Southern Methodist University SMU Scholar Statistical Science Theses and Dissertations Statistical Science Summer 8-6-2019 Clinical Trial Design and Analysis Shuang Li Southern Methodist University, [email protected] Follow this and additional works at: https://scholar.smu.edu/hum_sci_statisticalscience_etds Recommended Citation Li, Shuang, "Clinical Trial Design and Analysis" (2019). Statistical Science Theses and Dissertations. 9. https://scholar.smu.edu/hum_sci_statisticalscience_etds/9 This Dissertation is brought to you for free and open access by the Statistical Science at SMU Scholar. It has been accepted for inclusion in Statistical Science Theses and Dissertations by an authorized administrator of SMU Scholar. For more information, please visit http://digitalrepository.smu.edu. CLINICAL TRIAL DESIGN AND ANALYSIS Approved by: ___________________________________ Dr. Daniel F. Heitjan Professor in Department of Statistical Sciences, SMU, and Population & Data Sciences, UTSW ___________________________________ Dr. Xinlei (Sherry) Wang Professor in Department of Statistical Sciences, SMU ___________________________________ Dr. Xian-Jin Xie Professor in Division of Biostatistics and Computational Biology, College of Dentistry, and Department of Biostatistics, College of Public Health, University of Iowa ___________________________________ Dr. Jarett Berry Associate Professor in Department of Internal Medicine, UTSW ___________________________________ Dr. Song Zhang Associate Professor in Department of Population & Data Sciences, UTSW CLINICAL TRIAL DESIGN AND ANALYSIS A Dissertation Presented to the Graduate Faculty of the Dedman College Southern Methodist University in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy with a Major in Statistical Science by Shuang Li B.S., Mathematics, University of Utah August 6, 2019 Copyright (2019) Shuang Li All Rights Reserved ACKNOWLEDGMENTS First of all, I would like to thank my advisor, Dr. Daniel F. Heitjan, for his mentoring during the past two years when I worked on my dissertation. Dr. Heitjan has set a great example showing me how to be a statistician, and how to present the materials that I have been working on for a long time to someone who has little background knowledge. With his help, I have received an award for Biopharm Scholar at the 74th Annual Deming Conference in December 2018. I also appreciate working with Dr. Xian-Jin Xie on part of my dissertation about dose- finding designs for phase I oncology trials. He has provided many helpful ideas about the area. And I am also grateful for the rest of my committee members: Dr. Xinlei (Sherry) Wang, Dr. Jarett Berry, and Dr. Song Zhang. They have given thoughtful comments and suggestions to help improve my dissertation. In addition, I would like express my gratitude to my parents and family members living in Salt Lake City, Utah. I would not have received this PhD degree without their support. Last but not at least, many thanks to my boyfriend Dr. Yu Lan for his love and encour- agement to share with me my ups and downs for the past three years. iv Li, Shuang B.S., Mathematics, University of Utah Clinical Trial Design and Analysis Advisor: Dr. Daniel F. Heitjan Doctor of Philosophy degree conferred August 6, 2019 Dissertation completed July 22, 2019 Clinical trials are experiments tested on human to compare the effect of certain inter- vention. Any intervention has to be tested in different phases of clinical trials. In early-stage (phase 0, I, and II) trials, fewer number of patients are enrolled to get preliminary informa- tion on safety and efficacy. In late-stage (phase III and IV) trials, larger number of patients are randomized to further confirm the efficacy and safety. The purpose of each phase may change depending on the therapeutic area and patient characteristics. In Chapter2, we propose a family of designs for phase I oncology trials. In these trials, oncologists assign different patients at a varying range of dose levels to find the dose that gives the highest acceptable rate of dose-limiting toxicities, which will be the recommended dose for phase II trials. In current practice, most such trials are