. 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 2.

Simulation Results with Simple Confounding Structures (True effect size α_Z=1.00 and 1.50)

(p, q)

Average α̂_Z

Monte Carlo SE(α̂_Z)

Conventional Modeling

Analytic Modeling

Bootstrapping

\sqrt{{\hat{Var}}_{C} ({\hat{α}}_{Z})}

95% CI Coverage

\sqrt{{\hat{Var}}_{A} ({\hat{α}}_{Z})}

95% CI Coverage

Average

\sqrt{{\hat{Var}}_{B} ({\hat{α}}_{Z})}

95% CI Coverage

True effect size α_Z=1.00

5000

(10, 0)

1.000

0.034

0.048

99.6

0.033

94.2

0.033

94.2

True effect size α_Z=1.50

5000

(10, 0)

1.499

0.033

0.048

99.4

0.033

94.8

0.033

94.6

Note: n=sample size; p=# of confounding covariates and q=# of nuisance covariates