Table 5.

Performance of Penalized Quasi-likelihood and Adaptive Gaussian Hermite Quadrature estimation approaches in large data sets^a with greater (Top panel) and lesser (Bottom panel) heterogeneity of random effects^b

	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

^aLarge data sets had 15 studies and on average 3000 total subjects

^bBold text represent “best value” of performance

^cMedian (25th and 75th percentile) were reported for AB and RMSE, the proportion was reported for coverage and convergence

^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)

^e(τ ²₀, τ ²₁): (Random treatment-effect variance, random study-effect variance)