. Author manuscript; available in PMC: 2025 Aug 25.

Published in final edited form as: Clin Trials. 2025 Aug 21;22(6):667–675. doi: 10.1177/17407745251358233

Table 1.

Simulation results for $H_{0} : p = 0.1$ and $H_{1} : p = 0.3$ with Simon’s optimal sample size.

Data	( $n_{1}$ , $n_{2}$ )	Par	Simon	logit(0.1)	logit(0.2)	logit(0.3)
$H_{0}$	(3, 21)	$\hat{p}$	0.13 (0.07)	0.10 (0.06)	0.11 (0.06)	0.10 (0.06)
		FPR	0.04	0.08	0.08	0.08
		PET	0.73	0.63	0.59	0.56
		ESS	8.69	10.75	11.64	12.26
	(6, 18)	$\hat{p}$	0.13 (0.07)	0.13 (0.07)	0.11 (0.06)	0.11 (0.06)
		FPR	0.08	0.07	0.08	0.08
		PET	0.53	0.63	0.60	0.58
		ESS	14.43	12.65	13.21	13.60
	(8, 16)	$\hat{p}$	0.13 (0.07)	0.13 (0.07)	0.13 (0.07)	0.13 (0.07)
		FPR	0.08	0.08	0.08	0.08
		PET	0.43	0.62	0.59	0.57
		ESS	17.11	14.09	14.53	14.82
	(9, 15)	$\hat{p}$	0.12 (0.06)	0.12 (0.07)	0.13 (0.07)	0.13 (0.07)
		FPR	0.08	0.08	0.08	0.08
		PET	0.39	0.62	0.59	0.58
		ESS	18.18	14.72	15.10	15.37
$H_{1}$	(3, 21)	$\hat{p}$	0.32 (0.10)	0.29 (0.10)	0.30 (0.10)	0.30 (0.10)
		Power	0.63	0.88	0.89	0.89
	(8, 16)	$\hat{p}$	0.31 (0.09)	0.30 (0.10)	0.30 (0.10)	0.30 (0.10)
		Power	0.80	0.80	0.83	0.86
	(6, 18)	$\hat{p}$	0.31 (0.09)	0.30 (0.10)	0.30 (0.10)	0.31 (0.10)
		Power	0.85	0.85	0.85	0.86
	(9, 15)	$\hat{p}$	0.31 (0.09)	0.30 (0.10)	0.30 (0.10)	0.31 (0.10)
		Power	0.87	0.87	0.87	0.87

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