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The role of secondary outcomes in multivariate meta‐analysis
Author(s) -
Copas John B.,
Jackson Dan,
White Ian R.,
Riley Richard D.
Publication year - 2018
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/rssc.12274
Subject(s) - univariate , bivariate analysis , meta analysis , multivariate statistics , context (archaeology) , multivariate analysis , statistics , variance (accounting) , outcome (game theory) , random effects model , forest plot , econometrics , contrast (vision) , multivariate analysis of variance , mathematics , computer science , medicine , artificial intelligence , economics , paleontology , accounting , mathematical economics , biology
Summary Univariate meta‐analysis concerns a single outcome of interest measured across a number of independent studies. However, many research studies will have also measured secondary outcomes. Multivariate meta‐analysis allows us to take these secondary outcomes into account and can also include studies where the primary outcome is missing. We define the efficiency E as the variance of the overall estimate from a multivariate meta‐analysis relative to the variance of the overall estimate from a univariate meta‐analysis. The extra information gained from a multivariate meta‐analysis of n studies is then similar to the extra information gained if a univariate meta‐analysis of the primary effect had a further n (1− E )/ E studies. The variance contribution of a study's secondary outcomes (its borrowing of strength) can be thought of as a contrast between the variance matrix of the outcomes in that study and the set of variance matrices of all the studies in the meta‐analysis. In the bivariate case this is given a simple graphical interpretation as the borrowing‐of‐strength plot . We discuss how these findings can also be used in the context of random‐effects meta‐analysis. Our discussion is motivated by a published meta‐analysis of 10 antihypertension clinical trials.