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Statistical Methods in Clinical Trial Design Yu Du Statistical Methods in Clinical Trial Design by Yu Du A dissertation submitted to The Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy. Baltimore, Maryland March, 2018 c Yu Du 2018 All rights reserved Abstract Numerous human medical problems or diseases have been aided by the devel- opment of effective treatments such as drugs and medical devices. Clinical trials are an integral part of the development process, determining the safety and effi- cacy of the new proposed treatment, as required by the Food and Drug Admin- istration of the United States. A reliable, efficient and cost-effective way of con- ducting the clinical trials is important for advancing useful treatments/devices to market and screening out the useless ones, thus benefiting public health in a timely manner. I developed several statistical methods and applications toward this pur- pose, ranging from early, small scale Phase I studies to late, large scale Phase III studies in clinical trials. In Phase I studies, I establish a general framework for a multi-stage adaptive design where I jointly model a continuous efficacy outcome and continuous toxi- city endpoints from multiple treatment cycles, unlike the traditional method that only considers a binary toxicity endpoint (joint work with Mayo Clinic). Extensive simulations confirmed that the design had a high probability of making the correct ii ABSTRACT dose selection and good overdose control. To our best knowledge, this proposed Phase I dual-endpoint dose-finding design is the first to incorporate multiple cy- cles of toxicities and a continuous efficacy outcome. I also propose and evaluate a two-stage, adaptive clinical trial design for Phase II studies. Its goal is to determine whether future phase 3 (confirmatory) trials should be conducted, and if so, which population should be enrolled. I compute an approximate Bayes optimal design considering a combination of future health benefits and costs. Turning to Phase III studies, I analyze the performance of adaptive enrichment designs with delayed outcome, leveraging information in baseline variables and short-term outcomes to improve precision by using semiparametric, locally effi- cient estimators at each interim analysis. I also propose a prediction method for analyzing heterogeneity in treatment response, as a secondary analysis, through the identification of treatment covariate interactions honoring different hierarchi- cal conditions. Advisors: Michael Rosenblum, Ravi Varadhan, Vadim Zipunnikov Committee: Albert Wu, Sumithra Mandrekar Alternates: Elizabeth Ogburn, Casey Rebholz iii Acknowledgments First of all, I am filled with gratitude for my primary advisor, Dr. Michael Rosenblum, who has advised me ever since I was admitted into this PhD in Bio- statistics program. Michael, you mean a lot more than an advisor to me. In my first year, I was so afraid to fail the comprehensive exam since I did not have a solid math background. You cheered me up, you gave me confidence and you were the first to congratulate me on the best performance award in the comprehensive exam I received. You made me grow. You care a lot about your students. When I told you about my health issue, you kept that in mind, did many searches and forwarded me many helpful information. When you knew about my upcoming surgery, you asked me to put all the work off and relax, you also wondered if I have difficulty paying medical bills. You even marked my surgery on your busy calendar, send- ing your best wishes and giving encouragements around those days. You taught me techniques to care for baby just in time when I got struggled with my newborn. Academically, you brought me into the field of clinical trials, and I feel very lucky working with you on very interesting problems in this field. Whenever I got stuck iv ACKNOWLEDGMENTS in the research, you were always there to lead me through. I learned a lot from you on the subject expertise, writing, presentation skills, and so on. I would like to thank my two co-advisors, Dr. Ravi Varadhan and Dr. Vadim Zipunnikov. Ravi, I really enjoy the meetings with you every week, where, apart from academic discussion, we talk a lot on philosophical topics and life. You make me very productive. I knew you in the middle of my third year and just within a year, we had four papers planned under way (one is published, one is currently under review, one has a ready draft and another one is about to start). When one of the papers got rejected, I could not forget how confident you were in arguing against the referee in an appealing and it turned out the referee arguments were untenable. Vadim, thank you for introducing me into the world of wearable com- puting and an interesting project where we