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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","4.9 %","5.3 %","2.8 %","8.6 %","4.6 %","0.013 [0.581]","0.012 [0.577]","0.013 [0.595]","0.015 [0.539]","-0.017 [1.889]"]
["5","50","No Heterogeneity","Favouring treatment ecological bias","5.7 %","6.4 %","3.4 %","8 %","5.2 %","0.014 [0.591]","-0.011 [0.582]","-0.007 [0.599]","-0.029 [0.551]","-0.352 [1.926]"]
["5","50","No Heterogeneity","Favouring placebo ecological bias","5.1 %","6.1 %","3.7 %","9.1 %","5.2 %","0.013 [0.535]","0.056 [0.526]","0.038 [0.55]","0.096 [0.528]","0.674 [1.811]"]
["5","50","Medium heterogeneity","No ecological bias","4.9 %","4.5 %","3.3 %","6.8 %","6.2 %","0.007 [0.586]","0.005 [0.573]","0.01 [0.576]","-0.007 [0.552]","-0.049 [2.131]"]
["5","50","Medium heterogeneity","Favouring treatment ecological bias","4.9 %","5.3 %","3.2 %","6.4 %","5.5 %","0.007 [0.614]","-0.014 [0.596]","-0.008 [0.578]","-0.049 [0.542]","-0.394 [2.157]"]
["5","50","Medium heterogeneity","Favouring placebo ecological bias","5.6 %","6.1 %","3.9 %","8 %","6.7 %","0.006 [0.552]","0.035 [0.551]","0.032 [0.536]","0.068 [0.519]","0.613 [2.071]"]
["5","50","Large heterogeneity","No ecological bias","5.7 %","5.9 %","3 %","4.6 %","5.3 %","0.004 [0.603]","0.004 [0.598]","0.01 [0.598]","-0.019 [0.529]","-0.068 [2.844]"]
["5","50","Large heterogeneity","Favouring treatment ecological bias","5.1 %","5.6 %","3.4 %","4.1 %","5.5 %","0.004 [0.636]","-0.005 [0.633]","-0.004 [0.608]","-0.058 [0.551]","-0.404 [2.795]"]
["5","50","Large heterogeneity","Favouring placebo ecological bias","6.1 %","6.7 %","3.1 %","5 %","5.4 %","0.006 [0.561]","0.022 [0.558]","0.034 [0.556]","0.053 [0.536]","0.598 [2.829]"]
["5","100","No Heterogeneity","No ecological bias","5.3 %","5.6 %","4.5 %","9.2 %","4.8 %","-0.012 [0.393]","-0.013 [0.377]","-0.014 [0.408]","-0.011 [0.404]","0.027 [1.366]"]
["5","100","No Heterogeneity","Favouring treatment ecological bias","5.8 %","5.6 %","5.2 %","9.2 %","5.6 %","-0.008 [0.423]","-0.03 [0.409]","-0.018 [0.424]","-0.04 [0.417]","-0.312 [1.356]"]
["5","100","No Heterogeneity","Favouring placebo ecological bias","5.6 %","5.5 %","5.3 %","7.7 %","8 %","-0.013 [0.371]","0.027 [0.367]","-0.005 [0.374]","0.045 [0.364]","0.701 [1.333]"]
["5","100","Medium heterogeneity","No ecological bias","4.9 %","4.9 %","3.6 %","5.6 %","5.5 %","-0.012 [0.368]","-0.014 [0.365]","-0.016 [0.386]","-0.021 [0.38]","-0.03 [1.749]"]
["5","100","Medium heterogeneity","Favouring treatment ecological bias","5.5 %","6.1 %","4.2 %","6.7 %","5.5 %","-0.013 [0.4]","-0.029 [0.398]","-0.025 [0.402]","-0.048 [0.401]","-0.363 [1.738]"]
["5","100","Medium heterogeneity","Favouring placebo ecological bias","5.3 %","4.9 %","4.5 %","4.8 %","6.7 %","-0.011 [0.382]","0.009 [0.383]","-0.005 [0.37]","0.03 [0.364]","0.633 [1.72]"]
["5","100","Large heterogeneity","No ecological bias","4.6 %","4.5 %","3.9 %","3 %","4.7 %","-0.011 [0.388]","-0.012 [0.389]","-0.016 [0.38]","-0.032 [0.395]","-0.056 [2.577]"]
["5","100","Large heterogeneity","Favouring treatment ecological bias","5 %","4.8 %","4 %","3 %","5.1 %","-0.011 [0.394]","-0.018 [0.392]","-0.024 [0.403]","-0.056 [0.408]","-0.39 [2.521]"]
["5","100","Large heterogeneity","Favouring placebo ecological bias","5.1 %","5 %","4 %","2.9 %","5 %","-0.012 [0.366]","-0.004 [0.365]","-0.006 [0.376]","0.005 [0.371]","0.617 [2.491]"]
