Table 4.

Simulation results for $H_0:p=0.1$ and $H_1:p=0.3$ with an additional trial in the second stage.

Data	($n_1$, $n_2$)	Par	Simon	logit(0.1)	logit(0.2)	logit(0.3)
$H_0$	(3, 21)	$\widehat{p}$	0.14 (0.07)	0.10 (0.06)	0.11 (0.06)	0.11 (0.06)
		FPR	0.05	0.09	0.09	0.09
		PET	0.73	0.64	0.60	0.57
		ESS	8.69	10.55	11.46	12.09
	(6, 18)	$\widehat{p}$	0.13 (0.07)	0.12 (0.07)	0.11 (0.06)	0.11 (0.06)
		FPR	0.06	0.07	0.07	0.08
		PET	0.53	0.63	0.60	0.58
		ESS	14.43	12.70	13.25	13.64
	(8, 16)	$\widehat{p}$	0.12 (0.07)	0.12 (0.07)	0.13 (0.07)	0.12 (0.07)
		FPR	0.07	0.07	0.07	0.07
		PET	0.43	0.63	0.60	0.58
		ESS	17.11	13.97	14.41	14.72
	(9, 15)	$\widehat{p}$	0.12 (0.06)	0.12 (0.07)	0.12 (0.07)	0.13 (0.07)
		FPR	0.07	0.08	0.08	0.08
		PET	0.39	0.62	0.59	0.58
		ESS	18.19	14.72	15.11	15.36
$H_1$	(3, 21)	$\widehat{p}$	0.32 (0.09)	0.30 (0.10)	0.30 (0.10)	0.30 (0.10)
		Power	0.63	0.88	0.89	0.89
	(6, 18)	$\widehat{p}$	0.31 (0.09)	0.30 (0.10)	0.30 (0.10)	0.30 (0.10)
		Power	0.82	0.80	0.83	0.86
	(8, 16)	$\widehat{p}$	0.30 (0.09)	0.30 (0.10)	0.30 (0.10)	0.30 (0.10)
		Power	0.86	0.84	0.84	0.85
	(9, 15)	$\widehat{p}$	0.30 (0.09)	0.30 (0.10)	0.30 (0.10)	0.30 (0.10)
		Power	0.88	0.86	0.86	0.86

Note: $\text{logit}\left({\pi }_i\right)=\mu +v_i$, where $v_i~l(i\ne 4)N\left(0,{0.1}^2\right)+l(i=4)N\left(0,{0.3}^2\right)$.

FPR = false positive rate; PET = probability of early termination; ESS=expected sample size