Appendix Table 1Estimates with univariate and multivariate meta-analysis using normal approximation models in topics 1 through 43 (random effects)

TopicUnivariate exp (θ̂1)Univariate exp (θ̂2)Univariate exp (θ̂1θ̂2)Multivariate exp (θ̂1)Multivariate exp (θ̂2)Multivariate exp (θ̂1θ̂2)
10.591 (0.484, 0.723)0.651 (0.472, 0.899)0.908 (0.620, 1.331)0.590 (0.496, 0.702)0.666 (0.517, 0.859)0.885 (0.730, 1.074)
20.294 (0.229, 0.377)0.339 (0.264, 0.435)0.868 (0.610, 1.235)0.324 (0.249, 0.421)0.303 (0.235, 0.389)1.071 (0.954, 1.201)
31.833 (1.354, 2.481)1.618 (1.099, 2.383)1.133 (0.692, 1.855)1.831 (1.208, 2.774)1.460 (1.007, 2.116)1.254 (0.985, 1.596)
41.132 (0.692, 1.852)0.938 (0.664, 1.326)1.206 (0.661, 2.202)1.162 (0.690, 1.957)0.942 (0.650, 1.365)1.233 (0.757, 2.010)
50.788 (0.483, 1.285)0.789 (0.531, 1.174)0.998 (0.532, 1.873)0.851 (0.545, 1.330)0.761 (0.495, 1.171)1.118 (0.618, 2.020)
60.931 (0.569, 1.522)0.885 (0.612, 1.281)1.051 (0.568, 1.947)0.966 (0.606, 1.542)0.876 (0.601, 1.277)1.103 (0.802, 1.517)
70.486 (0.299, 0.791)0.354 (0.215, 0.583)1.373 (0.684, 2.755)0.510 (0.313, 0.832)0.373 (0.230, 0.606)1.368 (0.880, 2.127)
80.666 (0.298, 1.492)0.845 (0.655, 1.091)0.788 (0.338, 1.840)0.699 (0.303, 1.613)0.855 (0.651, 1.123)0.818 (0.373, 1.795)
91.922 (1.402, 2.634)1.021 (0.848, 1.231)1.881 (1.303, 2.716)1.794 (1.301, 2.475)1.055 (0.867, 1.283)1.701 (1.252, 2.312)
100.871 (0.762, 0.995)0.836 (0.745, 0.937)1.042 (0.873, 1.243)0.822 (0.732, 0.923)0.839 (0.751, 0.937)0.980 (0.925, 1.038)
111.003 (0.762, 1.320)1.137 (0.665, 1.945)0.882 (0.482, 1.612)0.990 (0.733, 1.337)1.092 (0.667, 1.785)0.907 (0.692, 1.190)
120.585 (0.430, 0.796)0.629 (0.451, 0.878)0.930 (0.589, 1.469)0.622 (0.463, 0.834)0.627 (0.468, 0.842)0.991 (0.883, 1.111)
130.790 (0.640, 0.974)0.801 (0.693, 0.926)0.985 (0.763, 1.273)0.795 (0.657, 0.961)0.830 (0.708, 0.973)0.958 (0.837, 1.095)
140.809 (0.607, 1.077)0.852 (0.657, 1.106)0.949 (0.644, 1.397)0.853 (0.639, 1.138)0.912 (0.711, 1.169)0.935 (0.769, 1.138)
150.377 (0.162, 0.880)0.706 (0.461, 1.079)0.535 (0.206, 1.386)0.389 (0.163, 0.927)0.673 (0.456, 0.994)0.577 (0.311, 1.072)
160.386 (0.262, 0.568)0.530 (0.443, 0.633)0.728 (0.474, 1.117)0.421 (0.317, 0.560)0.529 (0.444, 0.631)0.796 (0.677, 0.936)
170.342 (0.198, 0.589)0.517 (0.367, 0.728)0.661 (0.346, 1.263)0.326 (0.185, 0.576)0.519 (0.374, 0.720)0.629 (0.392, 1.011)
180.358 (0.240, 0.534)0.281 (0.216, 0.366)1.273 (0.785, 2.062)0.436 (0.311, 0.610)0.281 (0.216, 0.366)1.552 (1.238, 1.946)
1911.163 (5.810, 21.447)1.943 (0.683, 5.534)5.744 (1.651, 19.989)10.932 (5.797, 20.615)1.848 (0.666, 5.123)5.917 (2.034, 17.212)
205.529 (2.099, 14.569)3.296 (1.738, 6.254)1.677 (0.522, 5.394)5.668 (2.515, 12.774)3.670 (1.782, 7.561)1.544 (0.761, 3.132)
210.722 (0.572, 0.912)0.568 (0.486, 0.663)1.273 (0.961, 1.685)0.780 (0.613, 0.992)0.551 (0.464, 0.654)1.415 (1.079, 1.856)
220.985 (0.608, 1.594)1.096 (0.721, 1.667)0.899 (0.474, 1.702)0.964 (0.575, 1.615)1.161 (0.701, 1.924)0.830 (0.636, 1.083)
