Skip to main content

Table 5 Performance of Penalized Quasi-likelihood and Adaptive Gaussian Hermite Quadrature estimation approaches in large data setsa with greater (Top panel) and lesser (Bottom panel) heterogeneity of random effectsb

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

  Performance measuresc Data generation
Random-study and treatment effect (Eq. 1) Stratified-study effect (Eq. 2)
AGHQd PQLd AGHQ PQL
(τ 20 , τ 21 ) = (4, 4)e AB (\( \beta \) 1) 0.04 (0.02, 0.06) 0.03 (0.02, 0.06) 0.04 (0.01, 0.06) 0.04 (0.01, 0.06)
RMSE (\( \beta \) 1) 1.20 (0.55, 1.99) 1.07 (0.49, 1.84) 1.16 (0.58, 1.95) 1.11 (0.58, 1.87)
Coverage (\( \beta \) 1) 92.2 92.3 92.1 93.6
AB (τ 21 ) 0.13 (0.07,0.21) 0.12 (0.06, 0.20) 0.11 (0.05,0.18) 0.22 (0.20, 0.25)
RMSE (τ 21 ) 4.12 (2.06,6.77) 3.87 (1.81, 6.21) 3.42 (1.71,5.77) 6.99 (6.20, 7.80)
Coverage (τ 21 ) 81.9 78.9 84.7 1.0
Convergence 100 98.3 100 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) 0.60 (0.30, 1.06) 0.59 (0.29, 1.05) 0.63 (0.30, 1.05) 0.63 (0.30, 1.03)
Coverage (\( \beta \) 1) 91.7 91.9 92.4 93.3
AB (τ 21 ) 0.04 (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 ) 1.09 (0.52, 1.75) 1.03 (0.49, 1.68) 1.01 (0.49, 1.69) 0.57 (0.27, 1.00)
Coverage (τ 21 ) 83.6 82.5 82.5 76.5
Convergence 99.5 96.5 99.1 88.8
  1. aLarge data sets had 15 studies and on average 3000 total subjects
  2. bBold text represent “best value” of performance
  3. cMedian (25th and 75th percentile) were reported for AB and RMSE, the proportion was reported for coverage and convergence
  4. dResults are given for Adaptive Gaussian Hermite Quadrature (AGHQ) and Penalized Quasi-likelihood (PQL) for the One-stage random-intercept and random treatment effect model (Model 3)
  5. e(τ 20 , τ 21 ): (Random treatment-effect variance, random study-effect variance)