One‐stage individual participant data meta‐analysis models for continuous and binary outcomes: Comparison of treatment coding options and estimation methods. (11th May 2020) - Riley, Richard D.; Legha, Amardeep; Jackson, Dan; Morris, Tim P.; Ensor, Joie; Snell, Kym I.E.; White, Ian R.; Burke, Danielle L.
Abstract : A one‐stage individual participant data (IPD) meta‐analysis synthesizes IPD from multiple studies using a general or generalized linear mixed model. This produces summary results (eg, 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 synthesizing randomized trials with continuous or binary outcomes. Three key findings are identified. First, 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 with a z‐based approach. Second, when using ML estimation of a one‐stage model with a stratified intercept, the treatment variable should be coded using "study‐specific centering" (ie, 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 with 1/0 and other coding options). Third, REML estimation reduces downward bias in between‐study variance estimates compared with 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 (eg, when data are sparse). Two applied examples are used to illustrate the findings.