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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","13 %","12.8 %","5.8 %","14.5 %","4.2 %","-0.007 [0.841]","-0.014 [0.842]","0.039 [0.765]","0.043 [0.719]","-0.024 [2.784]"]
["5","50","No heterogeneity","Favouring treatment ecological bias","11.5 %","10.8 %","5.2 %","14.4 %","5.3 %","-0.017 [0.83]","0.006 [0.812]","0.044 [0.744]","0.078 [0.698]","0.417 [2.673]"]
["5","50","No heterogeneity","Favouring placebo ecological bias","11.4 %","9.8 %","5.3 %","10.2 %","7.9 %","-0.024 [0.784]","0.052 [0.773]","0.064 [0.691]","0.16 [0.665]","1.306 [2.403]"]
["5","50","Medium heterogeneity","No ecological bias","9.8 %","10.2 %","5 %","13.3 %","4.7 %","-0.003 [0.843]","-0.009 [0.812]","0.029 [0.726]","0.035 [0.71]","-0.002 [2.821]"]
["5","50","Medium heterogeneity","Favouring treatment ecological bias","11.6 %","11 %","6.7 %","12.9 %","4.3 %","-0.002 [0.803]","0.017 [0.801]","0.051 [0.707]","0.087 [0.701]","0.486 [2.668]"]
["5","50","Medium heterogeneity","Favouring placebo ecological bias","11.1 %","8.9 %","5 %","10.4 %","5 %","-0.007 [0.8]","0.059 [0.799]","0.076 [0.731]","0.163 [0.695]","1.338 [2.62]"]
["5","50","Large heterogeneity","No ecological bias","11 %","11.9 %","5.6 %","12 %","5.1 %","-0.003 [0.871]","-0.003 [0.852]","0.039 [0.767]","0.033 [0.736]","-0.014 [3.213]"]
["5","50","Large heterogeneity","Favouring treatment ecological bias","11.1 %","11.1 %","4.7 %","10.7 %","3.7 %","-0.03 [0.8]","-0.014 [0.789]","0.034 [0.72]","0.059 [0.67]","0.502 [3.204]"]
["5","50","Large heterogeneity","Favouring placebo ecological bias","12 %","11.2 %","5.5 %","7.5 %","5.5 %","0.01 [0.791]","0.055 [0.788]","0.095 [0.735]","0.162 [0.699]","1.317 [3.376]"]
["5","100","No heterogeneity","No ecological bias","19.4 %","19.7 %","14.6 %","22 %","5.2 %","-0.004 [0.626]","-0.001 [0.596]","0.015 [0.578]","0.02 [0.542]","0.029 [1.973]"]
["5","100","No heterogeneity","Favouring treatment ecological bias","18.6 %","17.8 %","13.9 %","20.5 %","4.7 %","-0.001 [0.596]","0.027 [0.57]","0.03 [0.563]","0.063 [0.522]","0.5 [1.835]"]
["5","100","No heterogeneity","Favouring placebo ecological bias","19.4 %","15.4 %","13.1 %","13.7 %","7.9 %","0.002 [0.567]","0.073 [0.566]","0.056 [0.541]","0.132 [0.516]","1.276 [1.73]"]
["5","100","Medium heterogeneity","No ecological bias","14.8 %","15.2 %","12.3 %","16.3 %","4.8 %","0.024 [0.533]","0.023 [0.523]","0.039 [0.514]","0.038 [0.486]","0.051 [2.067]"]
["5","100","Medium heterogeneity","Favouring treatment ecological bias","19.3 %","19 %","14.3 %","20.4 %","3.6 %","-0.013 [0.574]","0.009 [0.565]","0.015 [0.538]","0.043 [0.523]","0.468 [2.037]"]
["5","100","Medium heterogeneity","Favouring placebo ecological bias","20.4 %","18.4 %","15.8 %","14.6 %","5.9 %","-0.038 [0.525]","0.013 [0.516]","0.006 [0.497]","0.078 [0.482]","1.296 [2.093]"]
["5","100","Large heterogeneity","No ecological bias","17.4 %","18.2 %","12.8 %","13.6 %","5.2 %","-0.025 [0.545]","-0.027 [0.551]","-0.004 [0.519]","-0.019 [0.515]","0.024 [2.92]"]
["5","100","Large heterogeneity","Favouring treatment ecological bias","17.8 %","18.2 %","14 %","12.3 %","5 %","-0.008 [0.568]","0.003 [0.557]","0.016 [0.525]","0.028 [0.515]","0.516 [2.764]"]
["5","100","Large heterogeneity","Favouring placebo ecological bias","19.9 %","18.2 %","14.5 %","9.5 %","5.4 %","-0.02 [0.553]","0.015 [0.56]","0.023 [0.508]","0.076 [0.53]","1.34 [2.723]"]
