Network Meta-Analysis of Diagnostic Accuracy Studies by Wei Cheng B.S., Beijing Normal University, 2008 A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Biostatistics at Brown University Providence, Rhode Island May 2016 (cid:13)c Copyright March 2016 by Wei Cheng This dissertation by Wei Cheng is accepted in its present form by the Department of Biostatistics as satisfying the dissertation requirement for the degree of Doctor of Philosophy Date......................... ..................................................... Constantine A. Gatsonis, Advisor Recommended to the Graduate Council Date......................... ..................................................... Christopher H. Schmid, Co-advisor and Reader Date......................... ..................................................... Thomas A. Trikalinos, Co-advisor and Reader Approved by the Graduate Council Date......................... ..................................................... Peter M. Weber , Dean of the Graduate School iii The Vita of Wei Cheng Birthdate: May 30, 1986 Birthplace: Quzhou, Zhejiang Province, China Education: 2016 Doctor of Philosophy (Ph.D.), Biostatistics, School of Public Health, Brown University, Providence, RI, United States 2008 Bachelor of Science (B.S.), Mathematics and Applied Mathematics, School of Mathematical Sciences, Beijing Normal University, Beijing, China Areas of Interest: Evidencesynthesismethodology,especiallynetworkmeta-analysis(NMA)oftreatments and diagnostic accuracy studies; Bayesian inference and computation; statistical meth- ods for the evaluation of diagnostic tests; health technology assessment (HTA) and health economic evaluations; health services, policy and practices; comparative effec- tiveness research; clinical and patient-reported outcomes, among other topics. Research Papers: GuyotP,ChengW,TremblayG,CopherR,BurnettH,LiX,MakinC.Numberneeded to treat in indirect treatment comparison. To be submitted to Pharmacoeconomics, 2016. Cope S, Burnett H, Cheng W, Earley A, Dias S. Comparative effectiveness of alter- native pharmacological treatment classes and combinations for chronic heart failure: Choice of network meta-analysis model for overall mortality. To be submitted to BMC Medicine, 2016. Cope S, Zhang J, Hurry M, Sasane M, Cheng W, Bending M, Karabis A, Taylor R, Dahabreh I, Hoaglin DC. Methods for assessing the comparative effectiveness of iv oncology treatments based on single-arm studies from a health technology assessment decision-making perspective. To be submitted, 2016. Professional Experience: 05/2012-04/2016 Dissertation research with Professor Constantine Gatsonis, Professor Christopher Schmid, and Professor Thomas Trikalinos 08/2014-08/2015 Research Consultant, Mapi Group Evidence synthesis (especially the network meta-analysis of competing treatments) followed by health economic evaluations 06/2011-05/2012 The randomized test design for the assessment of test performance, Supervisor: Professor Constantine Gatsonis 01/2011-05/2011 Graduate Teaching Assistant, Brown University Teaching lab sessions for Applied Regression Analysis (PHP2511) Course Instructor: Crystal Linkletter, Ph.D. 09/2008-12/2010 Graduate Research Assistant, Brown University - Programming the Bootstrap confidence region for METADAS, a SAS macro for meta-analysis of diagnostic accuracy studies Supervisor: Professor Constantine Gatsonis - Data cleaning and SAS programming American College of Radiology Imaging Network (ACRIN), Providence, RI. Supervisor: Mr. Benjamin Herman 07/2007-06/2008 Internship with Professor Chen Yao Biostatistics Unit, Peking University First Hospital, Beijing, China v Acknowledgments Ioweadebtofgratitudetomyadvisorandmentor,ProfessorConstantineA.Gatsonis,who has offered me the opportunity to pursue my doctoral studies at Brown University, taught me the statistical methods for the evaluation of diagnostic test, and introduced me to other members of my dissertation committee in 2012. I am also deeply grateful to my co-advisors and mentors, Professor Thomas A. Trikalinos, director of the Center for Evidence-based Medicine(CEBM)atBrownUniversity,andProfessorChristopherH.Schmid,facultymem- beroftheDepartmentofBiostatisticsandacorememberoftheCEBM.Allthreeprofessors have motivated my exploration of the network meta-analysis of diagnostic accuracy studies and witnessed my endeavor, guided and supported me throughout my research with their patienceandknowledgewhilstallowingmetheroomtoworkinmyownway. Withouttheir advice and persistent help on the subject matter of network meta-analysis (and evidence synthesis in general), this dissertation would not have been possible. vi Table of Contents Table of Contents vii List of Tables xi List of Figures xii 1 Introduction and overview 1 1.1 Introduction to meta-analysis of diagnostic accuracy studies . . . . . . . . . 1 1.2 Network meta-analysis for competing treatments . . . . . . . . . . . . . . . 6 1.3 Considerations for the network meta-analysis of diagnostic accuracy studies 7 1.4 An illustrative example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Network meta-analysis shared-parameter modeling framework for diag- nostic accuracy studies with mixed study-types 14 2.1 Outline of this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 The shared-parameter modeling framework . . . . . . . . . . . . . . . . . . 