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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","30.5 %","30.8 %","16.2 %","26.1 %","4.7 %","0.018 [0.667]","0.017 [0.654]","-0.086 [0.635]","-0.133 [0.579]","-0.116 [2.181]"]
["5","50","No Heterogeneity","Favouring treatment ecological bias","26.5 %","24.9 %","12.7 %","22.2 %","5.3 %","0.014 [0.696]","-0.032 [0.677]","-0.094 [0.657]","-0.195 [0.6]","-0.782 [2.402]"]
["5","50","No Heterogeneity","Favouring placebo ecological bias","21 %","16.4 %","7.1 %","17.9 %","6.5 %","-0.002 [0.879]","-0.127 [0.855]","-0.101 [0.751]","-0.272 [0.689]","-1.915 [2.458]"]
["5","50","Medium Heterogeneity","No ecological bias","30.6 %","31.4 %","16.9 %","25.4 %","6 %","0.01 [0.699]","0.011 [0.666]","-0.083 [0.664]","-0.133 [0.615]","-0.018 [2.358]"]
["5","50","Medium Heterogeneity","Favouring treatment ecological bias","26.6 %","25.5 %","13.8 %","21.6 %","4.6 %","0.003 [0.744]","-0.032 [0.726]","-0.096 [0.686]","-0.191 [0.612]","-0.654 [2.452]"]
["5","50","Medium Heterogeneity","Favouring placebo ecological bias","18.3 %","13.9 %","7.5 %","15.4 %","5.4 %","-0.025 [0.828]","-0.133 [0.815]","-0.11 [0.693]","-0.295 [0.671]","-1.808 [2.723]"]
["5","50","Large Heterogeneity","No ecological bias","30.5 %","31 %","16.3 %","19.7 %","4.8 %","0.008 [0.691]","0.007 [0.701]","-0.088 [0.658]","-0.143 [0.618]","-0.017 [3.142]"]
["5","50","Large Heterogeneity","Favouring treatment ecological bias","25.9 %","25.9 %","13.9 %","17.5 %","4.6 %","0.001 [0.727]","-0.024 [0.722]","-0.096 [0.706]","-0.195 [0.618]","-0.657 [3.018]"]
["5","50","Large Heterogeneity","Favouring placebo ecological bias","19.8 %","16.3 %","7.9 %","12.6 %","4.6 %","-0.021 [0.825]","-0.103 [0.814]","-0.111 [0.699]","-0.297 [0.651]","-1.79 [3.282]"]
["5","100","No Heterogeneity","No ecological bias","54.6 %","55.5 %","41.3 %","50.9 %","6.1 %","0.024 [0.459]","0.017 [0.459]","-0.032 [0.461]","-0.058 [0.437]","-0.085 [1.549]"]
["5","100","No Heterogeneity","Favouring treatment ecological bias","48.2 %","44.6 %","37.4 %","40.5 %","5.2 %","0.019 [0.505]","-0.03 [0.489]","-0.036 [0.471]","-0.112 [0.426]","-0.748 [1.71]"]
["5","100","No Heterogeneity","Favouring placebo ecological bias","37.9 %","29.4 %","26.2 %","23 %","9.5 %","0.023 [0.599]","-0.089 [0.572]","-0.038 [0.553]","-0.21 [0.511]","-2.045 [1.95]"]
["5","100","Medium Heterogeneity","No ecological bias","52.4 %","53 %","39.7 %","42.2 %","6.3 %","0 [0.453]","-0.002 [0.449]","-0.058 [0.461]","-0.072 [0.438]","-0.013 [1.945]"]
["5","100","Medium Heterogeneity","Favouring treatment ecological bias","46.8 %","44.2 %","34.5 %","35.6 %","3.9 %","0.002 [0.485]","-0.031 [0.491]","-0.058 [0.48]","-0.119 [0.453]","-0.689 [2.037]"]
["5","100","Medium Heterogeneity","Favouring placebo ecological bias","36.3 %","28.7 %","23.8 %","20.1 %","8.9 %","-0.012 [0.62]","-0.107 [0.589]","-0.077 [0.566]","-0.228 [0.533]","-2.011 [2.185]"]
["5","100","Large Heterogeneity","No ecological bias","52.3 %","52.7 %","39.4 %","29.9 %","5.9 %","0.006 [0.467]","0.005 [0.456]","-0.053 [0.451]","-0.064 [0.464]","0.007 [2.614]"]
["5","100","Large Heterogeneity","Favouring treatment ecological bias","46.2 %","45.3 %","34.2 %","27.1 %","5 %","0 [0.492]","-0.019 [0.489]","-0.063 [0.497]","-0.112 [0.467]","-0.669 [2.633]"]
["5","100","Large Heterogeneity","Favouring placebo ecological bias","37.1 %","32.3 %","23 %","16.7 %","7.5 %","-0.011 [0.592]","-0.071 [0.565]","-0.077 [0.541]","-0.207 [0.549]","-1.984 [2.784]"]
