. 2015 Jul 21;10(7):e0133243. doi: 10.1371/journal.pone.0133243

Table 5. Relative mean bias percentage, RMSE, and coverage probability when N = 10000, m = 10, β ₁ = 0.2, β ₂ = 0.3, β ₃ = 0.3, β _b12 = 0.6, β _b13 = 0.7, ρ _b23 = 0.6, ρ _w12 = ρ _w13 = ρ _w23 = 0.

	Summary		Effects									Heterogeneity						Correlation
	data		% Bias			RMSE ^b			Coverage			% Bias			RMSE ^b			% Bias			%( ${\hat{ρ}}_{b j j'}) = \| 1 \|$
Method	scenario	I ², ^a	${\hat{β}}_{1}$	${\hat{β}}_{2}$	${\hat{β}}_{3}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	${\hat{β}}_{3}$	β ₁	β ₂	β ₃	${\hat{τ}}_{1}^{2}$	${\hat{τ}}_{2}^{2}$	${\hat{τ}}_{3}^{2}$	${\hat{τ}}_{1}^{2}$	${\hat{τ}}_{2}^{2}$	${\hat{τ}}_{3}^{2}$	${\hat{ρ}}_{b 12}$	${\hat{ρ}}_{b 13}$	${\hat{ρ}}_{b 23}$	${\hat{ρ}}_{b 12}$	${\hat{ρ}}_{b 13}$	${\hat{ρ}}_{b 23}$
MV	COM	50%	0	0	0	0	0	0	96.6	96.1	96.7	11	8	13	-3	-3	-3	-14	-17	-12	16.7	16.9	16.8
UV	COM		0	0	0	0	0	0	95.8	95.3	95.4	3	0	3	0	0	0	—	—	—	—	—	—
MV	COM ^c		0	0	0	0	0	0	96.7	96.1	96.6	11	8	11	-3	-3	-3	-14	-17	-12	16.7	16.8	16.7
MV	MAR		0	0	0	0	1	0	96.7	95.8	96.6	11	18	13	-3	3	0	-22	-18	-20	21.8	21.8	21.9
UV	MAR		0	0	0	0	0	0	95.8	96.6	95.4	3	3	3	0	0	0	—	—	—	—	—	—
MV	MIF		0	9	0	0	-3	0	96.5	86.1	96.4	11	-32	11	-3	-7	0	-29	-17	-28	26.1	25.8	26.2
UV	MIF		0	10	0	0	0	0	95.8	87.2	95.4	3	-47	3	0	0	0	—	—	—	—	—	—
MV	COM	75%	0	0	0	0	0	0	95.2	94.7	95.6	0	1	2	-1	0	-1	-4	-2	-3	2.9	3.5	2.9
UV	COM		0	0	0	0	0	0	95.0	94.7	95.1	-2	-1	0	0	0	0	—	—	—	—	—	—
MV	COM ^c		0	0	0	0	0	0	95.3	94.7	95.5	0	0	2	-1	0	-1	-4	-2	-3	2.7	3.3	2.9
MV	MAR		0	0	0	0	0	0	95.3	93.3	95.6	0	6	2	-1	5	-1	-9	-2	-8	5.1	4.9	5.1
UV	MAR		0	0	0	0	0	0	95.0	94.5	95.1	-2	1	0	0	0	0	—	—	—	—	—	—
MV	MIF		0	13	0	0	-7	0	95.3	78.3	95.7	0	-39	2	-1	1	-1	-18	-2	-19	7.5	6.4	6.8
UV	MIF		0	16	0	0	0	0	95.0	78.1	95.1	-2	-48	0	0	0	0	—	—	—	—	—	—

Abbreviation: RMSE, root mean square error; MV, multivariate meta-analysis; UV, Univariate meta-analysis; COM, complete data scenario; MAR, end point 2 missing at random for 30% studies; MAR, end point 2 missing informatively for 30% studies.

^aThe between-study variances for both end-points $τ_{j}^{2}, j = 1,2, 3$ are: $τ_{j}^{2}$ = 0.0036 for I ² = 50%, $τ_{j}^{2}$ = 0.0108 for I ² = 75%.

^bRMSE of estimates by MV method are expressed as % smaller (-) or larger (+) of corresponding estimates by UV method.

^{c ${\hat{ρ}}_{w}$} ignored.

Table 5. Relative mean bias percentage, RMSE, and coverage probability when N = 10000, m = 10, β 1 = 0.2, β 2 = 0.3, β 3 = 0.3, β b12 = 0.6, β b13 = 0.7, ρ b23 = 0.6, ρ w12 = ρ w13 = ρ w23 = 0.

Table 5. Relative mean bias percentage, RMSE, and coverage probability when N = 10000, m = 10, β ₁ = 0.2, β ₂ = 0.3, β ₃ = 0.3, β _b12 = 0.6, β _b13 = 0.7, ρ _b23 = 0.6, ρ _w12 = ρ _w13 = ρ _w23 = 0.