aim to monitor patient’s recovery using actigraphy data. Thank you for being very kind and patient to me, to someone who barely knows what wearable computing does. I wanted to thank Dr. Sumithra Mandrekar and Dr. Jun Yin for advising me during the internship at Mayo Clinic in summer 2016, where we produced two papers (under review) on Phase I study design and a published R package. Thank you for providing me with financial sponsorship for my fifth year in the PhD pro- gram, and fortunately we can continue to collaborate on the extension of our pre- vious work. Also, I would like to thank Dr. Alan Chiang and Dr. Yong Lin for being my v ACKNOWLEDGMENTS supervisors while I was doing internship at Eli Lilly in summer 2017. Thanks for the interesting project you have prepared for me on adaptive seamless trial de- signs, where we have an R Shiny Application developed that can be used in real trial planning as well as a paper in progress. Thank you for the full time job offer I received upon finishing the internship and I knew you gave the management level lots of positive comments on my performance. Thank Dr. Albert Wu, Dr. Michael Rosenblum, Dr. Ravi Varadhan, Dr. Vadim Zipunnikov, Dr. Sumithra Mandrekar, Dr. Elizabeth Ogburn, Dr. Casey Rebholz and Dr. Jodi Segal for being willing to serve on my thesis committee, most of whom were also on my preliminary exam committee. Thank you for your helpful comments and suggestions that would surely improve my research. I would also like to thank Dr. Gary Rosner for joining my Phase II studies and providing many useful comments to make our work in shape. I have been inspired a lot from the faculty members in the department, in- cluding Dr. Mei-Cheng Wang, Dr. Karen Bandeen-Roche, Dr. Marie Diener-West, Dr. Hongkai Ji, Dr. Daniel Scharfstein, Dr. Constantine Frangakis, among others. Thank you for showing great examples in research, teaching and service. Special thanks to my peers, including Tianchen Qian, Yuxin Zhu, Haoyu Zhang, Hong Zhang, among others. Tianchen, I was impressed that you were never an- noyed by the bombardment of my questions on research, and always ready and patient to discuss with me. Yuxin, I remember that I always troubled you with vi ACKNOWLEDGMENTS probability theory problems in the first year, and you spent quite a lot of time walking me through those problems. I have always been grateful for your help and admire your fast and rigorous math mind. Haoyu, thank you for organizing so many Ping-Pang nights and basketball nights where students and peers hang out together, a great opportunity for our friendship bonding and thank you for promoting student benefits as a departmental representative. Hong, as always, thank you for your helpful answer to my random research questions. Thank Mary Joy Argo for coordinating every thing in the department, in partic- ular, you reminded me many times not to forget about course registration. Thank you for your patience and also for providing grammar check on my papers. I still remember Brian once said "for anything you don’t know, ask Mary Joy!" Particularly, I am so grateful to my family, my wife Shuyuan Wu, my son Will Du, my parents Chunlin Du and Liying Xie, and my parents-in-law Zeyong Wu and Mingxiu Bu. Shuyuan, you are always by my side and very supportive of my career choice. I really appreciate the courage you had when you decided to marry someone who had no idea about his future five years ago, even before I was offered an admission into this PhD program. I could not imagine what I will be like without you. Thank you, my dear, Shuyuan. Hey Will, father thanks you for making me a father, and bettering my understanding about the responsibility I should take. I do enjoy the time watching you grow. Thank my parents for insisting on me studying abroad and for your constant supports. It has been seven vii ACKNOWLEDGMENTS years, and I assure you that you made the right choice. Thank my parents-in-law for coming to here, taking care of my wife for her postpartum recovery and the newborn so that I am able to spare some time working on this dissertation. In the very end, thank the department graduate program committee for offer- ing me admission into this PhD in Biostatistics program at Johns Hopkins Bloomberg School of Public Health, which makes a valuable and unforgettable five-year expe- rience in my life. viii Contents Abstract ii Acknowledgments iv List of Tables xiv List of Figures xvi 1 Introduction 1 2 Phase I Studies: An Adaptive, Multi-Stage Dose-finding Design 7 2.1 Background ................................. 8 2.2 Joint Model ................................. 13 2.2.1 Estimation .............................. 16 2.3 Dose-finding Algorithm .......................... 17 2.3.1 Stage 1 ...............................
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