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["Number of trials","Number of patients","Heterogeneity magnitude","Ecological Bias","Centered one-stage IPD-MA power","Naive one-stage IPD-MA power","MA of interaction terms power","Per-Subgroup MA power","Meta Regression power","Centered one-stage IPD-MA BIAS [IQR]","Naive one-stage IPD-MA BIAS [IQR]","MA of interaction terms BIAS [IQR]","Per-Subgroup MA BIAS [IQR]","Meta Regression BIAS [IQR]"]
["5","50","No Heterogeneity","No ecological bias","17.8 %","18.9 %","18.8 %","22.5 %","6.8 %","-0.014 [0.362]","-0.015 [0.35]","-0.014 [0.375]","-0.016 [0.386]","-0.078 [1.311]"]
["5","50","No Heterogeneity","Favouring treatment ecological bias","16.1 %","15.3 %","16.8 %","19.2 %","4.6 %","0.009 [0.35]","0.024 [0.343]","0.007 [0.365]","0.026 [0.354]","0.282 [1.265]"]
["5","50","No Heterogeneity","Favouring placebo ecological bias","17.1 %","14 %","17.1 %","16.2 %","7 %","0.004 [0.36]","0.039 [0.366]","0.006 [0.395]","0.045 [0.366]","0.712 [1.308]"]
["5","50","Medium Heterogeneity","No ecological bias","18.2 %","18.3 %","19.2 %","15.6 %","5.6 %","-0.002 [0.36]","-0.002 [0.357]","-0.002 [0.381]","-0.006 [0.387]","-0.083 [1.74]"]
["5","50","Medium Heterogeneity","Favouring treatment ecological bias","17.1 %","16.8 %","17.8 %","15.3 %","6.1 %","-0.005 [0.365]","0.004 [0.361]","-0.007 [0.391]","0.006 [0.376]","0.285 [1.838]"]
["5","50","Medium Heterogeneity","Favouring placebo ecological bias","17.1 %","15.8 %","17.7 %","11.6 %","6.1 %","0.007 [0.365]","0.027 [0.357]","0.007 [0.382]","0.039 [0.365]","0.719 [1.728]"]
["5","50","Large Heterogeneity","No ecological bias","13.6 %","15.2 %","16.2 %","5.6 %","5.6 %","0.001 [0.32]","0 [0.317]","-0.002 [0.34]","-0.001 [0.341]","0.039 [2.49]"]
["5","50","Large Heterogeneity","Favouring treatment ecological bias","17.1 %","17.5 %","17.9 %","6.5 %","4.9 %","-0.003 [0.356]","-0.001 [0.353]","-0.004 [0.369]","0.002 [0.353]","0.219 [2.613]"]
["5","50","Large Heterogeneity","Favouring placebo ecological bias","16.1 %","15.5 %","17.4 %","5.4 %","5.5 %","0 [0.344]","0.009 [0.347]","-0.002 [0.346]","0.018 [0.359]","0.709 [2.435]"]
["5","100","No Heterogeneity","No ecological bias","31.9 %","33 %","30.3 %","34.1 %","6.3 %","-0.012 [0.254]","-0.014 [0.25]","-0.011 [0.252]","-0.014 [0.255]","-0.052 [0.935]"]
["5","100","No Heterogeneity","Favouring treatment ecological bias","27.2 %","24.8 %","25.8 %","29.2 %","4.6 %","0.006 [0.253]","0.019 [0.24]","0.007 [0.253]","0.02 [0.238]","0.236 [0.892]"]
["5","100","No Heterogeneity","Favouring placebo ecological bias","26.6 %","21.6 %","25.3 %","21 %","8.9 %","0.005 [0.238]","0.041 [0.232]","0.007 [0.244]","0.048 [0.25]","0.742 [0.94]"]
["5","100","Medium Heterogeneity","No ecological bias","29.3 %","29.9 %","28.5 %","20.1 %","6 %","-0.009 [0.237]","-0.01 [0.239]","-0.008 [0.249]","-0.009 [0.24]","-0.008 [1.483]"]
["5","100","Medium Heterogeneity","Favouring treatment ecological bias","28 %","27 %","26.7 %","14.7 %","5 %","0.006 [0.258]","0.011 [0.257]","0.005 [0.259]","0.016 [0.253]","0.235 [1.467]"]
["5","100","Medium Heterogeneity","Favouring placebo ecological bias","28.4 %","25.2 %","28.2 %","13.4 %","6.3 %","0 [0.246]","0.015 [0.245]","0.003 [0.26]","0.031 [0.26]","0.724 [1.43]"]
["5","100","Large Heterogeneity","No ecological bias","28 %","28.2 %","28.5 %","6.2 %","5.4 %","0.003 [0.263]","0.002 [0.268]","0.002 [0.281]","0.002 [0.276]","-0.046 [2.295]"]
