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Table 1 Distributions and regression models used for simulating the data

From: Adaptive propensity score procedure improves matching in prospective observational trials

Variable Group Distribution Model
X 1 both Bin(1;0.5)  
X 2 both Bin(1;0.2)  
X 3 both N(70;15)  
Z    \(logit\left (\frac {P(Z=1)}{1-P(Z=1)}\right)\)
X 4 control Bin(10;0.8)  
X 4 treated Bin(10;0.75)  
X 5 control N(17;5)  
X 5 treated N(16;4)  
\(Y_{H_{0}}\) both Bin(1;0.5)  
\(Y_{H_{1}}\) both   \(logit\left (\frac {P(Y=1)}{1-P(Y=1)}\right)\)