["5","200","No Heterogeneity","No ecological bias","84.1 %","85.1 %","78.3 %","79.4 %","7.9 %","0.015 [0.327]","0.012 [0.318]","-0.009 [0.336]","-0.024 [0.314]","-0.06 [1.119]"]
["5","200","No Heterogeneity","Favouring treatment ecological bias","79.8 %","75.1 %","73.9 %","68.8 %","4.8 %","0.014 [0.353]","-0.029 [0.341]","-0.012 [0.345]","-0.071 [0.323]","-0.753 [1.141]"]
["5","200","No Heterogeneity","Favouring placebo ecological bias","65.2 %","54.3 %","56.6 %","34.3 %","15.1 %","0.006 [0.4]","-0.08 [0.399]","-0.024 [0.394]","-0.158 [0.359]","-2.065 [1.38]"]
["5","200","Medium Heterogeneity","No ecological bias","84.6 %","84.6 %","79.1 %","69 %","7 %","0.015 [0.319]","0.015 [0.315]","-0.01 [0.316]","-0.018 [0.31]","-0.013 [1.479]"]
["5","200","Medium Heterogeneity","Favouring treatment ecological bias","80.7 %","78.6 %","73.3 %","57.4 %","3.7 %","0.018 [0.345]","-0.005 [0.346]","-0.009 [0.346]","-0.054 [0.348]","-0.692 [1.452]"]
["5","200","Medium Heterogeneity","Favouring placebo ecological bias","67.9 %","61.2 %","58.1 %","31.2 %","11 %","0.023 [0.393]","-0.041 [0.404]","-0.013 [0.389]","-0.131 [0.363]","-2.03 [1.658]"]
["5","200","Large Heterogeneity","No ecological bias","85 %","85.1 %","79.1 %","43.1 %","6.2 %","0.016 [0.324]","0.016 [0.325]","-0.009 [0.319]","-0.012 [0.326]","0.005 [2.289]"]
["5","200","Large Heterogeneity","Favouring treatment ecological bias","81 %","79.8 %","74.4 %","39.2 %","5 %","0.02 [0.348]","0.01 [0.341]","-0.009 [0.352]","-0.037 [0.349]","-0.682 [2.338]"]
["5","200","Large Heterogeneity","Favouring placebo ecological bias","69.5 %","65.7 %","58.1 %","24.2 %","6.8 %","0.022 [0.389]","-0.015 [0.381]","-0.012 [0.381]","-0.101 [0.371]","-2.016 [2.297]"]
["10","50","No Heterogeneity","No ecological bias","53.7 %","55.2 %","32.4 %","46.6 %","6.8 %","0.014 [0.45]","0.015 [0.443]","-0.087 [0.45]","-0.138 [0.408]","-0.089 [1.465]"]
["10","50","No Heterogeneity","Favouring treatment ecological bias","49.1 %","44.6 %","27.1 %","34.6 %","5.1 %","0.013 [0.471]","-0.035 [0.466]","-0.092 [0.456]","-0.199 [0.425]","-0.743 [1.614]"]
["10","50","No Heterogeneity","Favouring placebo ecological bias","38 %","28.1 %","17 %","23.1 %","11.1 %","0.025 [0.557]","-0.106 [0.537]","-0.093 [0.502]","-0.279 [0.451]","-1.826 [1.749]"]
["10","50","Medium Heterogeneity","No ecological bias","53.3 %","54.4 %","31.2 %","42.1 %","6.6 %","0.009 [0.477]","0.012 [0.476]","-0.103 [0.468]","-0.148 [0.428]","-0.022 [1.592]"]
["10","50","Medium Heterogeneity","Favouring treatment ecological bias","49 %","45.1 %","28.1 %","33 %","2.9 %","0.008 [0.511]","-0.029 [0.504]","-0.104 [0.493]","-0.196 [0.426]","-0.65 [1.603]"]
["10","50","Medium Heterogeneity","Favouring placebo ecological bias","38.3 %","30 %","15.8 %","19.2 %","9.3 %","0.009 [0.569]","-0.107 [0.581]","-0.114 [0.519]","-0.293 [0.423]","-1.808 [1.776]"]
["10","50","Large Heterogeneity","No ecological bias","53.2 %","53.3 %","30.8 %","33 %","5.9 %","0.008 [0.47]","0.01 [0.472]","-0.103 [0.474]","-0.15 [0.455]","0 [1.926]"]
["10","50","Large Heterogeneity","Favouring treatment ecological bias","48.8 %","47.6 %","26.8 %","25.3 %","4.1 %","0.01 [0.5]","-0.013 [0.511]","-0.106 [0.502]","-0.202 [0.444]","-0.636 [1.984]"]
["10","50","Large Heterogeneity","Favouring placebo ecological bias","38.5 %","32.5 %","16.6 %","19 %","8.5 %","0.009 [0.576]","-0.073 [0.587]","-0.116 [0.533]","-0.292 [0.461]","-1.753 [2.039]"]