231.065 (0.632, 1.794)0.875 (0.643, 1.190)1.218 (0.665, 2.231)1.032 (0.573, 1.860)0.868 (0.629, 1.198)1.190 (0.672, 2.107)
240.753 (0.366, 1.552)0.815 (0.428, 1.551)0.925 (0.351, 2.434)0.786 (0.340, 1.818)0.740 (0.343, 1.598)1.062 (0.729, 1.546)
251.269 (0.576, 2.799)1.848 (1.060, 3.222)0.687 (0.261, 1.811)1.201 (0.601, 2.402)1.979 (1.061, 3.693)0.607 (0.358, 1.030)
260.467 (0.404, 0.540)0.315 (0.266, 0.374)1.481 (1.183, 1.854)0.502 (0.443, 0.570)0.347 (0.299, 0.401)1.450 (1.231, 1.707)
270.452 (0.398, 0.513)0.397 (0.344, 0.459)1.137 (0.938, 1.378)0.427 (0.367, 0.497)0.379 (0.317, 0.454)1.126 (0.918, 1.380)
280.342 (0.290, 0.403)0.278 (0.229, 0.338)1.228 (0.952, 1.585)0.352 (0.299, 0.414)0.272 (0.228, 0.325)1.292 (1.113, 1.500)
290.617 (0.519, 0.734)0.544 (0.461, 0.641)1.136 (0.895, 1.442)0.638 (0.542, 0.751)0.560 (0.478, 0.656)1.140 (1.024, 1.268)
300.237 (0.194, 0.289)0.244 (0.200, 0.298)0.971 (0.732, 1.288)0.248 (0.204, 0.302)0.176 (0.138, 0.224)1.412 (1.190, 1.676)
310.443 (0.333, 0.589)0.442 (0.320, 0.610)1.002 (0.651, 1.544)0.473 (0.364, 0.615)0.461 (0.344, 0.618)1.026 (0.781, 1.348)
320.637 (0.517, 0.784)0.410 (0.289, 0.580)1.554 (1.035, 2.334)0.653 (0.520, 0.821)0.423 (0.271, 0.661)1.544 (0.951, 2.507)
330.418 (0.241, 0.723)0.458 (0.264, 0.794)0.913 (0.416, 2.003)0.410 (0.241, 0.698)0.314 (0.186, 0.532)1.305 (0.788, 2.160)
342.921 (2.102, 4.060)3.060 (1.991, 4.702)0.955 (0.554, 1.644)2.953 (2.081, 4.192)3.544 (2.307, 5.443)0.833 (0.574, 1.210)
350.810 (0.574, 1.143)0.589 (0.428, 0.811)1.374 (0.858, 2.201)0.813 (0.571, 1.157)0.568 (0.413, 0.782)1.431 (1.003, 2.041)
360.289 (0.161, 0.516)0.208 (0.118, 0.367)1.387 (0.613, 3.137)0.298 (0.170, 0.522)0.192 (0.114, 0.325)1.550 (1.012, 2.375)
371.233 (0.605, 2.513)1.414 (0.780, 2.565)0.872 (0.345, 2.206)1.079 (0.568, 2.050)1.433 (0.817, 2.512)0.753 (0.468, 1.212)
380.676 (0.431, 1.060)0.661 (0.493, 0.886)1.023 (0.596, 1.755)0.583 (0.399, 0.852)0.624 (0.446, 0.872)0.934 (0.771, 1.132)
39*1.923 (0.986, 3.751)0.542 (0.351, 0.838)3.546 (1.594, 7.888)1.726 (0.995, 2.994)0.531 (0.337, 0.836)3.250 (1.258, 8.401)
40*0.792 (0.453, 1.385)0.709 (0.417, 1.205)1.117 (0.517, 2.414)0.830 (0.477, 1.442)0.671 (0.389, 1.157)1.236 (0.626, 2.441)
41*1.223 (1.069, 1.398)0.891 (0.764, 1.039)1.373 (1.118, 1.685)1.261 (1.071, 1.485)0.843 (0.711, 0.998)1.497 (1.099, 2.038)
42*0.908 (0.706, 1.167)0.972 (0.759, 1.244)0.934 (0.655, 1.332)0.869 (0.631, 1.197)0.950 (0.720, 1.252)0.915 (0.619, 1.352)
43*1.211 (1.077, 1.362)0.921 (0.780, 1.087)1.315 (1.069, 1.618)1.217 (1.086, 1.365)0.929 (0.798, 1.082)1.310 (1.033, 1.661)

Shown are means and 95% confidence intervals.

*

These topics refer to mutually exclusive outcomes.

From: Appendix A, Formulas, Figures, and Tables

Cover of Empirical and Simulation-Based Comparison of Univariate and Multivariate Meta-Analysis for Binary Outcomes
Empirical and Simulation-Based Comparison of Univariate and Multivariate Meta-Analysis for Binary Outcomes [Internet].
Trikalinos TA, Hoaglin DC, Schmid CH.

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