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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","47.8 %","47.9 %","47 %","50.8 %","8.5 %","0.003 [0.328]","0.005 [0.32]","0.001 [0.351]","0.002 [0.346]","0.038 [1.339]"]
["5","50","No Heterogeneity","Favouring treatment ecological bias","47 %","44.3 %","45.4 %","46 %","4.5 %","0.017 [0.342]","0.041 [0.339]","0.016 [0.369]","0.04 [0.359]","0.49 [1.341]"]
["5","50","No Heterogeneity","Favouring placebo ecological bias","48.4 %","41.9 %","47.9 %","31.3 %","12.5 %","0.001 [0.367]","0.057 [0.368]","-0.002 [0.376]","0.078 [0.372]","1.528 [1.317]"]
["5","50","Medium Heterogeneity","No ecological bias","50.1 %","49.5 %","48.7 %","40.8 %","6.4 %","-0.003 [0.352]","-0.002 [0.342]","-0.003 [0.383]","-0.003 [0.37]","0.033 [1.701]"]
["5","50","Medium Heterogeneity","Favouring treatment ecological bias","46.3 %","46.1 %","45.2 %","34.7 %","5.7 %","0.014 [0.345]","0.028 [0.344]","0.014 [0.363]","0.038 [0.373]","0.512 [1.565]"]
["5","50","Medium Heterogeneity","Favouring placebo ecological bias","47.1 %","42.4 %","44.6 %","26.6 %","8.6 %","0.012 [0.366]","0.047 [0.36]","0.014 [0.387]","0.077 [0.367]","1.487 [1.672]"]
["5","50","Large Heterogeneity","No ecological bias","48.7 %","49.4 %","47.7 %","23.4 %","5.2 %","-0.003 [0.369]","-0.001 [0.37]","-0.004 [0.378]","-0.002 [0.383]","0.03 [2.43]"]
["5","50","Large Heterogeneity","Favouring treatment ecological bias","47.2 %","47 %","45.7 %","19.5 %","6.3 %","0.003 [0.358]","0.009 [0.356]","0.007 [0.372]","0.017 [0.369]","0.497 [2.53]"]
["5","50","Large Heterogeneity","Favouring placebo ecological bias","47.4 %","45.8 %","46.3 %","14.4 %","6.1 %","0.013 [0.356]","0.03 [0.358]","0.014 [0.382]","0.061 [0.389]","1.517 [2.577]"]
["5","100","No Heterogeneity","No ecological bias","78.5 %","80.3 %","75.1 %","78.3 %","8.9 %","-0.006 [0.257]","-0.005 [0.258]","-0.006 [0.277]","-0.005 [0.263]","-0.009 [0.958]"]
["5","100","No Heterogeneity","Favouring treatment ecological bias","76.2 %","72.9 %","74.5 %","68.8 %","4.3 %","0.005 [0.259]","0.031 [0.255]","0.005 [0.273]","0.034 [0.264]","0.516 [0.912]"]
["5","100","No Heterogeneity","Favouring placebo ecological bias","77.8 %","71.9 %","77.5 %","46 %","18.8 %","0.001 [0.245]","0.042 [0.241]","0 [0.25]","0.071 [0.24]","1.515 [0.921]"]
["5","100","Medium Heterogeneity","No ecological bias","77.3 %","78.2 %","76.8 %","60.5 %","6.7 %","-0.001 [0.251]","-0.001 [0.247]","-0.003 [0.26]","-0.003 [0.247]","0 [1.411]"]
["5","100","Medium Heterogeneity","Favouring treatment ecological bias","79.7 %","79.4 %","78.1 %","53.8 %","4.8 %","-0.01 [0.242]","0 [0.249]","-0.01 [0.259]","0.007 [0.247]","0.449 [1.339]"]
["5","100","Medium Heterogeneity","Favouring placebo ecological bias","76.8 %","74 %","75.2 %","34.2 %","11.1 %","0.003 [0.246]","0.024 [0.255]","0.002 [0.25]","0.055 [0.247]","1.525 [1.373]"]
["5","100","Large Heterogeneity","No ecological bias","79.3 %","78.9 %","76.3 %","29 %","6.9 %","-0.002 [0.251]","-0.003 [0.255]","-0.001 [0.258]","-0.003 [0.268]","-0.063 [2.44]"]
["5","100","Large Heterogeneity","Favouring treatment ecological bias","77.4 %","76.9 %","76.4 %","23.5 %","4.2 %","0.001 [0.241]","0.005 [0.241]","-0.001 [0.255]","0.011 [0.261]","0.536 [2.179]"]
["5","100","Large Heterogeneity","Favouring placebo ecological bias","77.1 %","77 %","76.2 %","19.8 %","8.4 %","0.004 [0.248]","0.012 [0.242]","0.004 [0.25]","0.029 [0.265]","1.426 [2.454]"]
