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

Table 6 Performance of the stratified- and random-intercept^a models approaches in small data sets^b with greater (Top panel) and lesser (Bottom panel) heterogeneity of random effects^c

	Performance measures^d	Data generation
		Random-study and -treatment effect (Eq. 1)		Stratified-study effect (Eq. 2)
		Stratified-intercept	Random-intercept	Stratified-intercept	Random-intercept
(τ ²₀ , τ ²₁ ) = (4, 4)^e	AB (\( \beta \) ₁)	0.04 (0.02, 0.08)	0.04 (0.02, 0.07)	0.05 (0.02, 0.07)	0.04 (0.01, 0.07)
	RMSE (\( \beta \) ₁)	1.24 (0.49, 2.44)	1.19 (0.53, 2.12)	1.43 (0.70, 2.32)	1.23 (0.61, 2.14)
	Coverage (\( \beta \) ₁)	99.1	91.8	97.4	92.6
	AB (τ ²₁ )	0.16 (0.07, 0.25)	0.16 (0.08, 0.24)	0.15 (0.07,0.24)	0.24 (0.20, 0.27)
	RMSE (τ ²₁ )	5.01 (2.35,7.95)	4.93 (2.56, 7.51)	4..75 (2.23,7.64)	7.47 (6.28, 8.64)
	Coverage (τ ²₁ )	11.6	76.2	28.4	4.6
	Convergence	13.8	97.7	32.3	99.8
(τ ²₀ , τ ²₁ ) = (1, 1)	AB (\( \beta \) ₁)	0.03 (0.01, 0.04)	0.02 (0.01, 0.04)	0.03 (0.01, 0.05)	0.03 (0.01, 0.04)
	RMSE (\( \beta \) ₁)	0.83 (0.41, 1.38)	0.75 (0.37, 1.33)	0.90 (0.42, 1.47)	0.79 (0.39, 1.34)
	Coverage (\( \beta \) ₁)	96.4	90.6	94	91.6
	AB (τ ²₁ )	0.05 (0.03, 0.09)	0.04 (0.02, 0.1)	0.05 (0.02, 0.08)	0.03 (0.01, 0.07)
	RMSE (τ ²₁ )	1.72 (0.85, 2.78)	1.22 (0.53, 3.16)	1.55 (0.75, 1.61)	1.06 (0.46, 2.06)
	Coverage (τ ²₁ )	37.3	81.1	54.4	77.2
	Convergence	42.6	90.4	62.3	100

^aResults are given for Penalized Quasi-likelihood (PQL) for the One-stage random-intercept and random treatment effect model (Model 3) and the stratified-intercept and random-slope model (Model 4)
^bSmall data sets had 15 studies and on average 500 total subjects
^cBold text represent “best value” of performance
^dMedian (25th and 75th percentile) were reported for AB and RMSE, the proportion was reported for coverage and convergence
^e(τ ²₀ , τ ²₁ ): (Random treatment-effect variance, random study-effect variance)

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