, multivariate regression analyses revealed that only in that they both contained a strong negative first order two of the fourteen terms are statistically significant for flow rate term and a weak positive second order flow both the API and Epimer peak area models. In addition, rate term. the flow rate term and flow rate squared-terms are iden- The strong negative first order term can be explained tical for the two models, indicating the other three pa- by the exposure time of the analyte molecules to the de- rameters (final percentage strong solvent, oven tector. The UV detector used in the LC method is non- temperature, and EDTA concentration) have no signifi- destructive and concentration sensitive. Analyte mole- cant effect on peak area for both peaks. cules send signals to the detector when exposed to UV Oven temperature and EDTA concentration have neg- light while flowing through the fixed length detecting ligible effect on peak area and thus were not significant window in a band. As the molecules are not degraded by terms in the peak area models. The percentage of strong the UV light, the slower the flow rate, the longer the an- solvent was also not a significant term in the peak area alyte molecules are exposed to the UV light, allowing for models even though it did appear to influence peak increased signal to the detector and thus increased ana- height almost as much as flow rate, but not the peak lyte peak area. Simple direct linear regression of the peak area, as seen in Fig. 4. It was hypothesized that the two area against inverse flow rate confirmed both the API flow rate terms in the model consisted of a strong nega- and Epimer peak areas were proportional to the inverse tive first order term and a weak positive second order flow rate, with R values ≥ 0.99 (data not included). term, but more investigation was needed. As there was no obvious mechanistic explanation of Peak purity and peak integration are the primary fac- the weak positive second order term in the models, more tors affecting peak area. Partial or total peak overlap investigation was needed. Multivariate DOE customer (resolution < 1.5) due to analyte co-elution can impact models were pursued. The acquired customer models, the peak purity resulting in inaccurate integration of listed in Eqs. 4 and 5, used inverse flow rate “1/A” in both peaks. Peak integration may also be affected by un- place of the flow rate “A” for all pertinent terms among stable baseline and/or peak fronting and tailing due to the fourteen terms. The major model regression Fig. 4 Effects of final percentage of strong solvent and flow rate on the API peak area and peak height: run 15 (black) = 31%/0.9 mL/min; run 11 (red) = 33%/1.0 mL/min; run 19 (blue) = 35%/0.9 mL/min; run 9 (green) = 37%/1.0 mL/min; run 16 (purple) = 39%/0.9 mL/min Dong et al. AAPS Open (2021) 7:3 Page 9 of 14 statistics of the customer models are summarized in the Deemter equation (van Deemter et al. 1956), which “API (customer)” and “Epimer (customer)” rows in Table states that flow rate directly affects column plate height 2. Both customer models contain a single inverse flow and thus plate count. However, the missing flow rate rate term, confirming the negative effect of flow rate on term can be rationalized by the LC column that was peak area for both peaks. The customer models in Eqs. 4 used. According to the Van Deemter equation, plate and 5 provide more intuitive understanding of the flow height for the 150 × 4.6 mm, 3.5 μm column will remain rate effects on peak area than the “default” models in flat at a minimum level within the 0.7–1.1 mL/min flow Eqs. 2 and 3. The weak positive second order flow rate rate range used in this DOE study (Altiero 2018). As term in Eqs. 2 and 3 contributes less than 15% effect to plate count is inversely proportional to the plate height, the peak area and is very challenging to explain mechan- it will also remain flat at a maximal level within the 0.7– istically. This kind of model term replacing technique 1.1 mL/min flow rate range. may be of general value when using DOE to explore and The most dominating parameter in the API plate discover new scientific theory, including new chromato- count model was the final percentage of strong solvent. graphic theory. Its two terms B and B provided more than 60% positive Additionally, the peak area models in Eqs. 2–5 re- effects to the plate count response (see the Model Term vealed that the pump flow rate must be very consistent Ranking Pareto Chart in Fig. 2) and could be easily ex- among all injections during a quantitative chromato- plained by the inverse relationship between plate count graphic sequence. Currently, the best-in-industry flow and peak width when the gradient slope is increased. rate precision for a binary UPLC pump is “< 0.05% RSD or < 0.01 min SD” (Thermo Fisher Scientific, Vanquish Retention time models Pump Specification. 