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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","9.8 %","10.3 %","3.3 %","10.8 %","4 %","0.005 [0.686]","0.00600000000000001 [0.695]","-0.0539999999999999 [0.645]","-0.077 [0.595]","-0.109 [2.139]"]
["5","50","No Heterogeneity","Favouring treatment ecological bias","9.5 %","9.1 %","3.8 %","11.5 %","4.4 %","-0.001 [0.694]","-0.0219999999999999 [0.7]","-0.0529999999999999 [0.652]","-0.105 [0.629]","-0.425 [2.276]"]
["5","50","No Heterogeneity","Favouring placebo ecological bias","9.2 %","7.8 %","2.9 %","10.3 %","5.4 %","-0.00700000000000001 [0.783]","-0.072 [0.773]","-0.0429999999999999 [0.7]","-0.135 [0.65]","-1.011 [2.387]"]
["5","50","Medium Heterogeneity","No ecological bias","10.1 %","10.8 %","5.2 %","12.4 %","4.9 %","0.001 [0.693]","0.005 [0.681]","-0.0509999999999999 [0.677]","-0.07 [0.618]","0.035 [2.458]"]
["5","50","Medium Heterogeneity","Favouring treatment ecological bias","10.3 %","9.3 %","4.3 %","9.4 %","4.6 %","-0.00800000000000001 [0.705]","-0.0229999999999999 [0.693]","-0.0539999999999999 [0.672]","-0.105 [0.62]","-0.303 [2.517]"]
["5","50","Medium Heterogeneity","Favouring placebo ecological bias","9.1 %","8 %","3.3 %","7.9 %","5.1 %","-0.0279999999999999 [0.748]","-0.08 [0.729]","-0.0479999999999999 [0.688]","-0.146 [0.627]","-0.905 [2.572]"]
["5","50","Large Heterogeneity","No ecological bias","9.9 %","10.7 %","4.9 %","9.1 %","4.7 %","0 [0.712]","0.001 [0.695]","-0.0549999999999999 [0.694]","-0.078 [0.628]","0.027 [3.154]"]
["5","50","Large Heterogeneity","Favouring treatment ecological bias","10 %","10.5 %","4.6 %","8.8 %","4.3 %","-0.00800000000000001 [0.716]","-0.0199999999999999 [0.697]","-0.0539999999999999 [0.66]","-0.099 [0.615]","-0.295 [3.185]"]
["5","50","Large Heterogeneity","Favouring placebo ecological bias","8.3 %","7.8 %","3.6 %","7.8 %","4.8 %","-0.0259999999999999 [0.788]","-0.0659999999999999 [0.77]","-0.0509999999999999 [0.686]","-0.139 [0.665]","-0.903 [3.052]"]
["5","100","No Heterogeneity","No ecological bias","17 %","16.6 %","11.3 %","19.2 %","5 %","0.017 [0.47]","0.011 [0.456]","-0.0139999999999999 [0.46]","-0.0319999999999999 [0.42]","-0.081 [1.644]"]
["5","100","No Heterogeneity","Favouring treatment ecological bias","15.9 %","14.4 %","10.7 %","16.1 %","5.5 %","0.019 [0.486]","-0.00900000000000001 [0.474]","-0.01 [0.467]","-0.0509999999999999 [0.438]","-0.399 [1.657]"]
["5","100","No Heterogeneity","Favouring placebo ecological bias","15.2 %","11.5 %","10.1 %","12.7 %","5.9 %","0.021 [0.539]","-0.0469999999999999 [0.51]","0.003 [0.513]","-0.09 [0.46]","-1.058 [1.689]"]
["5","100","Medium Heterogeneity","No ecological bias","16.1 %","16.7 %","10.1 %","14.5 %","4.7 %","-0.002 [0.466]","-0.002 [0.464]","-0.0389999999999999 [0.467]","-0.0409999999999999 [0.462]","0.00700000000000001 [1.984]"]
