Mixed Hierarchical Models for the Process Environment

Transcription

1 Mixed Hierarchical Models for the Process Environment Barry M. Wise, Robert T. Roginski, Neal B. Gallagher and Jeremy M. Shaver Eigenvector Research Inc., Wenatchee, WA, USA

2 Abstract EffecFve monitoring and control of chemical processes ohen requires more than single quanftafve regression models or qualitafve classificafon models. MulFple models are ohen needed, and which model to apply can be a funcfon of current process condifons. The "which model" quesfon can be determined by rule- of- thumb heurisfcs, criteria based on single process variables, or the output of previously applied regression or classificafon models. Process problems are somefmes best solved with a hierarchical construcfon of "mixed models," e.g. different types of classificafon, regression, simple math and logic all in the same structure. Several examples of these mixed hierarchical models are demonstrated and discussed.

3 Mixed Hierarchical Models Many classificafon and regression problems are too complex to be handled with a single model Rules based on model outputs or single variables can be used to break problems into simple pieces

4 Example: ClassificaFon on ARCH ARCH classic data set of NaFve American arffacts measured by XRF (10 variables) 63 knowns from 4 sources Classify 12 unknowns

5 PCA Scores of ARCH 5 4 Samples/Scores Plot of arch K BL SH AN 3 Scores on PC 2 (21.12%) Complete separafon, use PCA to idenffy Scores on PC 1 (53.41%)

6 Scores Without ANA 3 2 Then use PLS- DA to split K from SH Samples/Scores Plot of arch K BL SH 1 Scores on PC 2 (19.41%) Use PLS- DA to split BL from other two classes Scores on PC 1 (50.38%)

7 Hierarchical Model Hierarchical model in HMB interface Output on unknowns

8 Nonlinear Dynamic Process Single input single output (SISO) process Lab system, intenfonally non- linear Use past 6 values of input to predicfon output (Finite Impulse Response)

9 Global PLS Model Results 14 Y CV Predicted 1 level R 2 = Latent Variables RMSEC = RMSECV = CV Bias = e-05 High Range Mid Range Y Measured 1 level Low Range

10 Low- Range Model Results

11 Mid- Range Model Results

12 High- Range Model Results

13 Single Layer Hierarchical Model If Q is too large, throw error If Predicted Y1 is > 8, apply "High- Range" model If Predicted Y1 is < 3.8, apply "Low- Range" model Otherwise, apply "Mid- Range" model

14 Hierarchical Model Output RMSEP = Predicted level Bad Q (no predicfon High- Range Low- Range Mid- Range level

15 Hierarchical Model Output Hotellings T^ level

16 Hierarchical Model Output Q Residuals level

17 Add Layer of Output TesFng If Predicted Y1 is > 8, apply "High- Range" local model and test outputs If Q from "High- Range" model is too high, error Otherwise, return High- Range predicfon Similar tests on Low- Range and Mid- Range Models

18 2- Layer Hierarchical Model Output RMSEP = 0.28 Predicted level level

19 2- Layer Hierarchical Model Output Q Residuals level

20 12 BPN- ANN Model (1 layer, 2 nodes) Y Predicted 1 level R 2 = Layer 1 Nodes RMSEC = RMSECV = RMSEP = Calibration Bias = CV Bias = Prediction Bias = Use Global PLS to filter out bad samples Y Measured 1 level

21 Filtering of PredicFons Apply Model If Q is too high, error If predicfon is > 0, return predicfon (re- apply model) If predicfon is <= 0, return zero

