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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","34.9 %","36.5 %","21.1 %","37.5 %","6.4 %","-0.03 [0.858]","-0.029 [0.854]","0.085 [0.751]","0.116 [0.719]","0.078 [2.799]"]
["5","50","No heterogeneity","Favouring treatment ecological bias","39 %","36.2 %","24.3 %","35.3 %","5.1 %","-0.023 [0.818]","0.038 [0.794]","0.109 [0.747]","0.193 [0.69]","0.97 [2.481]"]
["5","50","No heterogeneity","Favouring placebo ecological bias","43.9 %","36.6 %","29 %","20.7 %","11.3 %","-0.062 [0.778]","0.065 [0.766]","0.09 [0.719]","0.296 [0.663]","3.037 [2.431]"]
["5","50","Medium heterogeneity","No ecological bias","37.2 %","38.8 %","24.2 %","36 %","3.7 %","-0.034 [0.911]","-0.033 [0.868]","0.075 [0.799]","0.109 [0.686]","0.155 [2.905]"]
["5","50","Medium heterogeneity","Favouring treatment ecological bias","40.8 %","39.7 %","27.6 %","37.8 %","5 %","-0.085 [0.821]","-0.036 [0.812]","0.046 [0.739]","0.128 [0.722]","0.825 [2.615]"]
["5","50","Medium heterogeneity","Favouring placebo ecological bias","44 %","37.3 %","27.5 %","20.4 %","10 %","-0.058 [0.79]","0.047 [0.789]","0.087 [0.724]","0.281 [0.702]","2.892 [3.011]"]
["5","50","Large heterogeneity","No ecological bias","36.8 %","37.7 %","22 %","31.5 %","4.2 %","-0.049 [0.867]","-0.044 [0.868]","0.076 [0.792]","0.106 [0.711]","0.125 [3.33]"]
["5","50","Large heterogeneity","Favouring treatment ecological bias","39.6 %","37.7 %","22.2 %","26.9 %","4.7 %","-0.034 [0.78]","0.005 [0.761]","0.107 [0.683]","0.173 [0.652]","1.013 [3.148]"]
["5","50","Large heterogeneity","Favouring placebo ecological bias","41.4 %","37.4 %","27.5 %","19 %","8.4 %","-0.039 [0.821]","0.049 [0.819]","0.104 [0.747]","0.277 [0.7]","2.911 [3.03]"]
["5","100","No heterogeneity","No ecological bias","59 %","61.1 %","51.6 %","60.8 %","8.3 %","-0.008 [0.592]","-0.012 [0.595]","0.044 [0.573]","0.053 [0.526]","-0.026 [2.083]"]
["5","100","No heterogeneity","Favouring treatment ecological bias","70.5 %","66.1 %","61.1 %","60.7 %","5.8 %","-0.038 [0.572]","0.021 [0.56]","0.028 [0.543]","0.102 [0.516]","1.022 [1.872]"]
["5","100","No heterogeneity","Favouring placebo ecological bias","68.8 %","61.8 %","61 %","37 %","18.8 %","-0.013 [0.566]","0.075 [0.596]","0.06 [0.54]","0.216 [0.515]","2.984 [1.873]"]
["5","100","Medium heterogeneity","No ecological bias","62.9 %","65.5 %","55 %","59.2 %","8.2 %","-0.042 [0.618]","-0.043 [0.627]","0.018 [0.577]","0.03 [0.554]","0.01 [2.234]"]
["5","100","Medium heterogeneity","Favouring treatment ecological bias","69.9 %","66.4 %","60.8 %","55.4 %","3.7 %","-0.048 [0.563]","-0.003 [0.544]","0.017 [0.532]","0.085 [0.511]","1.008 [2.157]"]
["5","100","Medium heterogeneity","Favouring placebo ecological bias","70.2 %","65 %","62.7 %","35.2 %","14 %","-0.024 [0.553]","0.052 [0.572]","0.046 [0.53]","0.188 [0.532]","2.963 [2.133]"]
["5","100","Large heterogeneity","No ecological bias","60.7 %","62.2 %","50.9 %","46.5 %","6.1 %","-0.007 [0.611]","-0.01 [0.59]","0.049 [0.556]","0.049 [0.525]","-0.067 [2.839]"]
["5","100","Large heterogeneity","Favouring treatment ecological bias","66.5 %","64.7 %","56.7 %","43.1 %","3.4 %","-0.02 [0.554]","0.009 [0.559]","0.048 [0.538]","0.099 [0.518]","1.014 [2.737]"]
["5","100","Large heterogeneity","Favouring placebo ecological bias","68.3 %","64.7 %","57 %","28.6 %","10.1 %","-0.01 [0.577]","0.044 [0.569]","0.063 [0.563]","0.176 [0.515]","2.883 [2.701]"]
