Table 4.

Performance of Penalized Quasi-likelihood and Adaptive Gaussian Hermite Quadrature estimation approaches in small 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)	0.05 (0.02, 0.08)	0.04 (0.02, 0.07)	0.04 (0.02, 0.07)	0.04 (0.02, 0.07)
	RMSE ($\beta$ 1)	1.42 (0.64, 2.52)	1.19 (0.53, 2.12)	1.35 (0.65, 2.27)	1.23 (0.61, 2.14)
	Coverage ($\beta$ 1)	93.2	91.8	91.7	92.6
	AB (τ 21)	0.18 (0.09,0.29)	0.16 (0.08, 0.24)	0.15 (0.08,0.24)	0.24 (0.20, 0.27)
	RMSE (τ 21)	5.76 (2.80,9.07)	4.93 (2.56, 7.51)	4.79 (2.37,7.62)	7.47 (6.28, 8.64)
	Coverage (τ 21)	85.5	76.2	81.4	4.6
	Convergence	99	97.7	96.7	99.8
(τ 20, τ 21) = (1, 1)	AB ($\beta$ 1)	0.03 (0.01, 0.05)	0.02 (0.01, 0.04)	0.03 (0.01, 0.04)	0.03 (0.01, 0.04)
	RMSE ($\beta$ 1)	0.79 (0.41, 1.42)	0.75 (0.37, 1.33)	0.84 (0.42, 1.38)	0.79 (0.39, 1.34)
	Coverage ($\beta$ 1)	92.3	90.6	93.4	91.6
	AB (τ 21)	0.06 (0.03, 0.09)	0.04 (0.02, 0.1)	0.05 (0.02, 0.08)	0.03 (0.02, 0.07)
	RMSE (τ 21)	1.76 (0.84, 2.70)	1.22 (0.53, 3.16)	1.54 (0.72, 2.40)	1.06 (0.46, 2.06)
	Coverage (τ 21)	74.5	81.1	71.6	77.2
	Convergence	96.8	90.4	85.8	100

^aSmall data sets had 15 studies and on average 500 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)