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Case Studies in Bayesian Methods for Biopharmaceutical CMC The subject of this book is applied Bayesian methods for chemistry, manufactur- ing, and control (CMC) studies in the biopharmaceutical industry. The book has multiple authors from industry and academia, each contributing a case study (chapter). The collection of case studies covers a broad array of CMC topics, including stability analysis, analytical method development, specification setting, process development and optimization, process control, experimental design, dissolution testing, and comparability studies. The analysis of each case study includes a presentation of code and reproducible output. This book is written with an academic level aimed at practicing nonclinical biostatisticians, most of whom have graduate degrees in statistics. • First book of its kind focusing strictly on CMC Bayesian case studies • Case studies with code and output • Representation from several companies across the industry as well as academia • Authors are leading and well-known Bayesian statisticians in the CMC field • Accompanying website with code for reproducibility • Reflective of real-life industry applications/problems Chapman & Hall/CRC Biostatistics Series Series Editors Shein-Chung Chow, Duke University School of Medicine, USA Byron Jones, Novartis Pharma AG, Switzerland Jen-pei Liu, National Taiwan University, Taiwan Karl E. Peace, Georgia Southern University, USA Bruce W. Turnbull, Cornell University, USA Recently Published Titles Confidence Intervals for Discrete Data in Clinical Research Vivek Pradhan, Ashis Gangopadhyay, Sandeep Menon, Cynthia Basu, and Tathagata Banerjee Statistical Thinking in Clinical Trials Michael A. Proschan Simultaneous Global New Drug Development Multi-Regional Clinical Trials after ICH E17 Edited by Gang Li, Bruce Binkowitz, William Wang, Hui Quan, and Josh Chen Quantitative Methodologies and Process for Safety Monitoring and Ongoing Benefit Risk Evaluation Edited by William Wang, Melvin Munsaka, James Buchanan and Judy Li Statistical Methods for Mediation, Confounding and Moderation Analysis Using R and SAS Qingzhao Yu and Bin Li Hybrid Frequentist/Bayesian Power and Bayesian Power in Planning Clinical Trials Andrew P. Grieve Advanced Statistics in Regulatory Critical Clinical Initiatives Edited By Wei Zhang, Fangrong Yan, Feng Chen, Shein-Chung Chow Medical Statistics for Cancer Studies Trevor F. Cox Real World Evidence in a Patient-Centric Digital Era Edited by Kelly H. Zou, Lobna A. Salem, Amrit Ray Data Science, AI, and Machine Learning in Pharma Harry Yang Model-Assisted Bayesian Designs for Dose Finding and Optimization Methods and Applications Ying Yuan, Ruitao Lin and J. Jack Lee Digital Therapeutics: Strategic, Scientific, Developmental, and Regulatory Aspects Oleksandr Sverdlov, Joris van Dam Quantitative Methods for Precision Medicine Pharmacogenomics in Action Rongling Wu Drug Development for Rare Diseases Edited by Bo Yang, Yang Song and Yijie Zhou Case Studies in Bayesian Methods for Biopharmaceutical CMC Edited by Paul Faya and Tony Pourmohamad For more information about this series, please visit: https://www.routledge.com/Chapman--Hall-CRC- Biostatistics-Series/book-series/CHBIOSTATIS Case Studies in Bayesian Methods for Biopharmaceutical CMC Edited by Paul Faya Tony Pourmohamad MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. First edition published 2023 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN CRC Press is an imprint of Taylor & Francis Group, LLC © 2023 Taylor & Francis Group, LLC Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publica- tion and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged, please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, trans- mitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC, please contact [email protected] Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. ISBN: 978-1-032-18548-4 (hbk) ISBN: 978-1-032-18550-7 (pbk) ISBN: 978-1-003-25509-3 (ebk) DOI: 10.1201/9781003255093 Publisher’s note: This book has been prepared from camera-ready copy provided by the authors. Access the data and code for this book at https://github.com/BayesCMC/Book To our families: Erin, Quintin, and Owen Josie, Vincent, and Ava Taylor & Francis Taylor & Francis Group http://taylorandfrancis.com Contents Foreword ix Preface xi Contributors xiii 1 Introduction 1 Paul Faya and Tony Pourmohamad 2 An Overview of Bayesian Computation 5 David J. Kahle, John W. Seaman Jr., and James D. Stamey 3 Basic Bayesian Model Checking 25 John W. Seaman Jr., David J. Kahle, and James D. Stamey 4 QuantitativeDecision-Making,aCMCApplicationtoAnalyticalMethod