2021). Retention time (RT) and peak width are the primary at- tributes for a chromatographic peak. They are used to API Peak Area ¼þ21; 403; 748:42 calculate secondary attributes such as resolution, plate þ 100; 731:30ðÞ ðÞ 1=A ð4Þ count, and tailing. These peak attributes together define the overall quality of separation and subsequently quan- Epimer Peak Area ¼þ247; 286:48 tification of the analytes. RT is determined using all data þ 1; 173:90ðÞ ðÞ 1=A ð5Þ points on a peak and is thus a more reliable measurand than peak width, which uses only some data points on a peak. As such, peak width cannot provide the same level API peak plate count model of RT accuracy, especially for minor peaks, due to uncer- Column plate count is potentially useful in DOE model- tainty in the determination of peak start, end, and ing as it is a key parameter used in all modes of chroma- height. Consequently, RT is the most reliably measured tography for measuring and controlling column peak attribute. efficiency to assure separation of the analytes. The equa- The reliability of the RT measurement was confirmed tion for plate count (N) is shown below. It is calculated in this DOE study. As listed in Table 2, well-fitted RT using peak retention time (t ) and peak width at half models were acquired for the major API and Epimer height (w ) to mitigate any baseline effects and provide 1/2 peaks as well as the minor impurity 2 and impurity 3 a more reliable response for modeling-based QbD chro- peaks. The retention time models are listed in Eqs. 7–10 matographic method development. (note: reciprocal square for the Epimer and impurity 2, ðÞ t r and reciprocal for impurity 3 retention time data trans- N ¼ 5:54 formation before modeling inverted the positive and 1=2 negative nature of the model term effect in Eqs. 8–10, The peak plate count model for the API peak can be see the Model Term Ranking Pareto Charts in Fig. 2 for seen in Eq. 6. It was developed by reducing the fourteen the actual effect). The four models shared three com- terms. The major model quality attributes are summa- mon terms: flow rate, final percentage of strong solvent, rized in Table 2. and the square of final percentage of strong solvent. These three terms contributed more than 90% of the ef- API Peak Plate Count ¼þ19; 991:86 fect in all four RT models. Furthermore, in all four þ3; 322:41ðÞ B −767:71ðÞ D models the flow rate and final percentage of strong solv- 2 2 ent terms consistently produced a negative effect on RT, þ720:10ðÞ B −741:62ðÞ C −664:70ðÞ CD whereas the square of the final percentage of strong ð6Þ solvent term consistently produced positive effects. The flow rate was not a critical factor in the plate While the scientific rationale for the negative effects of count model. This seemingly goes against the Van the first two terms is well-established, the rationale for Dong et al. AAPS Open (2021) 7:3 Page 10 of 14 the positive effects of the third term lies beyond the four were statistically significant for the peak number scope of this study. model and only three were statistically significant for the resolved peak number model. Additionally, it is API RT ¼ 13:37632−0:99845ðÞ A −2:05511ðÞ B notable that the two models share three common þ 0:08980ðÞ C þ 0:14804ðÞ A terms (final percentage of strong solvent (B), flow rate þ 0:33645ðÞ B þ 0:21846ðÞ AB ð7Þ (A), and oven temperature (C)) and the orders of im- pact for the three terms is maintained as (B)>(A)> −1=2 ðÞ Epimer RT ¼ 0:01520 þ 0:00176ðÞ A (C), as seen in the Model Term Ranking Pareto þ0:00149ðÞ B −0:00008ðÞ C −0:00007ðÞ B Chart. The models indicated that within the evaluated þ0:00014ðÞ AB −0:00006ðÞ AD ranges the final percentage of strong solvent and flow rate have negative effects on the overall separation, ð8Þ while column temperature has a positive effect. These −1=2 ðÞ Imp 2 RT ¼ 0:01306 þ 0:00154ðÞ A observations align well with chromatographic scien- þ 0:00165ðÞ B tific principles. þ 0:00005ðÞ D −0:00011ðÞ B þ 0:00012ðÞ AB ð9Þ −1=2 ðÞ No:of Peaks ¼þ0:028 þ 0:003ðÞ A −1 þ 0:009ðÞ B −0:002ðÞ C −0:002ðÞ D ðÞ Imp 3 RT ¼ 0:09801 þ 0:00619ðÞ A þ 0:00918ðÞ B −0:00022ðÞ C ð11Þ 2 2 þ 0:00025ðÞ D −0:00026ðÞ A −0:00072ðÞ B −1=2 ð10Þ ðÞ No:of Peaks≥1:5−USP Resolution ¼þ0:039 þ 0:005ðÞ A þ 0:015ðÞ B −0:003ðÞ C ð12Þ As RT is typically the most reliable measured peak re- sponse, therefore, it produces most reliable models. One potential shortcoming of RT modeling-based method optimization is that the resolution of two neighboring Challenges and solutions to peak resolution modeling peaks is not only affected by the retention time, but also No appropriate model was found for the API peak reso- by peak width and peak shape, such as peak fronting lution response in this study, possibly due to very high and tailing. pure experimental error (34.2%) based on the replication runs. With this elevated level of resolution measurement Peak number models error, only large effects of the experiment variables A representative analytical sample is critical for AQbD would be discernable from an analysis of the resolution to use DOE to develop a chromatographic method cap- data. There are many potential reasons for the high pure able of resolving all potential related substances. Multi- experimental error: (1) error in the resolution value de- variate DOE chromatography of a forced degradation termination in each DOE run, especially with small peak sample may contain many minor peaks, which may elute size or tailing of the reference impurity peaks; (2) the in different orders across the different runs of the study, use of different reference peaks to calculate the reso- making tracking of the individual peaks nearly impos- lution when elution order shifts between DOE runs; (3) sible. One way to solve this problem is to focus on the the column is not sufficiently re-equilibrated between number of peaks