["5","100","Medium Heterogeneity","Favouring treatment ecological bias","15.4 %","15 %","9.3 %","13 %","4.2 %","-0.003 [0.484]","-0.0209999999999999 [0.479]","-0.0389999999999999 [0.497]","-0.0659999999999999 [0.455]","-0.342 [2.019]"]
["5","100","Medium Heterogeneity","Favouring placebo ecological bias","14.4 %","12.4 %","8 %","11.3 %","5.1 %","-0.0169999999999999 [0.545]","-0.0679999999999999 [0.523]","-0.0379999999999999 [0.511]","-0.105 [0.481]","-1.002 [2.099]"]
["5","100","Large Heterogeneity","No ecological bias","15.7 %","17 %","9.8 %","10.3 %","4.2 %","-0.001 [0.474]","-0.002 [0.463]","-0.0399999999999999 [0.472]","-0.0309999999999999 [0.473]","0.023 [2.682]"]
["5","100","Large Heterogeneity","Favouring treatment ecological bias","14.1 %","15.2 %","9.1 %","8.7 %","4.6 %","-0.00700000000000001 [0.48]","-0.0159999999999999 [0.483]","-0.0429999999999999 [0.492]","-0.0509999999999999 [0.465]","-0.298 [2.678]"]
["5","100","Large Heterogeneity","Favouring placebo ecological bias","13.6 %","12.7 %","7.7 %","7.9 %","5.8 %","-0.01 [0.557]","-0.0399999999999999 [0.542]","-0.0349999999999999 [0.532]","-0.082 [0.493]","-0.984 [2.719]"]
["5","200","No Heterogeneity","No ecological bias","28.7 %","29.5 %","24.6 %","31.3 %","5.3 %","0.012 [0.334]","0.00900000000000001 [0.324]","-0.001 [0.34]","-0.011 [0.318]","-0.0599999999999999 [1.15]"]
["5","200","No Heterogeneity","Favouring treatment ecological bias","28.3 %","26.2 %","23.7 %","26.6 %","4.7 %","0.011 [0.329]","-0.0129999999999999 [0.336]","0 [0.342]","-0.0329999999999999 [0.329]","-0.4 [1.175]"]
["5","200","No Heterogeneity","Favouring placebo ecological bias","25 %","19.6 %","21.7 %","18.3 %","8.1 %","0.004 [0.385]","-0.0549999999999999 [0.377]","-0.005 [0.372]","-0.076 [0.359]","-1.061 [1.24]"]
["5","200","Medium Heterogeneity","No ecological bias","31.4 %","32.7 %","25.2 %","23.1 %","5.2 %","0.014 [0.342]","0.014 [0.338]","-0.002 [0.336]","-0.003 [0.328]","-0.00600000000000001 [1.439]"]
["5","200","Medium Heterogeneity","Favouring treatment ecological bias","29 %","28.4 %","23.2 %","22.2 %","3.7 %","0.015 [0.353]","0.002 [0.352]","0 [0.344]","-0.0209999999999999 [0.354]","-0.342 [1.497]"]
["5","200","Medium Heterogeneity","Favouring placebo ecological bias","24.9 %","22.4 %","20.3 %","15.7 %","6.7 %","0.015 [0.366]","-0.0219999999999999 [0.368]","0.003 [0.361]","-0.0549999999999999 [0.359]","-1.025 [1.509]"]
["5","200","Large Heterogeneity","No ecological bias","31.6 %","31.3 %","24.2 %","11.7 %","5.5 %","0.015 [0.342]","0.015 [0.337]","-0.002 [0.33]","0.00600000000000001 [0.343]","0.019 [2.245]"]
["5","200","Large Heterogeneity","Favouring treatment ecological bias","29.9 %","29.4 %","24.3 %","11.7 %","4.3 %","0.017 [0.349]","0.012 [0.347]","0.002 [0.348]","-0.002 [0.358]","-0.324 [2.259]"]
["5","200","Large Heterogeneity","Favouring placebo ecological bias","26 %","25.1 %","20.9 %","9.1 %","5.4 %","0.016 [0.361]","0 [0.373]","0.00700000000000001 [0.364]","-0.0259999999999999 [0.359]","-1.015 [2.303]"]
