Meta-analysis using individual participant data: one-stage and two-stage approaches, and why they may differ

Abstract

Meta‐analysis using individual participant data (IPD) obtains and synthesises the raw, participant‐level data from a set of relevant studies. The IPD approach is becoming an increasingly popular tool as an alternative to traditional aggregate data meta‐analysis, especially as it avoids reliance on published results and provides an opportunity to investigate individual‐level interactions, such as treatment‐effect modifiers. There are two statistical approaches for conducting an IPD meta‐analysis: one‐stage and two‐stage. The one‐stage approach analyses the IPD from all studies simultaneously, for example, in a hierarchical regression model with random effects. The two‐stage approach derives aggregate data (such as effect estimates) in each study separately and then combines these in a traditional meta‐analysis model. There have been numerous comparisons of the one‐stage and two‐stage approaches via theoretical consideration, simulation and empirical examples, yet there remains confusion regarding when each approach should be adopted, and indeed why they may differ.In this tutorial paper, we outline the key statistical methods for one‐stage and two‐stage IPD meta‐analyses, and provide 10 key reasons why they may produce different summary results. We explain that most differences arise because of different modelling assumptions, rather than the choice of one‐stage or two‐stage itself. We illustrate the concepts with recently published IPD meta‐analyses, summarise key statistical software and provide recommendations for future IPD meta‐analyses. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

A comparison of methods for meta‐analysis of a small number of studies with binary outcomes

“…The models described above are 2 stage models. This means that in the first step, aggregated measures are calculated for each study separately and in the second, subsequent step these measures are combined . Opposed to this, the beta‐binominal regression is a 1 stage model.…”

“…Opposed to this, the beta‐binominal regression is a 1 stage model. This means the analysis is performed in 1 step similar to individual patient data regression analysis . Moreover, the beta‐binomial model is a true (study‐specific) random effects regression model …”

Opportunistic screening for heart failure with natriuretic peptides in patients with atrial fibrillation: a meta-analysis of individual participant data of four screening studies

“…Subsequently, we performed two-stage mixed-effects regression meta-analysis21 by calculating the diagnostic indices in each imputed dataset, which were then combined using Rubin’s rule. Finally, as the second stage we performed random-effects meta-analysis to combine the four studies.…”

A comparison of one‐stage vs two‐stage individual patient data meta‐analysis methods: A simulation study

“…Various modelling choices are possible within the 1‐stage IPD approach, under different assumptions for the intercept (random, fixed common, or fixed study specific) and similarly for the exposure effect and any covariates, including any baseline information. It is known that the correct specification of the 1‐stage model is critical, and guides and software to aid researchers in this are available . Fewer modelling options are available for two‐stage analysis, and they are mainly around the choice of the second step model, fixed effect, or one of the numerous random‐effects options .…”

“…However, it has recently been suggested that one‐stage analyses of interactions can lead to deluded evaluations in certain scenarios, namely, when the covariate of interest is grossly imbalanced across trials (for example, when assessing the interaction between gender and the intervention of interest, but some studies have only enrolled men) . But it has also been argued that most differences between the two approaches arise because of different modelling assumptions, rather than the choice of one‐stage or two‐stage itself …”