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Table 7 Performance of the stratified- and random-intercepta models approaches in large data setsb with greater (Top panel) and lesser (Bottom panel) heterogeneity of random effectsc

From: A comparison of analytic approaches for individual patient data meta-analyses with binary outcomes

  Performance measuresd Data generation
Random-study and -treatment effect (Eq. 1) Stratified-study effect (Eq. 2)
Stratified-intercept Random-intercept Stratified-intercept Random-intercept
(τ 20 , τ 21 ) = (4, 4)e AB (\( \beta \) 1) 0.04 (0.02, 0.06) 0.03 (0.02, 0.06) 0.04 (0.02, 0.06) 0.04 (0.01, 0.06)
RMSE (\( \beta \) 1) 1.11 (0.55, 1.94) 1.07 (0.49, 1.84) 1.15 (0.58, 1.98) 1.11 (0.58, 1.87)
Coverage (\( \beta \) 1) 95.2 92.3 92.3 93.6
AB (τ 21 ) 0.13 (0.06, 0.20) 0.12 (0.06, 0.20) 0.11 (0.05,0.18) 0.22 (0.20, 0.25)
RMSE (τ 21 ) 4.05 (1.85,6.25) 3.87 (1.81, 6.21) 3.39 (1.57,5.56) 6.99 (6.20, 7.80)
Coverage (τ 21 ) 53.7 78.9 89.8 1.0
Convergence 63.8 98.3 99.7 89.9
(τ 20 , τ 21 ) = (1, 1) AB (\( \beta \) 1) 0.02 (0.01, 0.03) 0.02 (0.01, 0.03) 0.02 (0.01, 0.03) 0.02 (0.01, 0.03)
RMSE (\( \beta \) 1) 0.63 (0.29, 1.07) 0.59 (0.29, 1.05) 0.63 (0.30, 1.05) 0.63 (0.30, 1.03)
Coverage (\( \beta \) 1) 91.8 91.9 93.1 93.3
AB (τ 21 ) 0.03 (0.02, 0.06) 0.03 (0.02, 0.05) 0.03 (0.02, 0.05) 0.02 (0.01, 0.03)
RMSE (τ 21 ) 1.06 (0.52, 1.74) 1.03 (0.49, 1.68) 0.98 (0.48, 1.69) 0.57 (0.27, 1.00)
Coverage (τ 21 ) 86.3 82.5 87.9 76.5
Convergence 95.3 96.5 99.2 88.8
  1. aResults are given for Penalized Quasi-likelihood (PQL) for the One-stage random-intercept and random treatment effect model (Model 3) and the stratified-intercept and random-slope model (Model 4)
  2. bLarge data sets had 15 studies and on average 3000 total subjects
  3. cBold text represent “best value” of performance
  4. dMedian (25th and 75th percentile) were reported for AB and RMSE, the proportion was reported for coverage and convergence
  5. e(τ 20 , τ 21 ): (Random treatment-effect variance, random study-effect variance)