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A comparison of arm‐based and contrast‐based models for network meta‐analysis
Author(s) -
White Ian R.,
Turner Rebecca M.,
Karahalios Amalia,
Salanti Georgia
Publication year - 2019
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8360
Subject(s) - random effects model , contrast (vision) , fixed effects model , statistics , meta analysis , data set , missing data , computer science , econometrics , marginal model , mathematics , regression analysis , medicine , panel data , artificial intelligence
Differences between arm‐based (AB) and contrast‐based (CB) models for network meta‐analysis (NMA) are controversial. We compare the CB model of Lu and Ades (2006), the AB model of Hong et al(2016), and two intermediate models, using hypothetical data and a selected real data set. Differences between models arise primarily from study intercepts being fixed effects in the Lu‐Ades model but random effects in the Hong model, and we identify four key difference. (1) If study intercepts are fixed effects then only within‐study information is used, but if they are random effects then between‐study information is also used and can cause important bias. (2) Models with random study intercepts are suitable for deriving a wider range of estimands, eg, the marginal risk difference, when underlying risk is derived from the NMA data; but underlying risk is usually best derived from external data, and then models with fixed intercepts are equally good. (3) The Hong model allows treatment effects to be related to study intercepts, but the Lu‐Ades model does not. (4) The Hong model is valid under a more relaxed missing data assumption, that arms (rather than contrasts) are missing at random, but this does not appear to reduce bias. We also describe an AB model with fixed study intercepts and a CB model with random study intercepts. We conclude that both AB and CB models are suitable for the analysis of NMA data, but using random study intercepts requires a strong rationale such as relating treatment effects to study intercepts.