. Author manuscript; available in PMC: 2017 Sep 10.

Published in final edited form as: Stat Med. 2016 Mar 21;35(20):3537–3548. doi: 10.1002/sim.6943

Table 3.

Simulation Results with Complex Confounding Structures (True effect size α_Z=0.5)

n	Average α̂_Z	Monte Carlo SE(α̂_Z)	Conventional Modeling		Analytic Modeling		Bootstrapping
n	Average α̂_Z	Monte Carlo SE(α̂_Z)	Average $\sqrt{{\hat{Var}}_{C} ({\hat{α}}_{Z})}$	95% CI Coverage	Average $\sqrt{{\hat{Var}}_{A} ({\hat{α}}_{Z})}$	95% CI Coverage	Average $\sqrt{{\hat{Var}}_{B} ({\hat{α}}_{Z})}$	95% CI Coverage
Complex Confounding Structure I^a: treatment generated by (7) and response generated by (6)
500	0.497	0.120	0.283	100.0	0.125	94.7	0.118	93.6

5000	0.499	0.037	0.087	100.0	0.039	96.6	0.037	95.4

Complex Confounding Structure II^b: treatment generated by (5) and response generated by (8)
500	0.502	0.238	0.330	98.9	0.251	95.4	0.243	95.2

5000	0.503	0.077	0.100	98.9	0.079	95.4	0.077	95.2

See Table 1 for the table legends

p = 10 and q = 0

Quadratic covariate term in the treatment assignment

Quadratic covariate term in the outcome