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

Table 2 Performance of the one- and two-stage approaches in small 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)	0.04 (0.02 0.06)	0.04 (0.02, 0.07)	0.04 (0.02, 0.06)	0.04 (0.01, 0.07)
	RMSE (β ₁)	1.11 (0.49, 1.94)	1.19 (0.53, 2.12)	1.18 (0.59, 1.96)	1.23 (0.61, 2.14)
	Coverage (β ₁)	89.3	91.8	92	92.6
	AB (τ ²₁ )	0.23 (0.14,0.30)	0.16 (0.08, 0.24)	0.15 (0.08,0.24)	0.24 (0.20, 0.27)
	RMSE (τ ²₁ )	7.26 (4.39,7.51)	4.93 (2.56, 7.51)	4.81 (2.38,7.42)	7.47 (6.28, 8.64)
	Coverage (τ ²₁ ) ^f	NA	NA	NA	NA
	Convergence	100	97.7	100	99.8
(τ ²₀ , τ ²₁ ) = (1, 1)	AB (β ₁)	0.02 (0.01, 0.04)	0.02 (0.01, 0.04)	0.03 (0.01, 0.04)	0.03 (0.01, 0.04)
	RMSE (β ₁)	0.73 (0.35, 1.29)	0.75 (0.37, 1.33)	0.80 (0.37, 1.30)	0.79 (0.39, 1.34)
	Coverage (β ₁)	89.1	90.6	91.1	91.6
	AB (τ ²₁ )	0.06 (0.03, 0.08)	0.04 (0.02, 0.1)	0.05 (0.03, 0.08)	0.03 (0.01, 0.07)
	RMSE (τ ²₁ )	1.73 (0.85, 2.65)	1.22 (0.53, 3.16)	1.59 (0.80, 2.46)	1.06 (0.46, 2.06)
	Coverage (τ ²₁ )	NA	NA	NA	NA
	Convergence	100	90.4	100	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
^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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