Multivariate meta-analysis using individual participant data

Abstract

When combining results across related studies, a multivariate meta-analysis allows the joint synthesis of correlated effect estimates from multiple outcomes. Joint synthesis can improve efficiency over separate univariate syntheses, may reduce selective outcome reporting biases, and enables joint inferences across the outcomes. A common issue is that within-study correlations needed to fit the multivariate model are unknown from published reports. However, provision of individual participant data (IPD) allows them to be calculated directly. Here, we illustrate how to use IPD to estimate within-study correlations, using a joint linear regression for multiple continuous outcomes and bootstrapping methods for binary, survival and mixed outcomes. In a meta-analysis of 10 hypertension trials, we then show how these methods enable multivariate meta-analysis to address novel clinical questions about continuous, survival and binary outcomes; treatment-covariate interactions; adjusted risk/prognostic factor effects; longitudinal data; prognostic and multiparameter models; and multiple treatment comparisons. Both frequentist and Bayesian approaches are applied, with example software code provided to derive within-study correlations and to fit the models.

Keywords: bivariate meta-analysis; correlation; individual participant data (IPD); individual patient data; multiple outcomes; multivariate meta-analysis.

Figure 1.

Relationship between the treatment effect estimates on systolic blood pressure (SBP) and diastolic blood pressure (DBP), within and across trials. The crosses indicate a pair of estimates from one trial, and the angle of the confidence ellipse around each estimate indicates the within-study correlation. The solid circle denotes the pair of summary estimates from the meta-analysis, and the circle around it denotes its confidence ellipse. 50% (rather than 95%) confidence ellipses are given for cosmetic reasons, as otherwise the regions are large and overlap considerably. * estimated from a Bayesian bivariate meta-analysis model, with prior distributions as specified in section 3.2. This is the proportion of the joint posterior distribution for the underlying treatment effects of these two outcomes that falls within this region.

Figure 2.

Relationship between the treatment effect estimates on systolic blood pressure (SBP) and stroke, within and across trials. The crosses indicate a pair of estimates from one trial, and the angle of the confidence ellipse around each estimate indicates the within-study correlation. The solid circle denotes the pair of summary estimates from the meta-analysis, and the circle around it denotes its confidence ellipse. 50% (rather than 95%) confidence ellipses are given for cosmetic reasons, as otherwise the regions are large and overlap considerably. * estimated from a Bayesian four-outcome multivariate meta-analysis model, with prior distributions as specified in section 3.2 and Web Appendix 1. This is the proportion of the joint posterior distribution for the underlying treatment effects of these two outcomes that falls within this region.