["5","200","No Heterogeneity","No ecological bias","96.7 %","97.2 %","95.9 %","94.5 %","11.4 %","0.005 [0.178]","0.005 [0.178]","0.004 [0.182]","0.006 [0.181]","0.016 [0.629]"]
["5","200","No Heterogeneity","Favouring treatment ecological bias","97.4 %","96.1 %","96.4 %","93.8 %","6.1 %","-0.002 [0.174]","0.022 [0.173]","-0.002 [0.181]","0.026 [0.181]","0.505 [0.633]"]
["5","200","No Heterogeneity","Favouring placebo ecological bias","97.4 %","95.7 %","96.9 %","72.5 %","30.3 %","-0.003 [0.167]","0.023 [0.173]","-0.002 [0.172]","0.055 [0.169]","1.468 [0.612]"]
["5","200","Medium Heterogeneity","No ecological bias","97.2 %","97.7 %","96.2 %","71 %","7.9 %","0.008 [0.171]","0.008 [0.176]","0.009 [0.174]","0.008 [0.176]","-0.001 [1.383]"]
["5","200","Medium Heterogeneity","Favouring treatment ecological bias","97.2 %","96.6 %","96.3 %","70.2 %","5.1 %","-0.002 [0.182]","0.003 [0.176]","-0.002 [0.186]","0.013 [0.182]","0.485 [1.271]"]
["5","200","Medium Heterogeneity","Favouring placebo ecological bias","98.5 %","97.6 %","97.9 %","48.2 %","14 %","-0.002 [0.165]","0.009 [0.171]","-0.003 [0.172]","0.032 [0.178]","1.492 [1.27]"]
["5","200","Large Heterogeneity","No ecological bias","96.7 %","97.1 %","96.5 %","30.8 %","5.9 %","-0.001 [0.165]","-0.001 [0.17]","-0.001 [0.171]","0 [0.178]","0.019 [2.236]"]
["5","200","Large Heterogeneity","Favouring treatment ecological bias","97.1 %","97.2 %","96.6 %","29.1 %","4.6 %","0.001 [0.171]","0.003 [0.174]","0.001 [0.175]","0.008 [0.18]","0.558 [2.157]"]
["5","200","Large Heterogeneity","Favouring placebo ecological bias","97.7 %","97.3 %","96.3 %","24 %","7.4 %","0.001 [0.191]","0.004 [0.191]","0.001 [0.19]","0.017 [0.191]","1.486 [2.24]"]
["10","50","No Heterogeneity","No ecological bias","75.5 %","77.9 %","72.9 %","75.2 %","11.6 %","0.014 [0.244]","0.011 [0.239]","0.015 [0.261]","0.012 [0.253]","-0.039 [0.94]"]
["10","50","No Heterogeneity","Favouring treatment ecological bias","77.3 %","73.7 %","74.9 %","71 %","4.4 %","0.008 [0.247]","0.037 [0.237]","0.008 [0.267]","0.036 [0.258]","0.489 [0.942]"]
["10","50","No Heterogeneity","Favouring placebo ecological bias","78.9 %","68.8 %","76.5 %","53.5 %","28.4 %","0.001 [0.249]","0.06 [0.259]","-0.004 [0.272]","0.081 [0.258]","1.517 [0.922]"]
["10","50","Medium Heterogeneity","No ecological bias","78.8 %","78.8 %","76.7 %","66.4 %","8.7 %","-0.006 [0.247]","-0.005 [0.255]","-0.007 [0.255]","-0.005 [0.262]","-0.011 [1.224]"]
["10","50","Medium Heterogeneity","Favouring treatment ecological bias","77.2 %","75.2 %","75.9 %","58.8 %","5 %","-0.007 [0.265]","0.01 [0.264]","-0.009 [0.273]","0.02 [0.274]","0.523 [1.151]"]
["10","50","Medium Heterogeneity","Favouring placebo ecological bias","77.9 %","72.2 %","75.7 %","45.2 %","18.4 %","-0.002 [0.246]","0.034 [0.249]","-0.003 [0.263]","0.066 [0.261]","1.488 [1.246]"]
["10","50","Large Heterogeneity","No ecological bias","75.8 %","76.5 %","74.9 %","39 %","6 %","-0.002 [0.262]","-0.001 [0.264]","0 [0.271]","0 [0.265]","0.014 [1.809]"]
["10","50","Large Heterogeneity","Favouring treatment ecological bias","77.6 %","77.3 %","76.9 %","35.7 %","5.7 %","0.004 [0.237]","0.01 [0.238]","0.002 [0.246]","0.019 [0.247]","0.519 [1.761]"]
["10","50","Large Heterogeneity","Favouring placebo ecological bias","77.8 %","74.9 %","78.4 %","26.3 %","10.1 %","-0.003 [0.236]","0.014 [0.24]","-0.003 [0.249]","0.04 [0.25]","1.444 [1.829]"]
