title: Borrowing of strength and study weights in multivariate and network meta-analysis.
abstract: Multivariate and network meta-analysis have the potential for the estimated mean of one effect to borrow strength from the data on other effects of interest. The extent of this borrowing of strength is usually assessed informally. We present new mathematical definitions of 'borrowing of strength'. Our main proposal is based on a decomposition of the score statistic, which we show can be interpreted as comparing the precision of estimates from the multivariate and univariate models. Our definition of borrowing of strength therefore emulates the usual informal assessment. We also derive a method for calculating study weights, which we embed into the same framework as our borrowing of strength statistics, so that percentage study weights can accompany the results from multivariate and network meta-analyses as they do in conventional univariate meta-analyses. Our proposals are illustrated using three meta-analyses involving correlated effects for multiple outcomes, multiple risk factor associations and multiple treatments (network meta-analysis).
authors.affiliation: 1 MRC Biostatistics Unit, Cambridge, UK.
authors.forename: Dan
authors.initials: D
authors.lastname: Jackson
authors.affiliation: 1 MRC Biostatistics Unit, Cambridge, UK.
authors.forename: Ian R
authors.initials: IR
authors.lastname: White
authors.affiliation: 2 Department of Public Health, Epidemiology & Biostatistics, University of Birmingham, Birmingham, UK.
authors.forename: Malcolm
authors.initials: M
authors.lastname: Price
authors.affiliation: 3 Department of Statistics, University of Warwick, Coventry, UK.
authors.forename: John
authors.initials: J
authors.lastname: Copas
authors.affiliation: 4 Department of Primary Care & Health Sciences, University of Keele, Staffordshire, UK.
authors.forename: Richard D
authors.initials: RD
authors.lastname: Riley
mesh_terms: D056808:Biostatistics / Q000379:methods; D001794:Blood Pressure / Q000187:drug effects; D002318:Cardiovascular Diseases / Q000517:prevention & control; D006801:Humans; D006973:Hypertension / Q000188:drug therapy / Q000503:physiopathology; D016013:Likelihood Functions; D015233:Models, Statistical; D015999:Multivariate Analysis; D009203:Myocardial Infarction / Q000188:drug therapy; D000071076:Network Meta-Analysis as Topic; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D020521:Stroke / Q000517:prevention & control; D015912:Thrombolytic Therapy / Q000379:methods
keywords: Borrowing of strength; correlation; descriptive statistics; mixed treatment comparisons; multiple treatments meta-analysis; multivariate meta-analysis; random-effects models; study weights