. 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 1.

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

n	(p, q)	Average α̂_Z	Monte Carlo SE(α̂_Z)	Conventional Modeling		Analytic Modeling		Bootstrapping
n	(p, q)	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
500	(10, 0)	0.496	0.117	0.277	100.0	0.117	95.4	0.117	95.3
500	(10,10)	0.501	0.117	0.281	100.0	0.115	94.7	0.119	95.4

5000	(10, 0)	0.501	0.037	0.086	100.0	0.036	94.2	0.036	94.4
5000	(10, 10)	0.500	0.038	0.086	100.0	0.036	94.1	0.036	94.3

n	(p, q)	PS Stratification				IPW by PS
n	(p, q)	Average α̂_Z	Monte Carlo SE(α̂_Z)	Average $\sqrt{\hat{Var} ({\hat{α}}_{Z})}$	95% CI Coverage	Average α̂_Z	Monte Carlo SE(α̂_Z)	Average $\sqrt{\hat{Var} ({\hat{α}}_{Z})}$	95% CI Coverage
500	(10, 0)	0.534	0.107	0.161	99.5	0.501	0.145	0.132	93.3
500	(10,10)	0.531	0.110	0.163	99.3	0.504	0.151	0.132	91.9

5000	(10, 0)	0.533	0.033	0.050	97.4	0.499	0.046	0.044	94.5
5000	(10, 10)	0.533	0.035	0.05	97.8	0.499	0.047	0.044	93.3

Note: n=sample size; p=# of confounding covariates and q=# of nuisance covariates; 5 strata were used for PS stratification