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. Author manuscript; available in PMC: 2010 Jun 28.
Published in final edited form as: Biometrics. 2009 Jun 9;66(2):512–522. doi: 10.1111/j.1541-0420.2009.01282.x

Table 1.

Simulation Results for ÂBopt; BT represent back-transformed confidence intervals while DT represents delta-theorem based confidence intervals

Simulation 1 2 3 4 5 6 7
n 1000 1000 1000 1000 1000 1000 1000
Reps 10000 10000 10000 10000 10000 10000 10000
α0 −1.25 −1.25 −1.25 −1.25 −1 0.25 −1.25
α1 2 2 2 0 −1 1 2
β0 −2.5 −2.5 −2.5 −2.5 1 −2 −2.5
β1 1.25 1.25 1.25 1.25 1 0.75 0
β2 1.1 1.1 1.1 1.1 1 1.2 1.1
β3 0 2 −1 −2 −1 1.5 0
P(T = 1) 0.318 0.318 0.318 0.223 0.303 0.551 0.318
P(Y = 1) 0.184 0.263 0.122 0.143 0.786 0.304 0.111
P{Y*(0) = 1} 0.111 0.111 0.111 0.111 0.697 0.164 0.111
P{Y*(1) = 1} 0.267 0.363 0.223 0.2545 0.881 0.169 0.111
P{Y*(gopt) = 1} 0.111 0.108 0.1 0.068 0.691 0.348 0.111
ABdom 0.396 0.577 0.094 0.223 0.113 0.446 0
ABopt 0.396 0.588 0.184 0.523 0.121 0.461 0
AB^opt(0)
0.3953 0.5897 0.1982 0.5277 0.1251 0.4627 0.1073
SE^{ABopt(0)}mc
0.0799 0.0584 0.0605 0.0538 0.0168 0.0632 0.0773
SE^{ABopt(0)}dt
0.0786 0.0578 0.0593 0.0536 0.0169 0.0626 0.0944
BT Lower 95% 0.2195 0.4587 0.0720 0.4098 0.0914 0.3245 −0.1024
BT Upper 95% 0.5310 0.6885 0.3055 0.6218 0.1574 0.5723 0.2715
BT Coverage 0.9415 0.9428 0.9477 0.9492 0.9579 0.9455 0.9320
DT Lower 95% 0.2413 0.4764 0.0820 0.4226 0.0920 0.3400 −0.0776
DT Upper 95% 0.5493 0.7030 0.3144 0.6328 0.1581 0.5855 0.2922
DT Coverage 0.9384 0.9352 0.9420 0.9418 0.9568 0.9420 0.8897