One-stage individual participant data meta-analysis models for continuous and binary outcomes: comparison of treatment coding options and estimation methods

Abstract

A one-stage individual participant data (IPD) meta-analysis synthesises IPD from multiple studies using a general or generalised linear mixed model. This produces summary results (e.g. about treatment effect) in a single step, whilst accounting for clustering of participants within studies (via a stratified study intercept, or random study intercepts) and between-study heterogeneity (via random treatment effects). We use simulation to evaluate the performance of restricted maximum likelihood (REML) and maximum likelihood (ML) estimation of one-stage IPD meta-analysis models for synthesising randomised trials with continuous or binary outcomes. Three key findings are identified. Firstly, for ML or REML estimation of stratified intercept or random intercepts models, a t-distribution based approach generally improves coverage of confidence intervals for the summary treatment effect, compared to a z-based approach. Secondly, when using ML estimation of a one-stage model with a stratified intercept, the treatment variable should be coded using ‘study-specific centering’ (i.e. 1/0 minus the study-specific proportion of participants in the treatment group), as this reduces the bias in the between-study variance estimate (compared to 1/0 and other coding options). Thirdly, REML estimation reduces downward bias in between-study variance estimates compared to ML estimation, and does not depend on the treatment variable coding; for binary outcomes, this requires REML estimation of the pseudo-likelihood, although this may not be stable in some situations (e.g. when data are sparse). Two applied examples are used to illustrate the findings.