Individual participant data meta-analysis of continuous outcomes: A comparison of approaches for specifying and estimating one-stage models

One-stage individual participant data meta-analysis models should account for within-trial clustering, but it is currently debated how to do this. For continuous outcomes modeled using a linear regression framework, two competing approaches are a stratified intercept or a random intercept. The stratified approach involves estimating a separate intercept term for each trial, whereas the random intercept approach assumes that trial intercepts are drawn from a normal distribution. Here, through an extensive simulation study for continuous outcomes, we evaluate the impact of using the stratified and random intercept approaches on statistical properties of the summary treatment effect estimate. Further aims are to compare (i) competing estimation options for the one-stage models, including maximum likelihood and restricted maximum likelihood, and (ii) competing options for deriving confidence intervals (CI) for the summary treatment effect, including the standard normal-based 95% CI, and more conservative approaches of Kenward-Roger and Satterthwaite, which inflate CIs to account for uncertainty in variance estimates. The findings reveal that, for an individual participant data meta-analysis of randomized trials with a 1:1 treatment:control allocation ratio and heterogeneity in the treatment effect, (i) bias and coverage of the summary treatment effect estimate are very similar when using stratified or random intercept models with restricted maximum likelihood, and thus either approach could be taken in practice, (ii) CIs are generally best derived using either a Kenward-Roger or Satterthwaite correction, although occasionally overly conservative, and (iii) if maximum likelihood is required, a random intercept performs better than a stratified intercept model. An illustrative example is provided.