Table 3.

Performance of the one- and two-stage approaches in large data sets^a with greater (Top panel) and lesser (Bottom panel) heterogeneity of random effects^b

		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

^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

^dTwo-stage method via conventional DerSimonian and Laird (Model 2). One-stage (Random-intercept and random treatment effect with PQL (Model 3)

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

^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