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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","5.4 %","6 %","6.4 %","8.5 %","5.5 %","-0.012 [0.348]","-0.01 [0.342]","-0.014 [0.372]","-0.012 [0.349]","0.043 [1.409]"]
["5","50","No Heterogeneity","Favouring treatment ecological bias","5.1 %","5.1 %","5.8 %","7.3 %","6.2 %","-0.004 [0.349]","-0.032 [0.344]","0.001 [0.351]","-0.028 [0.352]","-0.518 [1.341]"]
["5","50","No Heterogeneity","Favouring placebo ecological bias","4.9 %","6.1 %","6.7 %","8.3 %","13.7 %","0.01 [0.341]","0.056 [0.352]","0.008 [0.375]","0.059 [0.356]","1.059 [1.296]"]
["5","50","Medium heterogeneity","No ecological bias","4.3 %","4.7 %","5.9 %","5.4 %","6 %","0.003 [0.354]","0.003 [0.346]","0.004 [0.375]","0.005 [0.36]","0.034 [1.626]"]
["5","50","Medium heterogeneity","Favouring treatment ecological bias","5.2 %","5 %","5.5 %","7.1 %","6.7 %","-0.002 [0.359]","-0.016 [0.353]","-0.001 [0.387]","-0.029 [0.375]","-0.538 [1.751]"]
["5","50","Medium heterogeneity","Favouring placebo ecological bias","5.2 %","5.7 %","4.9 %","6.1 %","7.7 %","0.007 [0.357]","0.034 [0.358]","0.011 [0.373]","0.055 [0.36]","0.997 [1.641]"]
["5","50","Large heterogeneity","No ecological bias","6 %","5.9 %","6.9 %","3.1 %","4.8 %","0.009 [0.374]","0.009 [0.371]","0.005 [0.373]","0.008 [0.387]","0.032 [2.465]"]
["5","50","Large heterogeneity","Favouring treatment ecological bias","5.3 %","5.3 %","6.5 %","2.8 %","6.1 %","-0.008 [0.342]","-0.013 [0.346]","-0.011 [0.367]","-0.023 [0.355]","-0.425 [2.603]"]
["5","50","Large heterogeneity","Favouring placebo ecological bias","6.1 %","6.1 %","7 %","3.5 %","6.2 %","-0.004 [0.324]","0.008 [0.326]","-0.008 [0.354]","0.025 [0.353]","0.923 [2.304]"]
["5","100","No Heterogeneity","No ecological bias","5.2 %","5.4 %","6.6 %","8.7 %","5.7 %","0 [0.24]","0 [0.231]","0.002 [0.25]","0.001 [0.245]","-0.021 [0.911]"]
["5","100","No Heterogeneity","Favouring treatment ecological bias","4.5 %","5.6 %","4.6 %","7.1 %","7.6 %","-0.001 [0.238]","-0.027 [0.242]","0 [0.241]","-0.028 [0.242]","-0.509 [0.97]"]
["5","100","No Heterogeneity","Favouring placebo ecological bias","5.5 %","6.8 %","5.3 %","6.7 %","17.3 %","-0.004 [0.245]","0.035 [0.247]","-0.006 [0.254]","0.047 [0.25]","1.006 [0.93]"]
["5","100","Medium heterogeneity","No ecological bias","4.9 %","4.9 %","4.9 %","4 %","6.4 %","-0.005 [0.234]","-0.007 [0.228]","-0.006 [0.237]","-0.009 [0.238]","-0.026 [1.365]"]
["5","100","Medium heterogeneity","Favouring treatment ecological bias","4.8 %","5.1 %","5.8 %","3.8 %","6 %","0.004 [0.256]","-0.005 [0.257]","0.003 [0.25]","-0.014 [0.254]","-0.468 [1.437]"]
["5","100","Medium heterogeneity","Favouring placebo ecological bias","4.5 %","5.5 %","4.8 %","2.9 %","10.5 %","-0.01 [0.266]","0.008 [0.262]","-0.01 [0.268]","0.027 [0.267]","0.998 [1.479]"]
["5","100","Large heterogeneity","No ecological bias","4.8 %","4.7 %","4.9 %","1.1 %","4.4 %","0.001 [0.243]","0.002 [0.242]","0.003 [0.257]","0.005 [0.247]","0.101 [2.37]"]
["5","100","Large heterogeneity","Favouring treatment ecological bias","6 %","6.5 %","6.1 %","1.6 %","3.9 %","0.006 [0.244]","0.003 [0.249]","0.006 [0.256]","-0.003 [0.236]","-0.404 [2.252]"]
["5","100","Large heterogeneity","Favouring placebo ecological bias","5.3 %","5.3 %","6.3 %","1.5 %","6 %","-0.002 [0.225]","0.004 [0.23]","-0.003 [0.248]","0.019 [0.245]","1.033 [2.264]"]
