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Table 3 Performance of the one- and two-stage 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

   Data generation
  Performance measuresc Random-study and treatment effect (Eq. 1) Stratified-study effect (Eq. 2)
Two-staged One-stage Two-stage One-stage
(τ 20 , τ 21 ) = (4, 4) e AB (β 1) 0.03 (0.02 0.06) 0.03 (0.02, 0.06) 0.04 (0.01, 0.06) 0.04 (0.01, 0.06)
  RMSE (β 1) 1.02 (0.50, 1.85) 1.07 (0.49, 1.84) 1.15 (0.57, 1.93) 1.11 (0.58, 1.87)
  Coverage (β 1) 91.9 92.3 92.4 93.6
  AB (τ 21 ) 0.14 (0.07,0.22) 0.12 (0.06, 0.20) 0.11 (0.05,0.17) 0.22 (0.20, 0.25)
  RMSE (τ 21 ) 4.36 (2.22,6.80) 3.87 (1.81, 6.21) 3.40 (1.70,5.47) 6.99 (6.20, 7.80)
  Coverage (τ 21 ) f NA NA NA NA
  Convergence 100 98.3 100 89.9
(τ 20 , τ 21 ) = (1, 1) AB (β 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 (β 1) 0.61 (0.30, 1.04) 0.59 (0.29, 1.05) 0.61 (0.30, 1.02) 0.63 (0.30, 1.03)
  Coverage (β 1) 91.2 91.9 93 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 ) 1.08 (0.53, 1.73) 1.03 (0.49, 1.68) 1.00 (0.51, 1.68) 0.57 (0.27, 1.00)
  Coverage (τ 21 ) NA NA NA NA
  Convergence 100 96.5 100 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. dTwo-stage method via conventional DerSimonian and Laird (Model 2). One-stage (Random-intercept and random treatment effect with PQL (Model 3)
  5. e(τ 20 , τ 21 ): (Random treatment-effect variance, random study-effect variance)
  6. fThe two-stage approach did not return a confidence interval for τ 21 , hence no coverage was estimated and comparison was not applicable (NA) to the one-stage method