rule-based designs that determine whether to escalate the dose using data from the current dose only. The 3+3 design is the most popular rule-based design. Our proposed design, which we denote the cohort-sequence design, addresses the deficiencies of the 3+3 design, while preserving its simplicity. We compare the proposed design with the 3+3 using simulation studies. Late-stage randomized clinical trials might lack external validity when there are treatment- by-covariate interactions involving factors whose distribution in the population differ from that in the trial. In Chapter3, we project the results from a trial to a population using post- stratification, and compare it with other approaches that use probabilities of trial inclusion. We use intention-to-treat estimate of the treatment effect, which compares the difference in average responses in assigned experimental treatment versus control groups. We demonstrate v this using data from Lipids Research Clinics Coronary Primary Prevention Trial. The intention-to-treat analysis focuses on the treatment effect of randomization on the outcome, without considering compliance. In Chapter4, we extend the interpolation ap- proaches using instrumental variables estimation of the complier average causal effect, which is the treatment effect on the outcome restricted to the subset of subjects who adhere to assigned treatment. We apply these methods to the data from Lipids Research Clinics Coro- nary Primary Prevention Trial and New York School Choice Experiment. vi TABLE OF CONTENTS LIST OF FIGURES . x LIST OF TABLES . xi CHAPTER 1. INTRODUCTION . 1 1.1. Background . 1 1.2. Flexible, rule-based dose escalation: The cohort-sequence design . 1 1.3. Projecting clinical trial results to a target population. 2 1.4. Projecting instrumental variable results to a target population . 2 2. FLEXIBLE, RULE-BASED DOSE ESCALATION: THE COHORT-SEQUENCE DESIGN . 4 2.1. Introduction . 4 2.2. Methods . 5 2.2.1. Escalation plan for the cohort-sequence design . 6 2.2.2. Identification of the critical value for a designated cohort size . 7 2.2.3. Identification of the cohort size for a designated critical value . 8 2.2.4. Selection of the number of cohort sizes . 8 2.2.5. Example designs . 9 2.3. Simulation . 11 2.3.1. Design . 11 2.3.2. Results . 12 2.4. Application . 13 2.5. DISCUSSION . 14 3. PROJECTING CLINICAL TRIAL RESULTS TO A TARGET POPULA- TION . 22 vii 3.1. Introduction . 22 3.2. Example: The LRC-CPPT . 23 3.3. Methods . 24 3.3.1. Estimating the treatment effect in the trial . 24 3.3.2. Interpolation with post-stratification. 26 3.3.2.1. Post-stratification with a discrete stratifier. 26 3.3.2.2. Post-stratification with a continuous stratifier. 28 3.3.3. Interpolation with inverse inclusion probability weighting . 29 3.3.4. Interpolation with inclusion probability stratification . 29 3.3.5. Computing standard errors with inclusion probabilities . 30 3.3.5.1. The standard error of the IIPW estimate . 30 3.3.5.2. The standard error of the IPS estimate . 31 3.4. Simulation study . 31 3.5. Analysis of the LRC-CPPT Data . 33 3.6. Discussion . 36 3.7. Acknowledgements . 38 4. PROJECTING INSTRUMENTAL VARIABLE RESULTS TO A TARGET POPULATION. 40 4.1. Introduction . 40 4.2. Examples . 41 4.2.1. LRC-CPPT . 42 4.2.2. New York School Choice Experiment . 42 4.3. Causal estimands and their estimates . 43 4.3.1. The ITT estimand . 43 4.3.2. The effect of randomization on compliance . 45 4.3.3. The complier average causal effect . 45 viii 4.4. Interpolation of estimands and estimates . 46 4.4.1. Interpolation with post-stratification. 46 4.4.1.1. Post-stratification of the ITT estimand . 47 4.4.1.2. Post-stratification estimate of CACE . 48 4.4.1.3. Standard errors of the interpolated estimates . 48 4.4.2. Interpolation with inverse inclusion probability weighting . 49 4.4.3. Interpolation with inclusion probability stratification . 50 4.4.4. Implementation . 51 4.4.4.1. Selection of stratifiers . 51 4.4.4.2. Standard errors for the IIPW estimates . 52 4.4.4.3. Standard errors for the inverse probability stratification estimates . 52 4.5. Simulation study . 53 4.6. Real-data applications . 54 4.6.1. LRC-CPPT . 55.