observed, instead of tracking of individ- different conditions (note: Mention of column equilibra- ual peaks. Furthermore, to avoid an impractical method tion was hypothetical in this case and only to stress the with too many partially resolved peaks, the number of importance of column conditioning during DOE in gen- peaks with ≥ 1.5 resolution could be an alternative re- eral. As Fusion QbD automatically inserts conditioning sponse for modeling. runs into the DOE sequence where needed, this was not Excellent models were acquired for both the num- found to be an issue in this case study). The respective ber of peak responses and the number of peaks with solutions to overcome these challenges are (1) when ref- ≥ 1.5 resolution in this DOE study. See Table 2 for erence materials are available, make a synthetic method- the major model statistics, Fig. 2 for the Model Term development sample composed of each analyte at con- Pareto Ranking Chart, and Eqs. 11 and 12 for the de- centrations at least ten times the limit of quantitation; tailed models (note: reciprocal square data transform- (2) keep the concentration of analytes in the synthetic ation before modeling reversed the positive and sample at distinguishably different levels so that the negative nature of the model term effect in Eqs. 11– peaks can be tracked by size; and (3) allow enough time 12; see the Model Term Ranking Pareto Charts in for the column to be sufficiently re-equilibrated between Fig. 2 for the actual effect). Of the 14 terms, only different conditions. Dong et al. AAPS Open (2021) 7:3 Page 11 of 14 Table 3 Critical method parameter settings for the optimized regulatory guidelines (FDA Guidance for industry- method analytical procedures and methods validation for drugs Variable Level setting and biologics. 2015). In this DOE study, solid C models were produced Pump flow rate (mL/min) 0.78 pk for the “API Plate Count” and “Number of Peaks ≥ 1.5 Final % strong solvent (%) 34.2 USP Resolution”. See Table 2 for the detailed model re- Oven temperature (°C) 30.8 gression statistics. EDTA concentration (mM) 0.42 Multiple responses method optimization Method robustness evaluation and optimization by Once models have been established for selected individ- Monte Carlo simulation ual method responses, overall method evaluation and The robustness of a method is a measure of its capacity optimization can be performed. This is usually substanti- to remain unaffected by small but deliberate variations ated by balancing and compromising among multiple in method parameters. It provides an indication of the method responses. Three principles must be followed in method’s reliability during normal usage. Robustness selecting method responses to be included in the final was demonstrated for critical method responses by run- optimization: (1) the selected response is critical to ning system suitability checks, in which selected method achieve the goal (see Table 4); (2) a response is included parameters were changed one factor at a time. In com- only when its model is of sufficiently high quality to parison, the AQbD approach quantifies method robust- meet the goals of validation; and (3) the total number of ness with process robustness indices, such as C and responses included should be kept to a minimum. C , through multivariate robustness DOE, in which crit- pk Following the above three principles, five method re- ical method parameters are systematically varied, simul- sponses were selected for the overall method evaluation taneously. Process robustness indices are standard and optimization. Best overall answer search identified a statistical process control matrices widely used to quan- new optimized method when the four critical method tify and evaluate process and product variations. In this parameters were set at the specific values as listed in AQbD case study, method capability indices were calcu- Table 3. The cumulative desirability for the five desired lated to compare the variability of a chromatographic method response goals reached the maximum value of method response to its specification limits. The com- 1.0. The desirability for each individual goal also reached parison is made by forming the ratio between the spread the maximum value of 1.0, as listed in Table 4. of the response specifications and the spread of the re- sponse values, as measured by six times standard devi- ation of the response. The spread of the response values Method Operable Design Region (MODR) is acquired through tens of thousands of virtual Monte The critical method parameter settings in Table 3 define Carlo simulation runs of the corresponding response a single method that can simultaneously fulfill all five model, with all critical method parameters varied around targeted method goals listed in Table 4 to the best ex- their setting points randomly and simultaneously ac- tent possible. However, the actual operational values of cording to specified distributions. A method with a the four critical parameters may drift around their set process capability of ≥ 1.33 is considered robust as it will points during routine method executions. Based on the only fail to meet the response specifications 63 times out models, contour plots for method response can be cre- of a million runs and thus is capable of providing much ated to reveal how the response value changes as the more reliable measurements