Methods for Data Analysis in Split-Mouth Randomized Clinical Trials: a Simulation Study by Romina Brignardello Petersen A thesis submitted in conformity with the requirements for the degree of Master of Science (Clinical Epidemiology and Health Care Research) Institute of Health Policy, Management & Evaluation University of Toronto © Copyright by Romina Brignardello Petersen 2012 Methods for Data Analysis in Split-Mouth Randomized Clinical Trials: a Simulation Study Romina Brignardello Petersen Master of Science (Clinical Epidemiology and Health Care Research) Institute of Health Policy, Management & Evaluation University of Toronto 2012 Abstract Split-mouth trials are a design of randomized controlled trial in dentistry in which divisions of the mouth are the units of randomization. Since there is more than one tooth in each mouth division, the structure of the data is complex, which can create difficulties in the statistical analysis. The aim of this study was to determine what is the most appropriate method to analyze split-mouth trials with continuous outcomes, with regards to the treatment effect estimates, power, type-I error, confidence interval coverage and confidence interval width. A superiority split-mouth trial in the field of periodontology was simulated, using two mouth divisions and varying underlying study characteristics such as correlation among teeth, treatment effects and sample size. Twenty-four statistical methods were compared across 315 scenarios. The performance of the statistical methods depended mainly on the correlation among the data, and a paired t-test performed the best across the different scenarios. ii Acknowledgments I would like to thank my supervisor, Dr. George Tomlinson, for his encouragement, guidance, efforts and patience to explain things clearly and through all this process. This thesis would not have been possible without his help and he exceeded all my expectations as a supervisor. I really hope that we continue working together. I thank my thesis committee members, Alex Jadad and Carlos Quiñonez, for their support and valuable advice and feedback. To Alonso, for believing in my project and coming with me to Canada. His motivation, support and love have been essential throughout this experience. iii Table of Contents ! List%of%Tables%........................................................................................................................................%vii! List%of%Figures%.....................................................................................................................................%viii! List%of%Appendices%................................................................................................................................%x! 1! Introduction%....................................................................................................................................%1! 2! Literature%review%...........................................................................................................................%3! 2.1! Split?mouth%randomized%controlled%trials%...................................................................................%3! 2.2! Periodontal%diseases%...........................................................................................................................%4! 2.3! Split?mouth%trials%in%periodontal%diseases%..................................................................................%7! 2.4! Statistical%analysis%in%split?mouth%trials%.......................................................................................%8! 2.4.1! Nested!nature!of!the!data!within!a!split!.................................................................................................!8! 2.4.2! Nested!nature!of!the!data!within!a!subject!........................................................................................!10! 2.4.3! Approaches!to!analyze!pre?post!treatment!data!.............................................................................!13! 2.5! Choice%between%the%different%methods%and%potential%consequences%of%an% inappropriate%analysis%...............................................................................................................................%15! 2.6! Simulation%studies%............................................................................................................................%17! 3! Rationale%for%this%study%............................................................................................................%23! 4! Research%question%......................................................................................................................%25! 5! Objectives%......................................................................................................................................%26! 5.1! General%objective%...............................................................................................................................%26! 5.2! Specific%objectives%.............................................................................................................................%26! 6! Methods%..........................................................................................................................................%27! 6.1! Study%design%........................................................................................................................................%27! 6.2! Rationale%for%using%a%simulation%study%......................................................................................%27! 6.3! Procedures%and%assumptions%........................................................................................................%28! 6.3.1! Models!to!generate!the!data!.....................................................................................................................!28! 6.3.2! Computational!methods!.............................................................................................................................!29! 6.3.3! Level!of!dependence!between!simulated!datasets!.........................................................................!30! iv 6.4! Scenarios%investigated%.....................................................................................................................%30! 6.5! Analyses%performed%.........................................................................................................................%34! 6.5.1! Full!data!versus!collapsed!data!...............................................................................................................!34! 6.5.2! Statistical!methods!to!evaluate!...............................................................................................................!34! 6.5.3! Estimates!obtained!from!each!analysis!...............................................................................................!42! 6.5.4! Assessment!of!the!performance!of!each!of!the!methods:!outcomes!.......................................!42! 6.5.5! Weighting!of!the!criteria!of!performance!assessment!to!compare!the!methods!..............!45! 6.6! Number%of%simulations%....................................................................................................................%46! 6.7! Analysis%and%summary%of%the%results%..........................................................................................%47! 7! Results%............................................................................................................................................%48! 7.1! Bias%.........................................................................................................................................................%53! 7.2! Power%.....................................................................................................................................................%53! 7.2.1! Small!sized!trial!(Figure!7)!........................................................................................................................!53! 7.2.2! Medium!sized!trial!(Figure!8)!..................................................................................................................!56! 7.2.3! Large!sized!trial!(Figure!9)!.......................................................................................................................!58! 7.3! Type?I%error%rate%................................................................................................................................%60! 7.4! Confidence%interval%coverage%........................................................................................................%62! 7.5! Mean%square%error%............................................................................................................................%64! 7.6! Confidence%interval%width%..............................................................................................................%64! 7.7! Comparison%of%the%methods%of%analysis%.....................................................................................%66! 7.7.1! Small!sized!trial!(Table!6)!.........................................................................................................................!66! 7.7.2! Medium!sized!trial!(Table!7)!....................................................................................................................!68! 7.7.3! Large!sized!trial!(Table!8)!.........................................................................................................................!71!