["10","100","No Heterogeneity","No ecological bias","97.1 %","97.6 %","96 %","96.6 %","16 %","-0.004 [0.171]","-0.003 [0.165]","-0.004 [0.173]","-0.003 [0.169]","0.002 [0.644]"]
["10","100","No Heterogeneity","Favouring treatment ecological bias","97.2 %","95.3 %","96.5 %","92.6 %","5.5 %","-0.001 [0.183]","0.028 [0.179]","-0.001 [0.187]","0.029 [0.181]","0.49 [0.633]"]
["10","100","No Heterogeneity","Favouring placebo ecological bias","97.6 %","94.5 %","96.8 %","81.1 %","45.4 %","-0.005 [0.178]","0.038 [0.184]","-0.006 [0.182]","0.068 [0.179]","1.495 [0.725]"]
["10","100","Medium Heterogeneity","No ecological bias","96.8 %","96.5 %","96 %","86.5 %","8.3 %","0.006 [0.187]","0.006 [0.184]","0.006 [0.187]","0.005 [0.191]","-0.006 [1.004]"]
["10","100","Medium Heterogeneity","Favouring treatment ecological bias","97.7 %","97.4 %","97.2 %","82 %","5.3 %","0.007 [0.179]","0.017 [0.178]","0.005 [0.186]","0.027 [0.178]","0.544 [0.945]"]
["10","100","Medium Heterogeneity","Favouring placebo ecological bias","96.7 %","95.2 %","96.4 %","65.2 %","23.3 %","-0.001 [0.175]","0.02 [0.174]","-0.001 [0.179]","0.053 [0.174]","1.537 [0.983]"]
["10","100","Large Heterogeneity","No ecological bias","96.6 %","96.5 %","95.5 %","51 %","5.8 %","0.004 [0.177]","0.005 [0.177]","0.004 [0.184]","0.005 [0.186]","0.035 [1.651]"]
["10","100","Large Heterogeneity","Favouring treatment ecological bias","96.6 %","96.1 %","96.4 %","46.7 %","5.3 %","0.004 [0.174]","0.008 [0.174]","0.006 [0.178]","0.015 [0.175]","0.483 [1.617]"]
["10","100","Large Heterogeneity","Favouring placebo ecological bias","97.3 %","96.8 %","96.3 %","38.8 %","11.1 %","-0.005 [0.189]","0.005 [0.191]","-0.004 [0.196]","0.026 [0.198]","1.505 [1.546]"]
["10","200","No Heterogeneity","No ecological bias","100 %","99.9 %","100 %","99.9 %","26 %","-0.001 [0.125]","-0.002 [0.123]","-0.001 [0.13]","-0.002 [0.124]","0 [0.424]"]
["10","200","No Heterogeneity","Favouring treatment ecological bias","99.9 %","99.8 %","99.8 %","99.8 %","5 %","0.002 [0.121]","0.027 [0.123]","0.002 [0.124]","0.033 [0.119]","0.5 [0.424]"]
["10","200","No Heterogeneity","Favouring placebo ecological bias","100 %","99.9 %","100 %","97.6 %","74.6 %","-0.002 [0.117]","0.025 [0.119]","-0.002 [0.123]","0.057 [0.126]","1.506 [0.471]"]
["10","200","Medium Heterogeneity","No ecological bias","100 %","99.9 %","100 %","98.3 %","11.2 %","-0.005 [0.124]","-0.004 [0.125]","-0.004 [0.12]","-0.005 [0.121]","-0.016 [0.861]"]
["10","200","Medium Heterogeneity","Favouring treatment ecological bias","99.9 %","99.9 %","99.9 %","97.3 %","6.8 %","0.001 [0.127]","0.007 [0.128]","0.001 [0.127]","0.016 [0.127]","0.474 [0.897]"]
["10","200","Medium Heterogeneity","Favouring placebo ecological bias","99.9 %","99.9 %","99.9 %","88.4 %","25.8 %","-0.005 [0.13]","0.007 [0.13]","-0.005 [0.134]","0.031 [0.136]","1.495 [0.82]"]
["10","200","Large Heterogeneity","No ecological bias","100 %","100 %","100 %","61.1 %","6.9 %","0.006 [0.119]","0.006 [0.119]","0.007 [0.124]","0.007 [0.122]","0.033 [1.64]"]
["10","200","Large Heterogeneity","Favouring treatment ecological bias","99.9 %","99.9 %","99.9 %","60.4 %","5.5 %","0.001 [0.126]","0.003 [0.128]","0.001 [0.13]","0.006 [0.127]","0.415 [1.611]"]
["10","200","Large Heterogeneity","Favouring placebo ecological bias","100 %","100 %","100 %","43.1 %","13 %","0.001 [0.122]","0.005 [0.121]","0.002 [0.128]","0.018 [0.128]","1.544 [1.641]"]