22 ClassificaFon of Placebo and AcFve FormulaFon FRESH PERSPECTIVES Enhanced Classification of Placebo and Active Formulations via Hierarchical Modeling Michael Dotlich, M.Sc. 1, Richard M. Kattner, M.Sc. 1, Robert Roginski, Ph.D. 2 and Jeremy Shaver, Ph.D. 2 1 Eli Lilly and Company 2 Eigenvector Research, Inc. Michael Dotlich, M.Sc., is a Research Scientist in analytical research and development at Eli Lilly and Company. He works in the Lilly Research Laboratories validating methods of testing for clinical trial materials release. His active research is focused on the development of spectroscopic methods using different analytical techniques and chemometrics for identification and quantitation of raw materials and drug products. He earned his M.Sc. in applications of Raman spectroscopy from Marquette University, Milwaukee WI. Dr. Bob Roginski is a Senior Applications Scientist with Eigenvector Research, Inc., where he provides consulting services, instruction, and software development in the area of chemometrics. Previously, Bob served in engineering roles specializing in process analytical technology at Eli Lilly & Co., Searle/Pharmacia/Pfizer, and Amoco Corporation. Bob received his Ph.D. in Chemical Engineering from the University of Illinois in 1987, and has collaborated on numerous peerreviewed publications and outside presentations. Bob has special interests in spectroscopy as applied to PAT and using chemometrics to determine the health of continuous processes. Richard M. Kattner, M.Sc., is Associate Consultant Chemist in the analytical research and development at Eli Lilly and Company. current work in the Lilly Research Laboratories deals with developing and validating methods for the testing and release of clinical trial materials. His His current focus is the development and validation of spectroscopic methods using different analytical techniques and chemometrics for testing active/placebo tablet and solutions. earned his M.Sc. in Chemistry focusing in Physical Organic Chemistry at the University of North Texas, Denton, TX. Dr. Jeremy Shaver is currently the Chief of Technology Development at Eigenvector Research, Inc., which he joined in He received a BA in Chemistry from the College of Wooster in 1991 and a Ph.D. in Analytical Chemistry from Duke University in He Introduction A placebo-controlled study is a means of testing a drug for safety and efficacy in a group of subjects that receive the treatment. Current placebo identity tests typically utilize an HPLC identity method for the active compound to confirm the absence of the active (i.e., negative identity). In this review, the development and application of transmission Raman spectroscopy (TRS) with chemometric modeling for positive placebo identification testing will be applied to drug products, illustrated for several compounds and their respective placebos. Placebo identification tests are a clinical manufacturing requirement, and when implemented in a negative mode, data are evaluated against the specification There is no active detected. Clinical placebos share the same physical appearance as the active tablets or capsules, as required for blinded studies, hence definitive identification of both the active and placebo (absence of active) are necessary release tests. Spectroscopic test methods utilizing a standard library provide a robust approach for evaluating the chemical identity of both placebos and actives. In addition, spectral testing using chemometric models can compare placebo results against a database of numerous placebos and active drugs instead of assaying for a single active ingredient. Spectroscopic methods utilizing rapid, chemometric-based spectroscopic technologies create efficiencies and minimize workload due to minimal sample preparation and automated data analysis. Finally, chemometric models provide benefits over traditional spectral comparisons such as eliminating a need for storage and maintenance of reference standards (e.g., API, tablets and capsules) and reduce subjectivity in determining if sample data compares favorably to a reference standard or demonstrates no active XYZ present, especially for complex drug excipient matrices. Experimental For the experiments reported here, a Cobalt transmission Raman instrument (TRS100) was used with the following settings: Laser Power: 0.65W Exposure: 0.5 sec. Accumulations: 180 Detector: CCD Read Optics: Small Laser Spot Diameter: 2mm Scan Range: cm -1 Placebo idenfficafon tests required Usually done by HPLC In this example used transmission Raman 12 unique acfve drugs and their placebos, 34 strengths, tablets and capsules 1 American Pharmaceutical Review Endotoxin Supplement 2013

23 Scores of Placebos Samples/Scores Plot of Multiple SPC Files 4 3 Samples/Scores Plot of Multiple SPC Files all other placebos NP 2 placebos NP 1 placebos 95% Confidence Level Scores on PC 3 (14.83%) all other placebos NP 2 placebo NP 1 placebo Scores on PC 2 (2.06%) % Confidence Level Scores on PC 2 (24.43%) Scores on PC 1 (97.25%) with GLS preprocessing

24 Class PredicFon ProbabiliFes Samples/Scores Plot of Multiple SPC Files Samples/Scores Plot of Multiple SPC Files Class Pred Probability capsule placebos capsule placebos Class Pred Probability tablet placebos tablet placebos Sample Sample Capsule placebos versus all other products Tablet placebos versus remaining products

25 Final Models Samples/Scores Plot of Multiple SPC Files Samples/Scores Plot of Multiple SPC Files Class Pred Probability NP 1 and NP 2 placebos NP 1 & NP 2 placebos NP 2 active Class Pred Probability NP 1 & NP 2 placebos NP 2 active NP 1 & NP 2 placebos Sample Sample

26 Final Hierarchical Model

27 Conclusions Many classificafon and even regression problems are too complex to be done with a single model Easier when broken into smaller pieces Different types of models may be most suitable for each step

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