["5","200","No Heterogeneity","No ecological bias","6 %","6.5 %","5.7 %","9.5 %","5.9 %","0.001 [0.166]","0.001 [0.166]","0.002 [0.17]","0.002 [0.163]","-0.025 [0.707]"]
["5","200","No Heterogeneity","Favouring treatment ecological bias","4.7 %","5.5 %","5.5 %","9.7 %","11.3 %","-0.005 [0.174]","-0.028 [0.168]","-0.006 [0.178]","-0.032 [0.17]","-0.489 [0.671]"]
["5","200","No Heterogeneity","Favouring placebo ecological bias","4.3 %","6.3 %","4.6 %","6.5 %","31.1 %","0.009 [0.18]","0.039 [0.177]","0.008 [0.18]","0.056 [0.176]","1.012 [0.669]"]
["5","200","Medium heterogeneity","No ecological bias","4.9 %","4.7 %","5.4 %","2.2 %","4.6 %","0.002 [0.176]","0.003 [0.176]","0.001 [0.178]","0.003 [0.179]","0.026 [1.29]"]
["5","200","Medium heterogeneity","Favouring treatment ecological bias","5.2 %","5.3 %","5.5 %","1.7 %","6.2 %","0 [0.172]","-0.006 [0.172]","0 [0.173]","-0.015 [0.177]","-0.497 [1.329]"]
["5","200","Medium heterogeneity","Favouring placebo ecological bias","4.9 %","5.5 %","4.8 %","2 %","11.9 %","0.001 [0.155]","0.011 [0.158]","0.001 [0.163]","0.029 [0.158]","0.98 [1.296]"]
["5","200","Large heterogeneity","No ecological bias","5.5 %","5.3 %","6 %","0.3 %","4.8 %","0.005 [0.182]","0.005 [0.18]","0.006 [0.191]","0.006 [0.187]","0.032 [2.204]"]
["5","200","Large heterogeneity","Favouring treatment ecological bias","6 %","5.5 %","5.2 %","0.1 %","5.8 %","0.004 [0.179]","0.003 [0.181]","0.005 [0.187]","-0.002 [0.196]","-0.504 [2.317]"]
["5","200","Large heterogeneity","Favouring placebo ecological bias","5.4 %","5.6 %","5.7 %","0.4 %","7.9 %","0.003 [0.174]","0.006 [0.172]","0.002 [0.175]","0.015 [0.171]","1.083 [2.188]"]
["10","50","No Heterogeneity","No ecological bias","5.4 %","5.5 %","6.7 %","8.5 %","6.5 %","0.003 [0.263]","0.002 [0.26]","0.006 [0.264]","0.003 [0.265]","-0.027 [1.038]"]
["10","50","No Heterogeneity","Favouring treatment ecological bias","4.9 %","5.7 %","6.2 %","7.3 %","9.6 %","0.01 [0.253]","-0.02 [0.25]","0.009 [0.262]","-0.023 [0.249]","-0.5 [0.972]"]
["10","50","No Heterogeneity","Favouring placebo ecological bias","4.9 %","6.1 %","6.3 %","6.5 %","24.4 %","-0.009 [0.235]","0.042 [0.238]","-0.006 [0.252]","0.049 [0.244]","0.974 [0.961]"]
["10","50","Medium heterogeneity","No ecological bias","4.5 %","5.2 %","6.1 %","3.9 %","5 %","-0.002 [0.237]","-0.003 [0.235]","-0.004 [0.25]","-0.006 [0.244]","-0.037 [1.173]"]
["10","50","Medium heterogeneity","Favouring treatment ecological bias","3.4 %","3.9 %","4 %","3.3 %","7.9 %","0.001 [0.226]","-0.015 [0.227]","0 [0.242]","-0.026 [0.24]","-0.469 [1.224]"]
["10","50","Medium heterogeneity","Favouring placebo ecological bias","5.5 %","5.6 %","7.3 %","4.1 %","17.9 %","-0.001 [0.253]","0.026 [0.252]","-0.002 [0.267]","0.045 [0.266]","1.004 [1.193]"]
["10","50","Large heterogeneity","No ecological bias","6.2 %","6.2 %","6.4 %","1 %","5.7 %","-0.003 [0.246]","-0.002 [0.248]","-0.003 [0.251]","-0.004 [0.259]","-0.018 [1.817]"]
["10","50","Large heterogeneity","Favouring treatment ecological bias","4 %","3.8 %","4.9 %","0.7 %","8.2 %","0.001 [0.231]","-0.005 [0.234]","0.005 [0.242]","-0.014 [0.242]","-0.5 [1.785]"]
["10","50","Large heterogeneity","Favouring placebo ecological bias","5.7 %","5.6 %","6.7 %","1.3 %","7.9 %","-0.001 [0.265]","0.011 [0.27]","0.002 [0.271]","0.03 [0.279]","0.97 [1.738]"]