["5","200","No heterogeneity","No ecological bias","88.3 %","89.4 %","86 %","87 %","10.2 %","-0.007 [0.42]","-0.003 [0.43]","0.021 [0.432]","0.029 [0.419]","0.065 [1.399]"]
["5","200","No heterogeneity","Favouring treatment ecological bias","92.3 %","90.3 %","90 %","86.6 %","5.3 %","-0.006 [0.399]","0.048 [0.401]","0.024 [0.407]","0.083 [0.379]","0.99 [1.22]"]
["5","200","No heterogeneity","Favouring placebo ecological bias","95.5 %","93.1 %","92.8 %","60.9 %","33.3 %","-0.019 [0.377]","0.038 [0.382]","0.016 [0.368]","0.135 [0.362]","2.959 [1.323]"]
["5","200","Medium heterogeneity","No ecological bias","89.1 %","88.3 %","86.3 %","80.5 %","7.3 %","-0.006 [0.421]","-0.003 [0.413]","0.017 [0.406]","0.027 [0.408]","0.101 [1.824]"]
["5","200","Medium heterogeneity","Favouring treatment ecological bias","92.8 %","90.9 %","89.8 %","79 %","4.1 %","-0.007 [0.37]","0.028 [0.371]","0.023 [0.366]","0.074 [0.365]","0.996 [1.662]"]
["5","200","Medium heterogeneity","Favouring placebo ecological bias","92.7 %","91.2 %","90.1 %","52.3 %","20.3 %","0.001 [0.391]","0.05 [0.386]","0.036 [0.372]","0.138 [0.368]","2.963 [1.61]"]
["5","200","Large heterogeneity","No ecological bias","89.2 %","89.6 %","85.6 %","64.5 %","7.3 %","0.002 [0.406]","0.002 [0.411]","0.03 [0.404]","0.033 [0.393]","0.108 [2.587]"]
["5","200","Large heterogeneity","Favouring treatment ecological bias","90.9 %","90.7 %","88.8 %","63 %","6.3 %","-0.01 [0.362]","0.006 [0.369]","0.023 [0.365]","0.057 [0.372]","0.971 [2.374]"]
["5","200","Large heterogeneity","Favouring placebo ecological bias","94.2 %","93 %","91.7 %","40.1 %","12 %","-0.012 [0.381]","0.019 [0.386]","0.021 [0.385]","0.094 [0.381]","2.97 [2.618]"]
["10","50","No heterogeneity","No ecological bias","60.2 %","61.7 %","44.7 %","60.2 %","7.1 %","-0.013 [0.595]","-0.015 [0.565]","0.09 [0.513]","0.132 [0.479]","0.059 [1.857]"]
["10","50","No heterogeneity","Favouring treatment ecological bias","67.2 %","63.7 %","49.6 %","56 %","4.7 %","-0.014 [0.572]","0.048 [0.54]","0.103 [0.514]","0.206 [0.464]","1.016 [1.895]"]
["10","50","No heterogeneity","Favouring placebo ecological bias","72 %","60.4 %","52.9 %","36.6 %","25.4 %","-0.029 [0.519]","0.099 [0.543]","0.108 [0.515]","0.334 [0.488]","2.913 [1.805]"]
["10","50","Medium heterogeneity","No ecological bias","60.2 %","62 %","44.4 %","59.1 %","9.1 %","-0.003 [0.59]","-0.008 [0.581]","0.099 [0.524]","0.131 [0.483]","0.001 [2.044]"]
["10","50","Medium heterogeneity","Favouring treatment ecological bias","67.7 %","63.7 %","49.9 %","55 %","5 %","-0.03 [0.586]","0.025 [0.581]","0.096 [0.53]","0.188 [0.489]","0.923 [1.859]"]
["10","50","Medium heterogeneity","Favouring placebo ecological bias","70.5 %","59.5 %","49.9 %","32.2 %","22 %","-0.013 [0.522]","0.094 [0.541]","0.12 [0.496]","0.337 [0.471]","2.936 [1.815]"]
["10","50","Large heterogeneity","No ecological bias","60.5 %","62.5 %","43.6 %","53 %","7.6 %","-0.018 [0.599]","-0.022 [0.592]","0.088 [0.538]","0.115 [0.473]","-0.044 [2.323]"]
["10","50","Large heterogeneity","Favouring treatment ecological bias","67.2 %","65.2 %","49.5 %","45 %","5.9 %","-0.017 [0.557]","0.016 [0.566]","0.098 [0.532]","0.188 [0.484]","1.005 [2.256]"]
["10","50","Large heterogeneity","Favouring placebo ecological bias","70.8 %","62 %","50.3 %","27.6 %","16.9 %","-0.021 [0.536]","0.06 [0.543]","0.118 [0.497]","0.309 [0.447]","2.892 [2.332]"]