for informed decisions on method parameters drift. Furthermore, overlaying the drug development, manufacturing, and quality control. contour plots of all selected method responses reveal the Due to its intrinsic advantages over the OFAT approach, MODR, as shown in Figs. 4, 5, and 6. Note that for each multivariate DOE robustness evaluation was recom- response, a single unique color is used to shade the re- mended to replace the OFAT approach in the latest gion of the graph where the response fails the criteria; Table 4 Predicted results and confidence intervals for the selected responses of the optimized method Response Goal Predicted result Desirability − 2 Sigma conf. limit + 2 Sigma conf. limit No. of peaks Maximize 8.0 1.0000 6.3 10.5 No. of peaks ≥ 1.5 — USP resolution Maximize 6.2 1.0000 4.8 9.5 Max peak 1 – USP plate count Maximize 20,313 1.0000 17,560 23,067 Max peak 1 — USP plate count — C Maximize 2.01 1.0000 1.78 2.24 pk No. of peaks ≥ 1.5 — USP resolution — C Maximize 3.59 1.0000 3.54 3.63 pk Dong et al. AAPS Open (2021) 7:3 Page 12 of 14 Fig. 5 Trellis overlay graph shows how the size of the MODR (unshaded area) changes as the four method parameters change Fig. 6 Single overlay graph shows the original as-is method at point T is not robust (pump flow rate = 0.90 mL/min; final % strong Fig. 7 Single overlay graph shows a much more robust method at solvent = 35%; oven temperature = 30 °C; EDTA concentration = point T (pump flow rate = 0.78 mL/min; final % strong solvent = 0.50 mM) 34.2%; oven temperature = 30.8 °C; EDTA concentration = 0.42 mM) Dong et al. AAPS Open (2021) 7:3 Page 13 of 14 thus, criteria for all responses are met in the unshaded Abbreviations AQbD: Analytical quality by design; DOE: Design of experiments; area. CCC: Circumscribed central composite; MODR: Method Operable Design The Trellis overlay graph in Fig. 5 reveals the MODR Region; QbD: Quality by design; ICH: The International Council for from the perspectives of all four critical method parame- Harmonization of Technical Requirements for Pharmaceuticals for Human Use; CQA: Critical quality attributes; TMU: Target measurement uncertainty; ters, among which flow rate and final percentage of ATP: Analytical target profile; ANOVA: Analysis of variance; strong solvent change continuously while oven EDTA: Ethylenediaminetetraacetic acid; MSR: Mean square regression; MS- temperature and EDTA additive concentration were LOF: Mean square lack of fit; OFAT: One factor at a time each set at three different levels. Figure 5 clearly demon- Acknowledgements strates how the size of the MODR changes with the four The authors would like to thank KBP Biosciences for reviewing and giving method parameters. The single overlay graph in Fig. 6 permission to publish this case study. They would also like to thank Thermo Fisher Scientific and S Matrix for the Fusion QbD software, Lynette Bueno shows that the original as-is method (represented by the Perez for solution preparations, Dr. Michael Goedecke for statistical review, center point T) is on the edge of failure for two method and both Barry Gujral and Francis Vazquez for their overall support. responses, number of peaks (red) and number of peaks ≥ 1.5 resolution (blue), indicating that the original method Authors’ contributions YD designed the study and performed the data analysis. ZL was the primary is not robust. Conversely, point T in the single overlay scientist that executed the study. CL, EP, AP, TT, and WW contributed ideas graph in Fig. 7 is at the center of a relatively large un- and information to the study and reviewed and approved the manuscript. shaded area, indicating that the method is much more The authors read and approved the final manuscript. robust than the original method. Funding Not applicable; authors contributed case studies based on existing company Conclusion knowledge and experience. Through the collaboration of regulatory authorities and the industry, AQbD is the new paradigm to develop ro- Availability of data and materials The datasets used and/or analyzed during the current study are available bust chromatographic methods in the pharmaceutical from the corresponding author on reasonable request. industry. It uses a systematic approach to understand and control variability and build robustness into chro- Declarations matographic methods. This ensures that analytical re- Competing interests sults are always close to the product true value and meet The authors declare that they have no competing interests. the target measurement uncertainty, thus enabling in- formed decisions on drug development, manufacturing, Received: 27 May 2021 Accepted: 29 July 2021 and quality control. Multivariate DOE modeling plays an essential role in References AQbD and has the potential to elevate chromatographic Altiero, P. Why they matter, an introduction to chromatography equations. Slide methods to a robustness level rarely achievable via the 21. https://www.agilent.com/cs/library/eseminars/public/Agilent_Webinar_ Why_They_Matter_An_Intro_Chromatography_Equations_Nov262018.pdf. traditional OFAT approach. However, as demonstrated Accessed 13 May 2021. 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Journal

AAPS OpenSpringer Journals

Published: Sep 1, 2021

Keywords: AQbD; DOE; MODR; Statistical model validation; Scientific model validation; Multiple responses optimization

References