["5","200","No Heterogeneity","No ecological bias","4.6 %","4.6 %","4.1 %","6.9 %","4.3 %","0.004 [0.281]","0.003 [0.272]","0 [0.282]","-0.002 [0.269]","-0.009 [0.97]"]
["5","200","No Heterogeneity","Favouring treatment ecological bias","5 %","5 %","4.1 %","6.6 %","5.9 %","0.002 [0.288]","-0.02 [0.283]","-0.005 [0.278]","-0.028 [0.281]","-0.347 [1.002]"]
["5","200","No Heterogeneity","Favouring placebo ecological bias","4.5 %","5.4 %","3.6 %","7.6 %","10.1 %","0.001 [0.259]","0.036 [0.254]","0.004 [0.259]","0.043 [0.248]","0.663 [0.918]"]
["5","200","Medium heterogeneity","No ecological bias","6.4 %","6 %","4 %","3.9 %","4.9 %","0.006 [0.28]","0.005 [0.277]","0.003 [0.284]","-0.003 [0.283]","-0.003 [1.371]"]
["5","200","Medium heterogeneity","Favouring treatment ecological bias","6.3 %","6.5 %","4.9 %","3.8 %","5.7 %","0.01 [0.285]","0 [0.279]","0.004 [0.289]","-0.019 [0.279]","-0.346 [1.431]"]
["5","200","Medium heterogeneity","Favouring placebo ecological bias","5.3 %","5.4 %","5.2 %","3.1 %","8.4 %","0.003 [0.279]","0.018 [0.271]","0.007 [0.267]","0.032 [0.278]","0.661 [1.299]"]
["5","200","Large heterogeneity","No ecological bias","5.4 %","5.6 %","4.3 %","0.9 %","4.9 %","0.006 [0.277]","0.006 [0.275]","0.004 [0.288]","-0.009 [0.287]","-0.024 [2.339]"]
["5","200","Large heterogeneity","Favouring treatment ecological bias","5.4 %","5.6 %","4.5 %","1.2 %","5.5 %","0.007 [0.289]","0.003 [0.285]","0 [0.287]","-0.023 [0.299]","-0.348 [2.321]"]
["5","200","Large heterogeneity","Favouring placebo ecological bias","5.8 %","5.4 %","5.1 %","1.3 %","6.2 %","0.003 [0.273]","0.008 [0.276]","0.006 [0.272]","0.011 [0.277]","0.64 [2.19]"]
["10","50","No Heterogeneity","No ecological bias","5.8 %","6 %","2.8 %","6 %","4.5 %","0.002 [0.411]","0.001 [0.413]","-0.001 [0.424]","0.005 [0.382]","0.042 [1.297]"]
["10","50","No Heterogeneity","Favouring treatment ecological bias","6.1 %","6.3 %","3.3 %","6 %","5.4 %","0.001 [0.434]","-0.025 [0.425]","-0.02 [0.415]","-0.042 [0.374]","-0.284 [1.327]"]
["10","50","No Heterogeneity","Favouring placebo ecological bias","5.8 %","6.2 %","3.3 %","6.6 %","9.9 %","0.003 [0.392]","0.048 [0.387]","0.026 [0.398]","0.092 [0.361]","0.726 [1.233]"]
["10","50","Medium heterogeneity","No ecological bias","6.4 %","6.5 %","4.2 %","5.9 %","5.1 %","-0.016 [0.392]","-0.018 [0.39]","-0.014 [0.41]","-0.022 [0.345]","-0.023 [1.542]"]
["10","50","Medium heterogeneity","Favouring treatment ecological bias","5.2 %","6.3 %","4.1 %","6.4 %","6.1 %","-0.014 [0.392]","-0.036 [0.384]","-0.026 [0.423]","-0.06 [0.356]","-0.36 [1.553]"]
["10","50","Medium heterogeneity","Favouring placebo ecological bias","6.4 %","6.8 %","4.7 %","5.6 %","8.4 %","-0.015 [0.383]","0.016 [0.379]","0.009 [0.407]","0.058 [0.364]","0.647 [1.477]"]
["10","50","Large heterogeneity","No ecological bias","6 %","5.8 %","4.2 %","3.9 %","5.2 %","-0.018 [0.407]","-0.019 [0.396]","-0.015 [0.424]","-0.038 [0.361]","-0.047 [2.005]"]
["10","50","Large heterogeneity","Favouring treatment ecological bias","6.2 %","5.8 %","3.4 %","4.2 %","6.1 %","-0.015 [0.405]","-0.027 [0.402]","-0.028 [0.426]","-0.075 [0.382]","-0.382 [1.994]"]
["10","50","Large heterogeneity","Favouring placebo ecological bias","6 %","6.5 %","4.7 %","3.5 %","6.7 %","-0.018 [0.389]","-0.002 [0.392]","0.009 [0.418]","0.034 [0.377]","0.61 [1.927]"]
