Dataset for: Meta-analysis of quantitative individual patient data: two stage or not two stage?

Quantitative evidence synthesis through meta-analysis is central to evidence-based medicine. For well-documented reasons, the meta-analysis of individual patient data (IPD) is held in higher regard than aggregate data. With access to IPD, the analysis is not restricted to a ‘two-stage’ approach (combining estimates and standard errors) but can estimate parameters of interest by fitting a single model to all of the data; a so-called ‘one-stage’ analysis. There has been debate about the merits of one- and two-stage analysis. Arguments for one-stage analysis have typically noted that a wider range of models can be fitted and overall estimates may be more precise. The two-stage side has emphasised that the models that can be fitted in two-stages are sufficient to answer the relevant questions, with less scope less scope for mistakes because there are fewer modelling choices to be made in the two-stage approach. Considering Gaussian data, we consider the statistical arguments for flexibility and precision in the small-sample settings. Regarding flexibility, several of the models that can be fitted only in one stage may not be of serious interest to most meta-analysis practitioners. Regarding precision, we consider fixed- and random-effects meta-analysis, and see that, for a model making certain assumptions, the number of stages used to fit this model is irrelevant; the precision will be approximately equal. Meta-analysts should choose modelling assumptions carefully. Sometimes relevant models can only be fitted in one stage. Otherwise, meta-analysts are free to use whichever procedure is most convenient to fit the identified model.