["5","200","No heterogeneity","No ecological bias","32.1 %","33.1 %","29.7 %","36 %","5.6 %","-0.01 [0.416]","-0.01 [0.408]","-0.004 [0.393]","0.001 [0.395]","0.053 [1.451]"]
["5","200","No heterogeneity","Favouring treatment ecological bias","30.8 %","28.9 %","26.8 %","31.4 %","5.5 %","-0.005 [0.375]","0.022 [0.377]","0.007 [0.359]","0.035 [0.354]","0.441 [1.328]"]
["5","200","No heterogeneity","Favouring placebo ecological bias","32.9 %","26.7 %","27.2 %","19.9 %","11.3 %","0.002 [0.38]","0.065 [0.377]","0.021 [0.36]","0.096 [0.354]","1.357 [1.326]"]
["5","200","Medium heterogeneity","No ecological bias","31.2 %","31.7 %","28 %","26.6 %","5.3 %","0.001 [0.428]","-0.001 [0.414]","0.006 [0.414]","0.006 [0.384]","-0.012 [1.736]"]
["5","200","Medium heterogeneity","Favouring treatment ecological bias","30.7 %","29 %","25.7 %","26.3 %","5.5 %","0.012 [0.389]","0.03 [0.398]","0.03 [0.382]","0.048 [0.381]","0.419 [1.648]"]
["5","200","Medium heterogeneity","Favouring placebo ecological bias","34.3 %","29.1 %","28.9 %","18.7 %","7.9 %","0.001 [0.372]","0.038 [0.376]","0.021 [0.377]","0.078 [0.367]","1.297 [1.791]"]
["5","200","Large heterogeneity","No ecological bias","33.2 %","32.5 %","28.6 %","18 %","4.9 %","-0.018 [0.401]","-0.018 [0.396]","-0.01 [0.399]","-0.024 [0.391]","0.022 [2.582]"]
["5","200","Large heterogeneity","Favouring treatment ecological bias","35.5 %","34.3 %","29.4 %","16.5 %","4.9 %","-0.023 [0.377]","-0.015 [0.38]","-0.007 [0.377]","-0.002 [0.371]","0.469 [2.39]"]
["5","200","Large heterogeneity","Favouring placebo ecological bias","35.8 %","33.1 %","30.6 %","12.5 %","6.8 %","-0.012 [0.38]","0.008 [0.377]","0.01 [0.371]","0.042 [0.362]","1.364 [2.448]"]
["10","50","No heterogeneity","No ecological bias","20.8 %","21.1 %","11.1 %","21.7 %","5.1 %","-0.024 [0.618]","-0.027 [0.614]","0.008 [0.549]","0.027 [0.512]","0.059 [1.706]"]
["10","50","No heterogeneity","Favouring treatment ecological bias","20.2 %","18.3 %","10.8 %","17.7 %","4.3 %","-0.02 [0.575]","0.006 [0.549]","0.036 [0.503]","0.08 [0.467]","0.45 [1.74]"]
["10","50","No heterogeneity","Favouring placebo ecological bias","19.5 %","14.1 %","8.7 %","10.7 %","9.1 %","0.003 [0.53]","0.08 [0.54]","0.081 [0.503]","0.188 [0.451]","1.312 [1.8]"]
["10","50","Medium heterogeneity","No ecological bias","16.9 %","17.5 %","9.9 %","18.9 %","5.4 %","-0.006 [0.56]","-0.004 [0.563]","0.033 [0.527]","0.044 [0.495]","0.048 [1.981]"]
["10","50","Medium heterogeneity","Favouring treatment ecological bias","19.1 %","16.6 %","9.4 %","15 %","4.4 %","-0.006 [0.577]","0.018 [0.55]","0.053 [0.524]","0.09 [0.472]","0.43 [1.868]"]
["10","50","Medium heterogeneity","Favouring placebo ecological bias","19.8 %","15.3 %","8.3 %","10.5 %","8.2 %","-0.017 [0.547]","0.055 [0.523]","0.071 [0.493]","0.172 [0.452]","1.343 [1.836]"]
["10","50","Large heterogeneity","No ecological bias","17.8 %","18.7 %","8.9 %","14.9 %","3.7 %","-0.014 [0.604]","-0.014 [0.604]","0.027 [0.534]","0.022 [0.518]","0.011 [2.087]"]
["10","50","Large heterogeneity","Favouring treatment ecological bias","20.9 %","19.1 %","10.9 %","13.7 %","3.2 %","-0.021 [0.586]","-0.004 [0.585]","0.031 [0.518]","0.053 [0.498]","0.422 [2.142]"]
["10","50","Large heterogeneity","Favouring placebo ecological bias","20.6 %","18 %","9.4 %","8.3 %","7.7 %","-0.016 [0.549]","0.028 [0.561]","0.068 [0.507]","0.143 [0.476]","1.296 [2.23]"]