["10","100","No Heterogeneity","No ecological bias","5.2 %","6.1 %","4 %","6.1 %","4.6 %","-0.004 [0.277]","-0.004 [0.265]","-0.005 [0.293]","-0.002 [0.276]","0.028 [0.944]"]
["10","100","No Heterogeneity","Favouring treatment ecological bias","5.7 %","6.4 %","4.1 %","7.1 %","6.2 %","-0.001 [0.29]","-0.025 [0.281]","-0.011 [0.303]","-0.036 [0.271]","-0.311 [0.921]"]
["10","100","No Heterogeneity","Favouring placebo ecological bias","4.7 %","5.6 %","4.1 %","6.5 %","15.3 %","-0.004 [0.26]","0.039 [0.26]","0.006 [0.284]","0.06 [0.255]","0.698 [0.903]"]
["10","100","Medium heterogeneity","No ecological bias","5.8 %","6.5 %","5.3 %","4.9 %","5 %","0.014 [0.294]","0.013 [0.292]","0.013 [0.295]","0.009 [0.287]","0.008 [1.241]"]
["10","100","Medium heterogeneity","Favouring treatment ecological bias","6.6 %","7 %","6.6 %","5.1 %","5.7 %","0.013 [0.295]","-0.003 [0.295]","0.006 [0.304]","-0.023 [0.289]","-0.331 [1.218]"]
["10","100","Medium heterogeneity","Favouring placebo ecological bias","5.7 %","6.6 %","5.1 %","5.6 %","10.7 %","0.013 [0.288]","0.036 [0.278]","0.025 [0.293]","0.067 [0.28]","0.673 [1.156]"]
["10","100","Large heterogeneity","No ecological bias","6.5 %","6.7 %","5.5 %","1.9 %","4.9 %","0.014 [0.3]","0.013 [0.293]","0.013 [0.3]","-0.006 [0.286]","-0.02 [1.753]"]
["10","100","Large heterogeneity","Favouring treatment ecological bias","6.3 %","6.9 %","5.5 %","2.1 %","5.4 %","0.014 [0.308]","0.007 [0.296]","0.006 [0.303]","-0.033 [0.293]","-0.341 [1.769]"]
["10","100","Large heterogeneity","Favouring placebo ecological bias","5.6 %","6.4 %","5.5 %","1.9 %","7.1 %","0.012 [0.285]","0.021 [0.283]","0.024 [0.292]","0.039 [0.289]","0.642 [1.71]"]
["10","200","No Heterogeneity","No ecological bias","4.3 %","4.5 %","3.4 %","4.5 %","5.3 %","0.001 [0.201]","-0.001 [0.195]","-0.001 [0.198]","-0.003 [0.189]","-0.015 [0.653]"]
["10","200","No Heterogeneity","Favouring treatment ecological bias","4 %","5.1 %","4 %","5.8 %","9.4 %","0 [0.206]","-0.024 [0.205]","-0.006 [0.207]","-0.032 [0.198]","-0.35 [0.683]"]
["10","200","No Heterogeneity","Favouring placebo ecological bias","4.3 %","5.6 %","3.5 %","5.8 %","20 %","-0.002 [0.184]","0.036 [0.179]","0.003 [0.185]","0.047 [0.178]","0.651 [0.614]"]
["10","200","Medium heterogeneity","No ecological bias","4.9 %","4.8 %","4.9 %","2.8 %","5.3 %","0.004 [0.196]","0.003 [0.196]","0.005 [0.203]","-0.001 [0.192]","-0.019 [0.929]"]
["10","200","Medium heterogeneity","Favouring treatment ecological bias","5.5 %","5.3 %","4 %","3.4 %","7.2 %","0.006 [0.205]","-0.005 [0.2]","0.002 [0.202]","-0.023 [0.202]","-0.35 [0.928]"]
["10","200","Medium heterogeneity","Favouring placebo ecological bias","4.8 %","5.3 %","4.4 %","2.7 %","13.8 %","0.001 [0.182]","0.015 [0.178]","0.008 [0.192]","0.038 [0.184]","0.656 [0.909]"]
["10","200","Large heterogeneity","No ecological bias","5.6 %","5.6 %","4.2 %","0.4 %","5.3 %","0.005 [0.191]","0.004 [0.188]","0.005 [0.198]","-0.009 [0.197]","-0.031 [1.496]"]
["10","200","Large heterogeneity","Favouring treatment ecological bias","5.3 %","5.2 %","4.7 %","0.5 %","5.7 %","0.006 [0.194]","0.002 [0.195]","0.002 [0.197]","-0.025 [0.204]","-0.363 [1.489]"]
["10","200","Large heterogeneity","Favouring placebo ecological bias","4.2 %","4.6 %","4 %","0.3 %","9.1 %","0.002 [0.185]","0.006 [0.182]","0.008 [0.197]","0.014 [0.185]","0.637 [1.462]"]