One-stage individual participant data meta-analysis models for continuous and binary outcomes: Comparison of treatment coding options and estimation methods |
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Authors: | Richard D. Riley Amardeep Legha Dan Jackson Tim P. Morris Joie Ensor Kym I.E. Snell Ian R. White Danielle L. Burke |
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Affiliation: | 1. Centre for Prognosis Research, School of Primary, Community and Social Care, Keele University, Keele, UK;2. Statistical Innovation Group, Advanced Analytics Centre, AstraZeneca, Cambridge, UK;3. Institute of Clinical Trials and Methodology, MRC Clinical Trials Unit at UCL, London, UK |
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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. |
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Keywords: | estimation methods individual participant data IPD maximum likelihood meta-analysis treatment coding |
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