16 2.2.1 The full model for all tests and their complete cross-tables . . . . . . 17 2.2.2 Model for studies without cross-tables . . . . . . . . . . . . . . . . . 20 2.2.3 Rationale of the shared-parameter modeling framework . . . . . . . 23 vii 2.2.4 Identifiability constraints and prior specifications . . . . . . . . . . . 25 2.2.5 Construction of HSROC curves and other summary measures . . . 27 2.3 Defining Inconsistency Factors . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4 Network Meta-Analysis of the Prenatal Ultrasound Example . . . . . . . . 32 2.4.1 Assessment of consistency between different sources of evidence . . . 33 2.4.2 Estimation of summary measures assuming strict consistency equa- tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3 The network meta-analysis extension of the HSROC model 44 3.1 Outline of this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Extension of the HSROC model . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2.1 Model for studies with complete cross-tables . . . . . . . . . . . . . 46 3.2.2 Model for studies without cross-tables . . . . . . . . . . . . . . . . . 51 3.2.3 Construction of HSROC curves and other summary measures . . . . 56 3.3 Application to the Prenatal Ultrasound Example . . . . . . . . . . . . . . . 57 3.3.1 Assessment of consistency between different sources of evidence . . . 58 3.3.2 Estimation of summary measures assuming strict consistency equa- tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4 Network meta-analysis of diagnostic accuracy studies using beta-binomial marginals and multivariate Gaussian copulas 67 4.1 Background and introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.1.1 Dependence modeling with copulas . . . . . . . . . . . . . . . . . . . 69 4.1.2 Model using beta-binomial distributions and bivariate copulas . . . . 70 4.1.3 Outline of this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . 71 viii 4.2 Shared-parameter models for mixed study-types . . . . . . . . . . . . . . . . 71 4.2.1 Use of the beta-binomial distribution for margins . . . . . . . . . . . 72 4.2.2 Use of the multivariate Gaussian copula . . . . . . . . . . . . . . . . 73 4.2.3 Model for studies without cross-tables . . . . . . . . . . . . . . . . . 75 4.2.4 Modeling to accommodate available cross-tables . . . . . . . . . . . 78 4.2.5 Consideration of common parameters; Identifiability constraints. . . 80 4.2.6 The Poisson-Zeros approach for MCMC computation . . . . . . . . 82 4.3 Summary Measures of Diagnostic Performance . . . . . . . . . . . . . . . . 83 4.3.1 Posterior mean summary points, and contours for summary points . 83 4.3.2 Summary ROC curves . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.4 Application to the Prenatal Ultrasound Example . . . . . . . . . . . . . . . 84 4.4.1 Assessment of consistency between different sources of evidence . . . 85 4.4.2 Estimation of summary measures assuming strict consistency equa- tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5 Discussion 91 5.1 Exchangeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2 About missingness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3 Choosing among the three approaches . . . . . . . . . . . . . . . . . . . . . 94 5.3.1 Strength and limitations of the beta-binomial marginals and multi- variate Gaussian copulas model . . . . . . . . . . . . . . . . . . . . . 94 5.3.2 Advantages of the NMA extension of the HSROC model over the NMA extension of the bivariate normal model. . . . . . . . . . . . . 96 A Data used in the example 99 ix A.1 Aggregated study-level data Smith-Bindman et al. (2001) has extracted . . 99 A.2 Available or partially available cross-tables . . . . . . . . . . . . . . . . . . 102 B Appendices for Chapter 2 109 B.1 The covariance matrix to accommodate available cross-tables in the prenatal ultrasound example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 B.2 Extra constraints for the estimation purpose . . . . . . . . . . . . . . . . . . 110 B.3 Assessing consistency between different sources of evidence . . . . . . . . . 112 B.3.1 The direct and indirect sources of evidence between HS and NFT . . 112 B.3.2 Two sources of direct evidence between FS and HS . . . . . . . . . . 113 B.4 Sensitivity analysis: model with all but single-test studies . . . . . . . . . . 114 C Appendices for Chapter 3 120 C.1 Extra conditions for the NMA extension of bivariate normal model to be completely equivalent to the NMA extension of HSROC model . . . . . . . 120 C.2 Assessing consistency between different sources of evidence . . . . . . . . . 121 C.2.1 The direct and indirect sources of evidence between HS and NFT . . 122 C.2.2 Two sources of direct evidence between FS and HS . . . . . . . . . . 122 D Appendices for Chapter 4 125 D.1 The ranges for the study-type specific effects . . . . . . . . . . . . . . . . . 125 D.2 Constraints under consistency assumptions for estimation . . . . . . . . . . 126 D.3 Assessing consistency between different sources of evidence . . . . . . . . . 128 D.3.1 The direct and indirect sources of evidence between HS and NFT . . 129 D.3.2 Two sources of direct evidence between FS and HS . . . . . . . . . . 129 x