Table 2:

Results for simulation scenario 2 with binary Y, one Gaussian B and nine correlated X’s: for each method, we report mean (Monte Carlo standard deviation) [95 % coverage rate], average scaled Brier score and AUC across 500 simulated datasets

	Not including B	True value	Direct MLE	Synthetic Data Method
γ0	0.849	1	1.00 (0.17) [94%]	0.96 (0.08) [92%]
γX1	0.435	2	2.01 (0.29) [96%]	1.92 (0.24) [94%]
γX2	0.432	2	2.00 (0.28) [96%]	1.90 (0.23) [94%]
γX3	0.437	2	2.01 (0.28) [95%]	1.90 (0.23) [95%]
γX4	0.433	2	2.01 (0.30) [96%]	1.91 (0.24) [95%]
γX5	0.422	2	2.02 (0.28) [95%]	1.90 (0.24) [93%]
γX6	0.421	2	2.01 (0.28) [97%]	1.89 (0.23) [93%]
γX7	0.431	2	2.01 (0.29) [96%]	1.91 (0.23) [94%]
γX8	0.415	2	2.00 (0.27) [97%]	1.89 (0.23) [94%]
γX9	0.445	2	2.01 (0.29) [96%]	1.92 (0.23) [95%]
γB	−	−3	−3.02 (0.45) [97%]	−2.85 (0.43) [95%]
Scaled Brier score	0.801	0.680	0.702	0.686
AUC	0.767	0.837	0.828	0.835