["10","50","No Heterogeneity","No ecological bias","16.5 %","16.9 %","6.7 %","15.2 %","5.2 %","0.005 [0.465]","0.005 [0.462]","-0.0539999999999999 [0.466]","-0.078 [0.414]","-0.077 [1.503]"]
["10","50","No Heterogeneity","Favouring treatment ecological bias","15.4 %","15 %","6.3 %","12.9 %","4.5 %","0.005 [0.487]","-0.0179999999999999 [0.474]","-0.0469999999999999 [0.449]","-0.099 [0.417]","-0.38 [1.59]"]
["10","50","No Heterogeneity","Favouring placebo ecological bias","14.1 %","11.3 %","6.1 %","11.6 %","6.6 %","0.00700000000000001 [0.523]","-0.0619999999999999 [0.511]","-0.0309999999999999 [0.484]","-0.129 [0.429]","-0.956 [1.653]"]
["10","50","Medium Heterogeneity","No ecological bias","17.2 %","17 %","7.5 %","14.6 %","4.3 %","0.004 [0.501]","0.00700000000000001 [0.498]","-0.0629999999999999 [0.482]","-0.073 [0.424]","0.012 [1.545]"]
["10","50","Medium Heterogeneity","Favouring treatment ecological bias","16.1 %","15.4 %","7 %","12.7 %","3.3 %","0 [0.502]","-0.0169999999999999 [0.491]","-0.0589999999999999 [0.494]","-0.1 [0.418]","-0.305 [1.603]"]
["10","50","Medium Heterogeneity","Favouring placebo ecological bias","14.7 %","12 %","6.2 %","9.5 %","6.2 %","-0.004 [0.542]","-0.0619999999999999 [0.517]","-0.0499999999999999 [0.497]","-0.143 [0.431]","-0.892 [1.709]"]
["10","50","Large Heterogeneity","No ecological bias","16 %","16.9 %","7.4 %","11.5 %","3.8 %","0.004 [0.474]","0.00600000000000001 [0.474]","-0.0629999999999999 [0.472]","-0.071 [0.455]","0.028 [1.823]"]
["10","50","Large Heterogeneity","Favouring treatment ecological bias","15.9 %","15.1 %","6.5 %","9.4 %","3.8 %","0.002 [0.493]","-0.00900000000000001 [0.5]","-0.0619999999999999 [0.486]","-0.09 [0.453]","-0.281 [1.896]"]
["10","50","Large Heterogeneity","Favouring placebo ecological bias","15.3 %","12.7 %","6.3 %","7.4 %","5.4 %","-0.002 [0.536]","-0.0399999999999999 [0.51]","-0.0519999999999999 [0.494]","-0.141 [0.426]","-0.87 [1.946]"]
["10","100","No Heterogeneity","No ecological bias","29.4 %","29.5 %","20.6 %","26.8 %","6.9 %","0.004 [0.351]","0.001 [0.338]","-0.0259999999999999 [0.324]","-0.0409999999999999 [0.319]","-0.0609999999999999 [1.188]"]
["10","100","No Heterogeneity","Favouring treatment ecological bias","28.1 %","25.4 %","18.5 %","24.7 %","5.7 %","0.003 [0.348]","-0.0229999999999999 [0.347]","-0.0229999999999999 [0.334]","-0.0629999999999999 [0.319]","-0.379 [1.192]"]
["10","100","No Heterogeneity","Favouring placebo ecological bias","25.2 %","18.1 %","17.7 %","16.8 %","9.7 %","0.005 [0.387]","-0.0619999999999999 [0.367]","-0.0129999999999999 [0.379]","-0.104 [0.343]","-1.02 [1.237]"]
["10","100","Medium Heterogeneity","No ecological bias","31.1 %","31.3 %","20.5 %","24.1 %","6.1 %","0.00800000000000001 [0.349]","0.00800000000000001 [0.345]","-0.0209999999999999 [0.335]","-0.0329999999999999 [0.311]","-0.01 [1.233]"]
["10","100","Medium Heterogeneity","Favouring treatment ecological bias","28.3 %","27.1 %","19.4 %","21.2 %","6.3 %","0.00900000000000001 [0.345]","-0.00700000000000001 [0.348]","-0.0159999999999999 [0.344]","-0.0529999999999999 [0.334]","-0.335 [1.305]"]
