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

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 measures^c	Random-study and treatment effect (Eq. 1)		Stratified-study effect (Eq. 2)
	Performance measures^c	Two-stage^d	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

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