Search

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.

Collecting data for an individual participant data meta-analysis (IPDMA) project can be time consuming and resource intensive and could still have insufficient power to answer the question of interest. Therefore, researchers should consider the power of their planned IPDMA before collecting IPD. Here we propose a method to estimate the power of a planned IPDMA project aiming to synthesise multiple cohort studies to investigate the (unadjusted or adjusted) effects of potential prognostic factors for a binary outcome. We consider both binary and continuous factors and provide a three-step approach to estimating the power in advance of collecting IPD, under an assumption of the true prognostic effect of each factor of interest. The first step uses routinely available (published) aggregate data for each study to approximate Fisher's information matrix and thereby estimate the anticipated variance of the unadjusted prognostic factor effect in each study. These variances are then used in step 2 to estimate the anticipated variance of the summary prognostic effect from the IPDMA. Finally, step 3 uses this variance to estimate the corresponding IPDMA power, based on a two-sided Wald test and the assumed true effect. Extensions are provided to adjust the power calculation for the presence of additional covariates correlated with the prognostic factor of interest (by using a variance inflation factor) and to allow for between-study heterogeneity in prognostic effects. An example is provided for illustration, and Stata code is supplied to enable researchers to implement the method.