Equivalence 41 Misbah Ahmed and Mike Denham 5 Bayesian Dissolution Testing 57 Tony Pourmohamad and Robert Richardson 6 A Non-Normal Bayesian Model for the Estimation and Comparison of Immunogenicity Screening Assay Cut-Points 85 David LeBlond, Robert Singer, Lu Xu, and Rong Zeng 7 Application of Bayesian Hierarchical Models to Experimental Design 119 Adam P. Rauk and Paul Faya 8 Bayesian Prediction for Staged Testing Procedures 135 Katherine E.D. Giacoletti and Tara Scherder 9 A Bayesian Approach to Multivariate Conditional Regression Surrogate Modeling with Application to Real Time Release Testing 149 Stan Altan, Dwaine Banton, Hans Coppenolle, Martin Kovarik and Martin Otava, and Christian Schmid 10 Bayesian Approach for Demonstrating Analytical Similarity 177 Harry Yang and Steven Novick 11 Bayesian Evaluation and Monitoring of Process Comparability 195 Ke Wang and Aili Cheng vii viii Contents 12 Bayesian Alternatives to Traditional Methods for Estimating Product Shelf-Life and Internal Release Limits 225 Perceval Sondag, Ji Young Kim, Laurent Natalis, and Tara Scherder 13 Application of Bayesian Methods for Specification Setting 257 Chris Thompson and Guillermo Miro-Quesada 14 Calculating Statistical Tolerance Intervals Using SAS 275 Richard Lewis and Buffy Hudson-Curtis 15 A Bayesian Application in Process Monitoring – Establishing Limits for Dosage Units in Early Phase Process Control 299 Yanbing Zheng, James Reynolds, Man Tang, Mark Johnson and Hesham Fahmy Bibliography 321 Foreword StatisticalinferenceproblemsthatnaturallyariseinChemistryandManufacturingControl (CMC) experiments are rather varied and sometimes quite challenging. Proper solutions often do not fit into common categories of two-sample t-tests or simple linear regression. In fact, I would say that in my consulting experience in the CMC area, I was driven to embrace Bayesian statistical methods simply as a way to adequately solve some of these statisticalproblems.ThefirstCMCproblemthatstruckmeasawkwardtoformulatewithin the frequentist realm of inference was that of ICH Q8 design space. The solution seemed to fallelegantlyintoplace,however,whentakingaBayesianapproachtotheproblem.But,as time passed, I could see from my own work and that of other Bayesians, that this methodology was also a natural and effective tool for many other CMC statistical problems, such asspecificationsetting,shelf-lifeestimation,dissolutiontesting,andassayoptimizationand validation.TheBayesianapproachhastheaddedbenefitthatsolutionstomultiple-response generalizations of these problems are obtained within this methodological framework in a straightforward manner. In addition, the Bayesian paradigm allows for the use of informa- tivepriors(e.g.,builtusinghistoricaldata)tobringinmuch-neededsupportinginformation in small sample size situations. I believe that a good acronym for Bayesian methods, par- ticularly within the CMC and Quality-by-Design areas is FIT. In addition to being “FIT for use,” a well-known quality definition, I like to think of FIT methodology as standing for “Flexible, Informative, Technology.” It is clearly flexible for handling tricky inferential problems of the type that arise in CMC situations. It is informative for the scientific way it quantifies information, both current and historical. It is also clearly a technology with clever algorithms and software for powerful implementation. This book takes us through a tour of using this FIT system on a wide variety of CMC statisticalproblems.Thefirstthreechaptersgivepracticalmotivationforthereaderthrough explaining the industry and regulatory need for Bayesian statistics, followed by technical discussions of Bayesian methods implementation. The case studies that follow give sub- stantial evidence that Bayesian methods can successfully tackle all of the CMC inferential challenges presented. Currently, this is critical in that “the quality, safety, and efficacy of the final drug product are ultimately defined through CMC results and statistical tools to evaluatethem”(Chapter1).Soon,thisFITmethodologywillalsobeimportantaspharma- ceuticalmanufacturingisexpectedtofoldintothemanufacturing4.0industrialenvironment (i.e.,thesmartfactoryofthefuture).Here,thestatisticalchallengeswillonlygrowincom- plexity. Such an environment may generate a multitude of quality responses, measured at many points in time. Here, I believe Bayesian methods will continue to be an effective and much-needed approach. I wish to thank the editors, Paul Faya and Tony Pourmohamad, and all of the chapter authors for making this important and timely work possible. John J. Peterson, Ph.D. PDQ Research & Consulting Birdsboro, PA 19508 June, 2022 ix