Imputing Covariance for Meta-Analysis in the Presence of Interaction

Detecting interactions is a critical aspect of medical research. When interactions are present, it is essential to calculate confidence intervals for both the main effect and the interaction effect. This requires determining the covariance between the two effects. In a two-stage individual patient data (IPD) meta-analysis, the coefficients, as well as their variances and covariances, can be calculated for each study. These coefficients can then be combined into an overall estimate using either a fixed-effect or random-effects meta-analysis model. The overall variance of the combined coefficient is typically derived using the inverse-variance method. The most commonly used method for calculating the overall covariance between the main effect and the interaction effect in meta-analysis is multivariate meta-analysis. In this paper, we propose an alternative, straightforward, and transparent method for calculating this covariance when interactions are considered in a meta-analysis. To facilitate implementation, we have developed an R package, ‘covmeta’.