Table 3.

Naïve CPD-MA coefficient estimate bias (mean [IQR])

		Naive one-stage IPD-MA BIAS [IQR]
		Binary outcome			Continuous outcome			Survival outcome
Heterogeneity magnitude	Ecological Bias	Large subgroup effect	Medium subgroup effect	No sugroup effect	Large subgroup effect	Medium subgroup effect	No sugroup effect	Large subgroup effect	Medium subgroup effect	No sugroup effect
No heterogeneity	No ecological bias	-0.012 [0.595]	-0.001 [0.596]	0 [0.516]	-0.005 [0.258]	-0.014 [0.25]	0 [0.231]	0.017 [0.459]	0.011 [0.456]	-0.013 [0.377]
No heterogeneity	Favouring treatment ecological bias	0.021 [0.56]	0.027 [0.57]	-0.006 [0.596]	0.031 [0.255]	0.019 [0.24]	-0.027 [0.242]	-0.03 [0.489]	-0.009 [0.474]	-0.03 [0.409]
No heterogeneity	Favouring placebo ecological bias	0.075 [0.596]	0.073 [0.566]	-0.013 [0.585]	0.042 [0.241]	0.041 [0.232]	0.035 [0.247]	-0.089 [0.572]	-0.047 [0.51]	0.027 [0.367]
Medium heterogeneity	No ecological bias	-0.043 [0.627]	0.023 [0.523]	0.004 [0.562]	-0.001 [0.247]	-0.01 [0.239]	-0.007 [0.228]	-0.002 [0.449]	-0.002 [0.464]	-0.014 [0.365]
Medium heterogeneity	Favouring treatment ecological bias	-0.003 [0.544]	0.009 [0.565]	0.007 [0.599]	0 [0.249]	0.011 [0.257]	-0.005 [0.257]	-0.031 [0.491]	-0.021 [0.479]	-0.029 [0.398]
Medium heterogeneity	Favouring placebo ecological bias	0.052 [0.572]	0.013 [0.516]	-0.024 [0.563]	0.024 [0.255]	0.015 [0.245]	0.008 [0.262]	-0.107 [0.589]	-0.068 [0.523]	0.009 [0.383]
Large heterogeneity	No ecological bias	-0.01 [0.59]	-0.027 [0.551]	0.007 [0.591]	-0.003 [0.255]	0.002 [0.268]	0.002 [0.242]	0.005 [0.456]	-0.002 [0.463]	-0.012 [0.389]
Large heterogeneity	Favouring treatment ecological bias	0.009 [0.559]	0.003 [0.557]	-0.004 [0.586]	0.005 [0.241]	-0.006 [0.255]	0.003 [0.249]	-0.019 [0.489]	-0.016 [0.483]	-0.018 [0.392]
Large heterogeneity	Favouring placebo ecological bias	0.044 [0.569]	0.015 [0.56]	-0.008 [0.591]	0.012 [0.242]	0.001 [0.247]	0.004 [0.23]	-0.071 [0.565]	-0.040 [0.542]	-0.004 [0.365]