TY - JOUR

T1 - A comparison of arm-based and contrast-based models for network meta-analysis

AU - White, Ian R.

AU - Turner, Rebecca M.

AU - Karahalios, Amalia

AU - Salanti, Georgia

PY - 2019/11/30

Y1 - 2019/11/30

N2 - 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.

AB - 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.

KW - Bayesian

KW - missing data

KW - mixed treatment comparisons

KW - multiple treatments meta-analysis

KW - network meta-analysis

UR - http://www.scopus.com/inward/record.url?scp=85073925391&partnerID=8YFLogxK

U2 - 10.1002/sim.8360

DO - 10.1002/sim.8360

M3 - Article

C2 - 31583750

AN - SCOPUS:85073925391

SN - 0277-6715

VL - 38

SP - 5197

EP - 5213

JO - Statistics in Medicine

JF - Statistics in Medicine

IS - 27

ER -