Individual participant data meta‐analysis to examine linear or non‐linear treatment‐covariate interactions at multiple time‐points for a continuous outcome

Abstract

Individual participant data (IPD) meta‐analysis projects obtain, harmonise, and synthesise original data from multiple studies. Many IPD meta‐analyses of randomised trials are initiated to identify treatment effect modifiers at the individual level, thus requiring statistical modelling of interactions between treatment effect and participant‐level covariates. Using a two‐stage approach, the interaction is estimated in each trial separately and combined in a meta‐analysis. In practice, two complications often arise with continuous outcomes: examining non‐linear relationships for continuous covariates and dealing with multiple time‐points. We propose a two‐stage multivariate IPD meta‐analysis approach that summarises non‐linear treatment‐covariate interaction functions at multiple time‐points for continuous outcomes. A set‐up phase is required to identify a small set of time‐points; relevant knot positions for a spline function, at identical locations in each trial; and a common reference group for each covariate. Crucially, the multivariate approach can include participants or trials with missing outcomes at some time‐points. In the first stage, restricted cubic spline functions are fitted and their interaction with each discrete time‐point is estimated in each trial separately. In the second stage, the parameter estimates defining these multiple interaction functions are jointly synthesised in a multivariate random‐effects meta‐analysis model accounting for within‐trial and across‐trial correlation. These meta‐analysis estimates define the summary non‐linear interactions at each time‐point, which can be displayed graphically alongside confidence intervals. The approach is illustrated using an IPD meta‐analysis examining effect modifiers for exercise interventions in osteoarthritis, which shows evidence of non‐linear relationships and small gains in precision by analysing all time‐points jointly.