Conducting the non-inferiority test for the means with unknown coefficient of variation in a three-arm trial

Table 2 Under Log-normal distribution, the type I error rates for testing non-inferiority with non-inferiority limit = 0.8 in \(\tau_{R} = 1\), \(\mu_{R} - \mu_{P} =\) 9, 15 and 20, respectively

Distribution	\(\mu_{R} - \mu_{P}\)	\(\tau_{P}\)	\(n\)	Method
Distribution	\(\mu_{R} - \mu_{P}\)	\(\tau_{P}\)	\(n\)	GP	DM	EB
Log-Normal	9	0.5	60	0.0462	0.0002	0.0003
			90	0.0477	0.0002	0.0009
			120	0.0482	0.0003	0.0027
			480	0.0493	0.0027	0.0136
			900	0.0504	0.0036	0.0245
		1.0	60	0.0477	0.0006	0.0018
			90	0.0478	0.0008	0.0064
			120	0.0491	0.0010	0.0073
			480	0.0493	0.0012	0.0327
			900	0.0498	0.0015	0.0418
		2.0	60	0.0477	0.0001	0.0145
			90	0.0493	0.0002	0.0164
			120	0.0500	0.0005	0.0191
			480	0.0505	0.0008	0.0418
			900	0.0509	0.0011	0.0427
	15	0.5	60	0.0458	0.0020	0.0027
			90	0.0475	0.0023	0.0082
			120	0.0478	0.0029	0.0145
			480	0.0485	0.0047	0.0373
			900	0.0491	0.0054	0.0382
		1.0	60	0.0465	0.0013	0.0182
			90	0.0478	0.0016	0.0300
			120	0.0491	0.0019	0.0418
			480	0.0497	0.0020	0.0473
			900	0.0500	0.0023	0.0489
		2.0	60	0.0484	0.0002	0.0291
			90	0.0492	0.0003	0.0355
			120	0.0499	0.0005	0.0400
			480	0.0501	0.0012	0.0428
			900	0.0505	0.0015	0.0437
	20	0.5	60	0.0457	0.0038	0.0118
			90	0.0461	0.0046	0.0182
			120	0.0479	0.0055	0.0264
			480	0.0486	0.0059	0.0436
			900	0.0495	0.0065	0.0482
		1.0	60	0.0485	0.0011	0.0300
			90	0.0493	0.0023	0.0345
			120	0.0495	0.0026	0.0355
			480	0.0496	0.0030	0.0464
			900	0.0502	0.0040	0.0479
		2.0	60	0.0491	0.0003	0.0155
			90	0.0495	0.0007	0.0173
			120	0.0496	0.0010	0.0191
			480	0.0500	0.0013	0.0432
			900	0.0503	0.0015	0.0473

\(n\) The total sample sizes, GP The GPV-based method, DM The Delta method, and EB the empirical bootstrap method

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