title: Bayesian meta-analytical methods to incorporate multiple surrogate endpoints in drug development process.
abstract: A number of meta-analytical methods have been proposed that aim to evaluate surrogate endpoints. Bivariate meta-analytical methods can be used to predict the treatment effect for the final outcome from the treatment effect estimate measured on the surrogate endpoint while taking into account the uncertainty around the effect estimate for the surrogate endpoint. In this paper, extensions to multivariate models are developed aiming to include multiple surrogate endpoints with the potential benefit of reducing the uncertainty when making predictions. In this Bayesian multivariate meta-analytic framework, the between-study variability is modelled in a formulation of a product of normal univariate distributions. This formulation is particularly convenient for including multiple surrogate endpoints and flexible for modelling the outcomes which can be surrogate endpoints to the final outcome and potentially to one another. Two models are proposed, first, using an unstructured between-study covariance matrix by assuming the treatment effects on all outcomes are correlated and second, using a structured between-study covariance matrix by assuming treatment effects on some of the outcomes are conditionally independent. While the two models are developed for the summary data on a study level, the individual-level association is taken into account by the use of the Prentice's criteria (obtained from individual patient data) to inform the within study correlations in the models. The modelling techniques are investigated using an example in relapsing remitting multiple sclerosis where the disability worsening is the final outcome, while relapse rate and MRI lesions are potential surrogates to the disability progression.
authors.affiliation: Biostatistics Research Group, Department of Health Sciences, University of Leicester, University Road, Leicester, LE1 7RH, U.K.
authors.forename: Sylwia
authors.identifier: http://orcid.org/0000-0002-3003-9403
authors.initials: S
authors.lastname: Bujkiewicz
authors.affiliation: Genetic Epidemiology Group, Department of Health Sciences, University of Leicester, University Road, Leicester, LE1 7RH, U.K.
authors.forename: John R
authors.initials: JR
authors.lastname: Thompson
authors.affiliation: Research Institute of Primary Care and Health Sciences, Keele University, Staffordshire, ST5 5BG, U.K.
authors.forename: Richard D
authors.initials: RD
authors.lastname: Riley
authors.affiliation: Biostatistics Research Group, Department of Health Sciences, University of Leicester, University Road, Leicester, LE1 7RH, U.K.
authors.forename: Keith R
authors.initials: KR
authors.lastname: Abrams
mesh_terms: D001499:Bayes Theorem; D015415:Biomarkers / Q000032:analysis*; D003198:Computer Simulation; D018450:Disease Progression; D055808:Drug Discovery / Q000706:statistics & numerical data*; D006801:Humans; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D020529:Multiple Sclerosis, Relapsing-Remitting / Q000000981:diagnostic imaging / Q000503:physiopathology; D015999:Multivariate Analysis
chemical_list: D015415:Biomarkers
keywords: Bayesian analysis; multiple outcomes; multiple sclerosis; multivariate meta-analysis; surrogate endpoints