["10","100","No Heterogeneity","No ecological bias","5 %","4.9 %","5.6 %","7.1 %","4 %","0 [0.167]","0 [0.161]","0.001 [0.175]","0 [0.162]","-0.013 [0.639]"]
["10","100","No Heterogeneity","Favouring treatment ecological bias","5.7 %","5.8 %","5.6 %","6.7 %","16.2 %","-0.003 [0.164]","-0.033 [0.161]","-0.005 [0.173]","-0.035 [0.164]","-0.516 [0.671]"]
["10","100","No Heterogeneity","Favouring placebo ecological bias","4.4 %","6.7 %","5 %","6.9 %","41.6 %","0.001 [0.169]","0.044 [0.175]","0.003 [0.176]","0.059 [0.169]","0.979 [0.671]"]
["10","100","Medium heterogeneity","No ecological bias","5.3 %","5.3 %","6.5 %","3.1 %","4.6 %","-0.006 [0.175]","-0.006 [0.172]","-0.007 [0.177]","-0.006 [0.178]","-0.005 [1]"]
["10","100","Medium heterogeneity","Favouring treatment ecological bias","5.1 %","5.8 %","5.9 %","2.7 %","7.2 %","-0.002 [0.187]","-0.012 [0.188]","-0.003 [0.192]","-0.022 [0.185]","-0.45 [0.992]"]
["10","100","Medium heterogeneity","Favouring placebo ecological bias","5.4 %","5.3 %","6 %","2.3 %","23.4 %","0.005 [0.168]","0.023 [0.167]","0.006 [0.185]","0.045 [0.175]","1.019 [1.025]"]
["10","100","Large heterogeneity","No ecological bias","4.4 %","4.7 %","4.7 %","0.3 %","5 %","0.003 [0.174]","0.004 [0.172]","0.005 [0.18]","0.004 [0.178]","-0.018 [1.618]"]
["10","100","Large heterogeneity","Favouring treatment ecological bias","5.8 %","5.6 %","6.3 %","0.2 %","5.6 %","-0.003 [0.178]","-0.005 [0.178]","-0.003 [0.19]","-0.012 [0.181]","-0.456 [1.624]"]
["10","100","Large heterogeneity","Favouring placebo ecological bias","6 %","5.6 %","6.7 %","0.3 %","12 %","-0.005 [0.173]","0.002 [0.175]","-0.002 [0.18]","0.018 [0.179]","0.993 [1.667]"]
["10","200","No Heterogeneity","No ecological bias","4.4 %","4.3 %","4.7 %","6.9 %","5.3 %","0.002 [0.128]","0.001 [0.123]","0.002 [0.132]","0.001 [0.127]","-0.023 [0.468]"]
["10","200","No Heterogeneity","Favouring treatment ecological bias","5.9 %","6.4 %","6.2 %","8.1 %","25.4 %","-0.003 [0.125]","-0.027 [0.122]","-0.002 [0.129]","-0.032 [0.124]","-0.499 [0.446]"]
["10","200","No Heterogeneity","Favouring placebo ecological bias","5.6 %","7.6 %","5.7 %","6.9 %","72.3 %","0 [0.12]","0.03 [0.119]","0.001 [0.123]","0.052 [0.119]","1.019 [0.485]"]
["10","200","Medium heterogeneity","No ecological bias","4.8 %","4.9 %","5.4 %","0.9 %","5.4 %","-0.002 [0.117]","-0.001 [0.119]","-0.002 [0.123]","-0.001 [0.125]","0.013 [0.932]"]
["10","200","Medium heterogeneity","Favouring treatment ecological bias","5.5 %","5.4 %","6 %","0.7 %","9.1 %","-0.002 [0.133]","-0.008 [0.132]","-0.002 [0.137]","-0.017 [0.133]","-0.463 [0.855]"]
["10","200","Medium heterogeneity","Favouring placebo ecological bias","5.5 %","5.7 %","5.4 %","0.9 %","29.5 %","0.003 [0.127]","0.013 [0.125]","0.002 [0.126]","0.031 [0.124]","1.025 [0.927]"]
["10","200","Large heterogeneity","No ecological bias","4.4 %","4.5 %","4.8 %","0.1 %","4.9 %","0.001 [0.121]","0.001 [0.121]","0.001 [0.119]","0.001 [0.122]","-0.01 [1.62]"]
["10","200","Large heterogeneity","Favouring treatment ecological bias","5.5 %","5.7 %","4.9 %","0 %","5.4 %","-0.001 [0.128]","-0.003 [0.129]","-0.002 [0.136]","-0.009 [0.136]","-0.513 [1.542]"]
["10","200","Large heterogeneity","Favouring placebo ecological bias","4.3 %","4.3 %","4.5 %","0 %","11.8 %","0.001 [0.113]","0.003 [0.113]","0.001 [0.12]","0.013 [0.119]","0.992 [1.584]"]