["10","100","No heterogeneity","No ecological bias","87.3 %","89 %","83.6 %","88 %","11.8 %","-0.011 [0.452]","-0.016 [0.434]","0.042 [0.43]","0.059 [0.391]","0.009 [1.278]"]
["10","100","No heterogeneity","Favouring treatment ecological bias","91.8 %","89.8 %","87.7 %","86.8 %","5.2 %","-0.012 [0.406]","0.047 [0.396]","0.052 [0.401]","0.133 [0.365]","0.975 [1.308]"]
["10","100","No heterogeneity","Favouring placebo ecological bias","93.9 %","90.1 %","88.5 %","65.5 %","43.1 %","-0.007 [0.387]","0.075 [0.382]","0.067 [0.355]","0.242 [0.356]","2.91 [1.395]"]
["10","100","Medium heterogeneity","No ecological bias","85.9 %","87.3 %","82.8 %","84.3 %","9.4 %","0 [0.431]","0.003 [0.427]","0.053 [0.413]","0.075 [0.388]","0.119 [1.48]"]
["10","100","Medium heterogeneity","Favouring treatment ecological bias","90.2 %","89.2 %","86 %","81.4 %","4.6 %","0.014 [0.388]","0.054 [0.39]","0.073 [0.377]","0.149 [0.365]","0.992 [1.494]"]
["10","100","Medium heterogeneity","Favouring placebo ecological bias","94.5 %","90.8 %","89.7 %","61.8 %","34.1 %","0.001 [0.396]","0.071 [0.391]","0.07 [0.369]","0.235 [0.357]","2.931 [1.362]"]
["10","100","Large heterogeneity","No ecological bias","87.9 %","88.6 %","82.3 %","75.7 %","7.7 %","-0.004 [0.419]","-0.004 [0.433]","0.048 [0.419]","0.064 [0.385]","0.102 [1.936]"]
["10","100","Large heterogeneity","Favouring treatment ecological bias","92.6 %","91.9 %","87.4 %","72.5 %","4.2 %","-0.013 [0.388]","0.012 [0.389]","0.052 [0.382]","0.11 [0.377]","0.957 [1.875]"]
["10","100","Large heterogeneity","Favouring placebo ecological bias","93.8 %","90.9 %","88.7 %","55.8 %","20.1 %","-0.014 [0.4]","0.034 [0.401]","0.053 [0.39]","0.182 [0.373]","2.862 [2.011]"]
["10","200","No heterogeneity","No ecological bias","99.6 %","99.7 %","99.2 %","99.5 %","21.2 %","-0.016 [0.276]","-0.015 [0.272]","0.01 [0.273]","0.02 [0.264]","0.02 [0.908]"]
["10","200","No heterogeneity","Favouring treatment ecological bias","100 %","99.9 %","100 %","99.8 %","4.1 %","-0.011 [0.267]","0.045 [0.272]","0.018 [0.268]","0.092 [0.262]","1.018 [0.825]"]
["10","200","No heterogeneity","Favouring placebo ecological bias","99.8 %","99.7 %","99.7 %","93.2 %","74.2 %","-0.003 [0.266]","0.048 [0.269]","0.029 [0.269]","0.161 [0.263]","2.961 [0.891]"]
["10","200","Medium heterogeneity","No ecological bias","99.3 %","99.4 %","98.9 %","98.9 %","13.7 %","-0.009 [0.301]","-0.009 [0.294]","0.015 [0.287]","0.023 [0.281]","0.035 [1.263]"]
["10","200","Medium heterogeneity","Favouring treatment ecological bias","99.8 %","99.6 %","99.6 %","98.4 %","5.1 %","-0.008 [0.289]","0.026 [0.288]","0.021 [0.294]","0.083 [0.275]","1.045 [1.215]"]
["10","200","Medium heterogeneity","Favouring placebo ecological bias","100 %","99.8 %","99.7 %","90.9 %","50.4 %","0 [0.262]","0.043 [0.265]","0.032 [0.27]","0.146 [0.255]","2.942 [1.185]"]
["10","200","Large heterogeneity","No ecological bias","99.9 %","99.9 %","99.5 %","94.9 %","10.8 %","-0.011 [0.304]","-0.011 [0.3]","0.012 [0.307]","0.013 [0.292]","0.012 [1.718]"]
["10","200","Large heterogeneity","Favouring treatment ecological bias","99.8 %","99.8 %","99.5 %","92.1 %","4.9 %","-0.002 [0.285]","0.015 [0.284]","0.03 [0.278]","0.068 [0.279]","1.04 [1.748]"]
["10","200","Large heterogeneity","Favouring placebo ecological bias","99.7 %","99.6 %","99.3 %","79.5 %","25 %","0.002 [0.245]","0.031 [0.249]","0.035 [0.249]","0.113 [0.24]","2.902 [1.796]"]