["10","100","No Heterogeneity","No ecological bias","82.5 %","83.6 %","71.6 %","76.9 %","11.5 %","0.007 [0.352]","0.004 [0.349]","-0.045 [0.334]","-0.073 [0.323]","-0.067 [1.158]"]
["10","100","No Heterogeneity","Favouring treatment ecological bias","79.4 %","73.2 %","66 %","65.8 %","5.9 %","0.005 [0.353]","-0.043 [0.35]","-0.049 [0.338]","-0.128 [0.318]","-0.73 [1.218]"]
["10","100","No Heterogeneity","Favouring placebo ecological bias","64 %","53.4 %","49.2 %","38.4 %","20.5 %","0.013 [0.434]","-0.096 [0.427]","-0.051 [0.405]","-0.226 [0.377]","-1.984 [1.332]"]
["10","100","Medium Heterogeneity","No ecological bias","83.7 %","84.7 %","74.3 %","72.9 %","7.5 %","0.009 [0.336]","0.009 [0.326]","-0.04 [0.318]","-0.069 [0.31]","-0.026 [1.185]"]
["10","100","Medium Heterogeneity","Favouring treatment ecological bias","77.7 %","75.2 %","66.5 %","59.5 %","5.4 %","0.013 [0.368]","-0.019 [0.364]","-0.038 [0.356]","-0.118 [0.339]","-0.692 [1.274]"]
["10","100","Medium Heterogeneity","Favouring placebo ecological bias","68.1 %","57.5 %","52.9 %","34.9 %","14.5 %","0.013 [0.408]","-0.077 [0.392]","-0.043 [0.385]","-0.214 [0.348]","-1.928 [1.462]"]
["10","100","Large Heterogeneity","No ecological bias","83.4 %","84.9 %","73.2 %","55 %","6.7 %","0.009 [0.34]","0.009 [0.328]","-0.039 [0.331]","-0.064 [0.314]","-0.003 [1.7]"]
["10","100","Large Heterogeneity","Favouring treatment ecological bias","79 %","78.4 %","67.1 %","47.1 %","4.7 %","0.01 [0.356]","-0.004 [0.356]","-0.039 [0.344]","-0.105 [0.317]","-0.658 [1.736]"]
["10","100","Large Heterogeneity","Favouring placebo ecological bias","67.7 %","62.6 %","52.8 %","28.3 %","11.3 %","0.012 [0.408]","-0.041 [0.382]","-0.039 [0.38]","-0.192 [0.356]","-1.886 [1.813]"]
["10","200","No Heterogeneity","No ecological bias","99.1 %","99.4 %","98.4 %","98.1 %","16.1 %","0.007 [0.221]","0.006 [0.217]","-0.017 [0.22]","-0.031 [0.207]","-0.043 [0.749]"]
["10","200","No Heterogeneity","Favouring treatment ecological bias","98.1 %","97 %","95.5 %","93.6 %","5.1 %","0.006 [0.248]","-0.038 [0.244]","-0.019 [0.25]","-0.083 [0.234]","-0.734 [0.804]"]
["10","200","No Heterogeneity","Favouring placebo ecological bias","91.8 %","82.9 %","86.8 %","61 %","36 %","0.003 [0.292]","-0.08 [0.289]","-0.027 [0.269]","-0.174 [0.282]","-2.035 [0.941]"]
["10","200","Medium Heterogeneity","No ecological bias","98.5 %","98.8 %","97.9 %","95 %","11.7 %","0.005 [0.223]","0.005 [0.222]","-0.019 [0.226]","-0.03 [0.235]","-0.026 [1.048]"]
["10","200","Medium Heterogeneity","Favouring treatment ecological bias","97.6 %","97.4 %","95.7 %","88.3 %","5.9 %","0.005 [0.228]","-0.017 [0.229]","-0.021 [0.231]","-0.075 [0.237]","-0.706 [1.083]"]
["10","200","Medium Heterogeneity","Favouring placebo ecological bias","92.9 %","87.7 %","88.5 %","59.1 %","24 %","0.008 [0.272]","-0.052 [0.271]","-0.022 [0.264]","-0.154 [0.246]","-2.014 [1.206]"]
["10","200","Large Heterogeneity","No ecological bias","98.7 %","98.6 %","97.3 %","77.2 %","7.8 %","0.004 [0.222]","0.004 [0.221]","-0.019 [0.225]","-0.023 [0.231]","0.001 [1.627]"]
["10","200","Large Heterogeneity","Favouring treatment ecological bias","97.5 %","97.2 %","95.3 %","70.9 %","5.3 %","0.004 [0.236]","-0.004 [0.236]","-0.02 [0.232]","-0.052 [0.243]","-0.686 [1.638]"]
["10","200","Large Heterogeneity","Favouring placebo ecological bias","93.1 %","91.1 %","88.3 %","46.9 %","13.3 %","0.007 [0.263]","-0.024 [0.269]","-0.022 [0.255]","-0.118 [0.267]","-1.973 [1.697]"]