Research Synthesis Methods

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

Journal Article


Individual patient data (IPD) meta‐analysis allows for the exploration of heterogeneity and can identify subgroups that most benefit from an intervention (or exposure), much more successfully than meta‐analysis of aggregate data. One‐stage or two‐stage IPD meta‐analysis is possible, with the former using mixed‐effects regression models and the latter obtaining study estimates through simpler regression models before aggregating using standard meta‐analysis methodology. However, a comprehensive comparison of the two methods, in practice, is lacking.


We generated 1000 datasets for each of many simulation scenarios covering different IPD sizes and different between‐study variance (heterogeneity) assumptions at various levels (intercept and exposure). Numerous simulation settings of different assumptions were also used, while we evaluated performance both on main effects and interaction effects. Performance was assessed on mean bias, mean error, coverage, and power.


Fully specified one‐stage models (random study intercept or fixed study‐specific intercept; random exposure effect; and fixed study‐specific effects for covariate) were the best performers overall, especially when investigating interactions. For main effects, performance was almost identical across models unless intercept heterogeneity was present, in which case the fully specified one‐stage and the two‐stage models performed better. For interaction effects, differences across models were greater with the two‐stage model consistently outperformed by the two fully specified one‐stage models.


A fully specified one‐stage model should be preferred (accounting for potential exposure, intercept, and, possibly, interaction heterogeneity), especially when investigating interactions. If non‐convergence is encountered with a random study intercept, the fixed study‐specific intercept one‐stage model should be used instead.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.