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Table 3 Between-trial variance estimates (posterior distribution median) for the comparisons that were also informed by head-to-head evidence in the treatment network in the second illustrative example

From: Modelling heterogeneity variances in multiple treatment comparison meta-analysis – Are informative priors the better solution?

 

Between-trial variance estimates

Model fit statistics

Models

Trt1 vs Placebo

Trt2 vs Placebo

Trt3 vs Placebo

Trt4 vs Placebo

Trt2 vs Trt1

pD

DIC

Random-effects pair wise meta-analysis

Frequentist (DerSimonian-Laird)

0.086

0.110

0.016

0.075

0.106

--

--

Frequentist (Hartung-Makimbi)

0.083

0.103

0.040

0.072

0.112

--

--

Bayesian (weakly informative)

0.100

0.371

0.023

0.103

0.334

--

--

Bayesian (frequentist informed)

0.087

0.121

0.036

0.067

0.093

--

--

Bayesian (empirically informed)

0.088

0.110

0.021

0.054

0.059

--

--

Random-effects MTC models

       

Weakly informed variance models

Homogeneous variance model

0.078

0.078

0.078

0.078

0.078

138.8

1229.1

  Unrestricted variances

0.100

0.469

0.023

0.104

0.214

138.3

1229.9

  Exchangeable variances*

0.092

0.226

0.009

0.066

0.047

133.7

1232.2

  Consistency variances structure

0.091

0.172

0.033

0.075

0.133

136.6

1230.0

Moderately informed variance models

       

  Frequentist informed priors

0.087

0.172

0.036

0.069

0.064

135.6

1226.4

  Empirically informed priors

0.087

0.199

0.020

0.054

0.042

133.8

1229.5

  1. * The’average’ variance was 0.173.
  2. Abbreviations: DIC (Deviance information criterion); pD (effective number of model parameters); Trt (Treatment).