["10","100","No heterogeneity","No ecological bias","30.1 %","31.4 %","24.7 %","32.8 %","6.6 %","0.005 [0.412]","0.006 [0.403]","0.025 [0.395]","0.031 [0.369]","0.028 [1.422]"]
["10","100","No heterogeneity","Favouring treatment ecological bias","34.4 %","33 %","26.2 %","31.5 %","4.1 %","-0.013 [0.392]","0.014 [0.393]","0.013 [0.381]","0.052 [0.37]","0.442 [1.281]"]
["10","100","No heterogeneity","Favouring placebo ecological bias","33.4 %","24.3 %","23 %","17.6 %","12.9 %","0.007 [0.36]","0.08 [0.358]","0.05 [0.356]","0.145 [0.322]","1.348 [1.21]"]
["10","100","Medium heterogeneity","No ecological bias","30.9 %","31.5 %","25.1 %","29.2 %","6 %","0.004 [0.415]","0.004 [0.414]","0.021 [0.388]","0.023 [0.374]","0.028 [1.502]"]
["10","100","Medium heterogeneity","Favouring treatment ecological bias","30 %","28.7 %","23.1 %","22.2 %","4.1 %","0.02 [0.385]","0.039 [0.39]","0.049 [0.386]","0.075 [0.352]","0.443 [1.499]"]
["10","100","Medium heterogeneity","Favouring placebo ecological bias","34.1 %","28.6 %","23.8 %","17.6 %","11.2 %","-0.01 [0.36]","0.04 [0.374]","0.037 [0.356]","0.115 [0.348]","1.273 [1.448]"]
["10","100","Large heterogeneity","No ecological bias","30.2 %","29.9 %","25 %","21.6 %","5.6 %","-0.007 [0.412]","-0.009 [0.404]","0.008 [0.379]","-0.009 [0.384]","-0.057 [2.07]"]
["10","100","Large heterogeneity","Favouring treatment ecological bias","34.4 %","34 %","25.2 %","20 %","5.5 %","-0.006 [0.397]","0.006 [0.398]","0.023 [0.389]","0.032 [0.367]","0.426 [1.942]"]
["10","100","Large heterogeneity","Favouring placebo ecological bias","34.4 %","31.8 %","25.4 %","11.8 %","6.4 %","-0.009 [0.387]","0.02 [0.384]","0.033 [0.383]","0.083 [0.357]","1.253 [1.843]"]
["10","200","No heterogeneity","No ecological bias","56.1 %","57 %","52.9 %","58.6 %","7.7 %","-0.004 [0.271]","-0.002 [0.27]","0.002 [0.273]","0.009 [0.261]","0.051 [0.952]"]
["10","200","No heterogeneity","Favouring treatment ecological bias","58.4 %","53.2 %","53.5 %","50.8 %","4 %","-0.003 [0.272]","0.026 [0.268]","0.01 [0.271]","0.044 [0.272]","0.465 [0.957]"]
["10","200","No heterogeneity","Favouring placebo ecological bias","61.9 %","49.8 %","54.3 %","34.4 %","21.5 %","-0.005 [0.252]","0.055 [0.262]","0.015 [0.258]","0.098 [0.246]","1.333 [0.935]"]
["10","200","Medium heterogeneity","No ecological bias","55.2 %","55.1 %","48.9 %","45.4 %","6.1 %","-0.001 [0.274]","0 [0.27]","0.008 [0.27]","0.006 [0.253]","0.019 [1.087]"]
["10","200","Medium heterogeneity","Favouring treatment ecological bias","59 %","56 %","52.7 %","44.4 %","4.5 %","-0.011 [0.277]","0.008 [0.277]","0.003 [0.282]","0.03 [0.269]","0.469 [1.1]"]
["10","200","Medium heterogeneity","Favouring placebo ecological bias","58.6 %","52.4 %","51 %","30.2 %","15.4 %","0.002 [0.283]","0.039 [0.282]","0.025 [0.283]","0.09 [0.27]","1.337 [1.22]"]
["10","200","Large heterogeneity","No ecological bias","52.6 %","53.6 %","48.3 %","30.1 %","6.1 %","0.005 [0.285]","0.004 [0.293]","0.01 [0.294]","-0.007 [0.292]","-0.02 [1.69]"]
["10","200","Large heterogeneity","Favouring treatment ecological bias","56.8 %","56.9 %","52 %","28.1 %","4.2 %","-0.01 [0.279]","-0.004 [0.29]","0.002 [0.29]","0.004 [0.29]","0.42 [1.787]"]
["10","200","Large heterogeneity","Favouring placebo ecological bias","58.3 %","55.4 %","52 %","17.4 %","8.4 %","-0.001 [0.277]","0.016 [0.274]","0.019 [0.281]","0.05 [0.263]","1.282 [1.78]"]