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 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.

Efficacy of Acupuncture in Subpopulations with Constipation: A protocol for a Systematic Review and Individual Patient data Meta-analysis

“…The primary analysis will be conducted by a one-stage approach [41], which means that all IPDs are modelled simultaneously while accounting for the clustering of participants within studies. The IPD of the primary outcome will be synthesized by a generalized linear mixed model [42].…”

Reducing Self-harm in Adolescents. An individual participant data meta-analysis (RISA-IPD): systematic review protocol

“…Analyses will be conducted in accordance with current recommendations for IPD meta-analyses [18][19][20][21][22][23] and will consider appropriate adjustment for baseline covariates (prognostic factors), handling of multiple treatment groups and control arms, missing data, [24][25][26][27] repeated measures, 28 29 timing of outcomes, randomisation, withinstudy treatment-related clustering 30 31 and non-adherence. Analysis populations will be based on the intention-totreat principle, including all randomised participants in the groups to which they were randomised, regardless of withdrawal or protocol compliance.…”

“…CIs will be derived using an approach to account for uncertainty in variance estimates, such as the Hartung-Knapp-Sidik-Jonkmann 22 approach in the two-stage analysis, and the Kenward-Roger or Satterthwaite approach following the one-stage analysis. 21 After the meta-analysis, we will report estimated summary treatment effects, 95% CIs and 95% prediction intervals alongside forest plots with study-specific estimates of treatment effect. Heterogeneity will be assessed using the τ 2 statistic (variability of the true effect sizes under the random effects model, estimated using REML) and the I 2 statistic (proportion of total variability due to between-study heterogeneity).…”

“…1 One in twenty 11-16 yearolds, and one in seven 17-19 year-olds, report having self-harmed or attempted suicide at some point; with rates in girls twice that of boys. 2 Self-harm in adolescents has serious consequences; rates of death from any cause show a fourfold and suicide a 10-fold excess risk, 3 and suicide is the second most common cause of Strengths and limitations of this study ► Much research in this field spans the adolescent and adult divide (ie, participants aged [14][15][16][17][18][19][20][21][22][23][24][25]; individual participant data meta-analysis (IPD-MA) allows us to increase the pool of studies and participants through the inclusion of subsets of participants from partially eligible studies. ► IPD-MA will provide an increased sample size to permit meaningful subgroup analyses unavailable to individual studies; a more reliable estimate of the effect of therapeutic interventions for self-harm; and flexibility in analysis to handle sources of betweenstudy and within-study heterogeneity.…”

Estimating interactions in individual participant data meta-analysis. A comparison of methods in practice.

“…Other authors have noted that a +0.5/-0.5 coding may be preferable in some circumstances, by ensuring a common variance for treatment and control groups and improving maximum likelihood estimation 6,16 , particularly in random effect models where trials are few and the estimation of correlation between two random effects is problematic 14 . Another option is "studyspecific centering" (coding 1/0 minus the study-specific proportion of participants in the treatment group) that may reduce the downward bias of between-study variance when using maximum likelihood estimation 16 . Overall, few analyses showed any clear evidence of treatment-covariate interaction, generally having wide confidence intervals.…”