One-stage random effects meta-analysis using linear mixed models for aggregate continuous outcome data.

The vast majority of meta-analyses uses summary/aggregate data retrieved from published studies in contrast to meta-analysis of individual participant data (IPD). When the outcome is continuous and IPD are available, linear mixed modelling methods canbe employed in a one-stage approach. This allows for flexible modelling of within-study variability and between-study effects and accounts for the uncertainty in the estimates of between-study and within-study residual variances. However, IPD are seldom available. For the normal outcome case we present a method to generate pseudo IPD from aggregate data using group mean, standard deviation and sample sizes within each study, i.e., the sufficient statistics. Analyzing the pseudo IPD with likelihood-based methods yields identical results as the analysis of the unknown true IPD. The advantage of this method is that we can employ the mixed modelling framework, implemented in many statistical software packages, and explore modelling options suitable for IPD, such as fixed study specific intercepts and fixed treatment effect model, fixed study specific intercepts and random treatment effects and both random study and treatment effects and different options to model the within-study residual variance. This allows choosing the most realistic (or potentially complex) residual variance structures across studies, instead of using an overly simple structure. We demonstrate these methods in two empirical datasets in Alzheimer's disease, where an extensive model, assuming all within-study variances to be free, fitted considerably better. In simulations the pseudo IPD approach showed adequate coverage probability, because it accounted for small sample effects.