["10","100","Medium Heterogeneity","Favouring placebo ecological bias","24.9 %","20.8 %","18.1 %","14.7 %","8.3 %","0.01 [0.365]","-0.0399999999999999 [0.356]","-0.00600000000000001 [0.346]","-0.093 [0.338]","-0.975 [1.322]"]
["10","100","Large Heterogeneity","No ecological bias","30.7 %","30.6 %","20.6 %","13.5 %","5.5 %","0.00900000000000001 [0.349]","0.00900000000000001 [0.343]","-0.0179999999999999 [0.334]","-0.0219999999999999 [0.313]","0.01 [1.718]"]
["10","100","Large Heterogeneity","Favouring treatment ecological bias","29.1 %","29 %","19 %","13.2 %","5.1 %","0.011 [0.352]","0.004 [0.343]","-0.0129999999999999 [0.344]","-0.0349999999999999 [0.315]","-0.315 [1.74]"]
["10","100","Large Heterogeneity","Favouring placebo ecological bias","25.3 %","23 %","17.2 %","9.5 %","7.5 %","0.01 [0.369]","-0.0149999999999999 [0.361]","-0.00600000000000001 [0.363]","-0.069 [0.348]","-0.936 [1.781]"]
["10","200","No Heterogeneity","No ecological bias","52.2 %","54.4 %","45.3 %","49.9 %","7 %","0.003 [0.241]","0.003 [0.232]","-0.01 [0.241]","-0.0179999999999999 [0.23]","-0.0379999999999999 [0.787]"]
["10","200","No Heterogeneity","Favouring treatment ecological bias","48.9 %","45.9 %","42.7 %","41.4 %","4.4 %","0.004 [0.246]","-0.0199999999999999 [0.236]","-0.00700000000000001 [0.247]","-0.0399999999999999 [0.23]","-0.377 [0.828]"]
["10","200","No Heterogeneity","Favouring placebo ecological bias","45.7 %","35.1 %","38.6 %","27.1 %","15 %","0.003 [0.267]","-0.0569999999999999 [0.268]","-0.004 [0.272]","-0.082 [0.265]","-1.037 [0.86]"]
["10","200","Medium Heterogeneity","No ecological bias","52.1 %","53 %","45 %","38.6 %","7.7 %","0.004 [0.222]","0.004 [0.222]","-0.01 [0.222]","-0.0129999999999999 [0.229]","-0.0139999999999999 [1.056]"]
["10","200","Medium Heterogeneity","Favouring treatment ecological bias","47.3 %","45.9 %","41 %","31.1 %","5.3 %","0.003 [0.224]","-0.00800000000000001 [0.226]","-0.00900000000000001 [0.236]","-0.0339999999999999 [0.228]","-0.355 [1.103]"]
["10","200","Medium Heterogeneity","Favouring placebo ecological bias","44.2 %","36.4 %","37.5 %","20.9 %","11 %","0.004 [0.26]","-0.0319999999999999 [0.259]","-0.003 [0.251]","-0.0679999999999999 [0.243]","-1.013 [1.162]"]
["10","200","Large Heterogeneity","No ecological bias","51 %","51.9 %","43.7 %","15.6 %","5.6 %","0.002 [0.223]","0.002 [0.224]","-0.01 [0.229]","-0.003 [0.23]","0.002 [1.624]"]
["10","200","Large Heterogeneity","Favouring treatment ecological bias","49.7 %","48.3 %","42.7 %","13.5 %","5.5 %","0.002 [0.234]","-0.001 [0.232]","-0.00900000000000001 [0.241]","-0.0139999999999999 [0.239]","-0.33 [1.628]"]
["10","200","Large Heterogeneity","Favouring placebo ecological bias","44.8 %","41.4 %","37.8 %","11.7 %","7.5 %","0.00600000000000001 [0.26]","-0.00900000000000001 [0.257]","-0.001 [0.242]","-0.0339999999999999 [0.253]","-0.982 [1.667]"]