. Author manuscript; available in PMC: 2022 Jan 3.

Published in final edited form as: Stat Med. 2018 Oct 23;38(6):917–932. doi: 10.1002/sim.8015

TABLE 2.

Conditional inferences for binary outcomes: $({\hat{w}}_{1}, {\hat{w}}_{2}, {\hat{w}}_{3}, {\hat{w}}_{4}) = {(0.242, 0.059, 0.536, 0.162)}^{'}$ and $({\hat{π}}_{1}, {\hat{π}}_{2}, {\hat{π}}_{3}, {\hat{π}}_{4}) = {(0.178, 0.444, 0.333, 0.510)}^{'}$ in Australia; $({\hat{w}}_{1}, {\hat{w}}_{2}, {\hat{w}}_{3}, {\hat{w}}_{4}) = {(0.272, 0.035, 0.570, 0.123)}^{'}$ and $({\hat{π}}_{1}, {\hat{π}}_{2}, {\hat{π}}_{3}, {\hat{π}}_{4}) = {(0.315, 0.320, 0.320, 0.382)}^{'}$ in Britain; $({\hat{w}}_{1}, {\hat{w}}_{2}, {\hat{w}}_{3}, {\hat{w}}_{4}) = {(0.196, 0.048, 0.511, 0.245)}^{'}$ and $({\hat{π}}_{1}, {\hat{π}}_{2}, {\hat{π}}_{3}, {\hat{π}}_{4}) = {(0.336, 0.257, 0.330, 0.335)}^{'}$ in USA. Bias stands for the empirical bias. ESE stands for the empirical standard errors. CP1 and CP2 stand for the empirical coverage levels of upper and lower 97.5% confidence intervals, respectively

Country	n	θ	Bias	ESE	CP1	CP2
Australia	302	$\hat{θ}$	−0.172	0.291	0.995	0.936
		${\hat{θ}}_{π w}$	−0.025	0.307	0.972	0.975
		${\hat{θ}}_{new}$	−0.018	0.308	0.970	0.976
		${\hat{θ}}_{S}$	−0.089	0.294	0.987	0.964

GBR	723	$\hat{θ}$	−0.014	0.180	0.978	0.976
		${\hat{θ}}_{π w}$	−0.005	0.182	0.972	0.975
		${\hat{θ}}_{new}$	−0.005	0.182	0.972	0.975
		${\hat{θ}}_{S}$	0.011	0.178	0.971	0.984

USA	3894	$\hat{θ}$	−0.052	0.079	0.997	0.911
		${\hat{θ}}_{π w}$	−0.001	0.080	0.973	0.975
		${\hat{θ}}_{new}$	0.000	0.080	0.972	0.977
		${\hat{θ}}_{S}$	−0.059	0.079	0.997	0.898