["5","100","Large Heterogeneity","Favouring treatment ecological bias","30.4 %","30.3 %","30.8 %","7.1 %","6.2 %","-0.008 [0.251]","-0.006 [0.255]","-0.008 [0.271]","-0.003 [0.266]","0.195 [2.22]"]
["5","100","Large Heterogeneity","Favouring placebo ecological bias","28 %","27.8 %","28 %","4.7 %","5.5 %","-0.002 [0.249]","0.001 [0.247]","-0.003 [0.257]","0.009 [0.264]","0.656 [2.562]"]
["5","200","No Heterogeneity","No ecological bias","49.8 %","51.3 %","48.3 %","51.6 %","7.1 %","0.002 [0.174]","0.001 [0.171]","0.002 [0.18]","0.001 [0.175]","-0.02 [0.62]"]
["5","200","No Heterogeneity","Favouring treatment ecological bias","49.2 %","46.6 %","47.9 %","48.2 %","5.5 %","0.003 [0.172]","0.016 [0.166]","0.005 [0.176]","0.018 [0.17]","0.239 [0.651]"]
["5","200","No Heterogeneity","Favouring placebo ecological bias","48.2 %","41.5 %","47.8 %","30.9 %","11.6 %","0.002 [0.193]","0.03 [0.19]","0.001 [0.191]","0.04 [0.183]","0.756 [0.654]"]
["5","200","Medium Heterogeneity","No ecological bias","47.4 %","47.6 %","45.1 %","20.3 %","5.7 %","0.001 [0.174]","0.001 [0.176]","0.001 [0.173]","0.001 [0.168]","0.002 [1.249]"]
["5","200","Medium Heterogeneity","Favouring treatment ecological bias","46.1 %","47.1 %","44.5 %","20.3 %","5.8 %","0.008 [0.175]","0.011 [0.177]","0.009 [0.184]","0.015 [0.182]","0.199 [1.312]"]
["5","200","Medium Heterogeneity","Favouring placebo ecological bias","52.2 %","50.2 %","50.7 %","16.5 %","7.3 %","-0.002 [0.188]","0.007 [0.186]","-0.001 [0.192]","0.021 [0.188]","0.746 [1.246]"]
["5","200","Large Heterogeneity","No ecological bias","47.4 %","47.8 %","47.4 %","6.1 %","6.4 %","-0.002 [0.176]","-0.002 [0.176]","-0.003 [0.177]","-0.003 [0.179]","-0.011 [2.194]"]
["5","200","Large Heterogeneity","Favouring treatment ecological bias","51 %","51.3 %","48.3 %","4.8 %","5 %","-0.004 [0.175]","-0.003 [0.176]","-0.005 [0.183]","-0.001 [0.187]","0.184 [2.302]"]
["5","200","Large Heterogeneity","Favouring placebo ecological bias","46.5 %","46.6 %","46.3 %","3.9 %","5.7 %","0.004 [0.177]","0.006 [0.179]","0.003 [0.183]","0.012 [0.184]","0.715 [2.223]"]
["10","50","No Heterogeneity","No ecological bias","28.3 %","28.4 %","28 %","31.4 %","8.3 %","0 [0.253]","0 [0.24]","-0.001 [0.262]","0.001 [0.257]","0.012 [0.96]"]
["10","50","No Heterogeneity","Favouring treatment ecological bias","28.1 %","26.3 %","28.1 %","27.3 %","4.6 %","0 [0.247]","0.014 [0.239]","0.001 [0.266]","0.015 [0.256]","0.237 [0.867]"]
["10","50","No Heterogeneity","Favouring placebo ecological bias","27.2 %","22.8 %","27.9 %","21.3 %","10.2 %","0.001 [0.259]","0.042 [0.249]","0.004 [0.271]","0.046 [0.26]","0.729 [0.937]"]
["10","50","Medium Heterogeneity","No ecological bias","25.5 %","26 %","25.1 %","19.2 %","6 %","0.009 [0.245]","0.007 [0.246]","0.01 [0.253]","0.008 [0.257]","-0.03 [1.204]"]
["10","50","Medium Heterogeneity","Favouring treatment ecological bias","27.3 %","25.7 %","28.2 %","17.6 %","5.2 %","-0.002 [0.241]","0.008 [0.239]","-0.003 [0.266]","0.011 [0.254]","0.268 [1.163]"]
["10","50","Medium Heterogeneity","Favouring placebo ecological bias","26.9 %","23.5 %","26.5 %","14.2 %","7 %","0.013 [0.256]","0.036 [0.249]","0.015 [0.264]","0.052 [0.253]","0.762 [1.136]"]
["10","50","Large Heterogeneity","No ecological bias","27.3 %","28.5 %","27.7 %","7.6 %","4.7 %","-0.001 [0.247]","0 [0.254]","0.001 [0.258]","0.002 [0.263]","-0.001 [1.842]"]
["10","50","Large Heterogeneity","Favouring treatment ecological bias","26.6 %","26.1 %","26.7 %","6.6 %","5.1 %","0.004 [0.256]","0.007 [0.247]","0.004 [0.268]","0.014 [0.271]","0.313 [1.865]"]
["10","50","Large Heterogeneity","Favouring placebo ecological bias","27.2 %","25.6 %","28.2 %","5.7 %","6.1 %","0 [0.242]","0.009 [0.239]","-0.001 [0.265]","0.023 [0.248]","0.739 [1.685]"]
["10","100","No Heterogeneity","No ecological bias","51 %","52.4 %","49.1 %","52.4 %","8.1 %","-0.005 [0.184]","-0.005 [0.175]","-0.006 [0.182]","-0.006 [0.183]","-0.009 [0.668]"]
["10","100","No Heterogeneity","Favouring treatment ecological bias","50.9 %","47.4 %","49.1 %","46.3 %","5.8 %","-0.001 [0.175]","0.015 [0.173]","0 [0.182]","0.015 [0.177]","0.253 [0.66]"]
["10","100","No Heterogeneity","Favouring placebo ecological bias","46.7 %","36.9 %","45.6 %","30 %","15.4 %","0.005 [0.175]","0.043 [0.174]","0.005 [0.188]","0.051 [0.187]","0.751 [0.647]"]
["10","100","Medium Heterogeneity","No ecological bias","49.4 %","50.2 %","47.4 %","29.2 %","6.9 %","-0.001 [0.177]","0 [0.177]","0.001 [0.182]","0 [0.179]","-0.007 [0.982]"]
["10","100","Medium Heterogeneity","Favouring treatment ecological bias","49.3 %","48.2 %","47.1 %","27.2 %","3.8 %","0.003 [0.166]","0.008 [0.166]","0.003 [0.177]","0.015 [0.178]","0.266 [0.912]"]
["10","100","Medium Heterogeneity","Favouring placebo ecological bias","52.2 %","47.5 %","50.9 %","21.5 %","7.4 %","-0.006 [0.178]","0.008 [0.176]","-0.006 [0.179]","0.025 [0.177]","0.726 [0.896]"]
["10","100","Large Heterogeneity","No ecological bias","48.5 %","49 %","47.1 %","7.8 %","5 %","0.001 [0.177]","0.001 [0.179]","0 [0.183]","-0.001 [0.189]","-0.005 [1.692]"]
["10","100","Large Heterogeneity","Favouring treatment ecological bias","46.2 %","45.8 %","44.5 %","6.9 %","4.7 %","0.006 [0.189]","0.007 [0.191]","0.007 [0.184]","0.011 [0.191]","0.238 [1.629]"]
["10","100","Large Heterogeneity","Favouring placebo ecological bias","49.2 %","48.4 %","47.6 %","5.1 %","5.9 %","0.004 [0.174]","0.009 [0.172]","0.003 [0.176]","0.018 [0.178]","0.723 [1.692]"]
["10","200","No Heterogeneity","No ecological bias","79.2 %","80.1 %","76.8 %","80.4 %","10.9 %","-0.001 [0.123]","-0.002 [0.119]","-0.002 [0.125]","-0.003 [0.121]","-0.018 [0.454]"]
["10","200","No Heterogeneity","Favouring treatment ecological bias","79.4 %","76 %","79 %","73.1 %","3.9 %","-0.003 [0.118]","0.012 [0.12]","-0.002 [0.124]","0.013 [0.124]","0.253 [0.475]"]
["10","200","No Heterogeneity","Favouring placebo ecological bias","76.9 %","67.5 %","76.4 %","53.7 %","24.9 %","0 [0.129]","0.029 [0.126]","0 [0.127]","0.043 [0.126]","0.745 [0.457]"]
["10","200","Medium Heterogeneity","No ecological bias","80.6 %","81.1 %","78.1 %","36.1 %","7 %","0 [0.109]","0 [0.111]","0 [0.117]","0 [0.116]","-0.016 [0.86]"]
["10","200","Medium Heterogeneity","Favouring treatment ecological bias","77.7 %","76.5 %","76.4 %","37.2 %","5.2 %","-0.002 [0.129]","0.002 [0.129]","-0.001 [0.128]","0.007 [0.127]","0.255 [0.897]"]
["10","200","Medium Heterogeneity","Favouring placebo ecological bias","79.4 %","76.1 %","77.1 %","28.1 %","10.7 %","-0.003 [0.129]","0.005 [0.129]","-0.005 [0.13]","0.017 [0.129]","0.732 [0.893]"]
["10","200","Large Heterogeneity","No ecological bias","78.4 %","78.9 %","76.6 %","6.7 %","5.1 %","-0.002 [0.124]","-0.001 [0.123]","-0.001 [0.127]","0 [0.126]","0.022 [1.475]"]
["10","200","Large Heterogeneity","Favouring treatment ecological bias","77.4 %","76.9 %","75.6 %","6 %","5 %","-0.002 [0.126]","-0.001 [0.127]","-0.001 [0.13]","0.003 [0.132]","0.296 [1.488]"]
["10","200","Large Heterogeneity","Favouring placebo ecological bias","76.9 %","76.4 %","75.2 %","3.4 %","7.5 %","0.001 [0.124]","0.003 [0.125]","0.001 [0.129]","0.011 [0.131]","0.758 [1.561]"]