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

Table 3 Under Gamma 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
Gamma	9	0.5	60	0.0489	0.0001	0.0001
			90	0.0497	0.0001	0.0009
			120	0.0500	0.0001	0.0036
			480	0.0506	0.0013	0.0236
			900	0.0509	0.0028	0.0373
		1.0	60	0.0493	0.0001	0.0009
			90	0.0501	0.0002	0.0027
			120	0.0506	0.0002	0.0045
			480	0.0512	0.0003	0.0209
			900	0.0516	0.0003	0.0273
		2.0	60	0.0486	0.0001	0.0109
			90	0.0495	0.0001	0.0136
			120	0.0499	0.0001	0.0191
			480	0.0505	0.0002	0.0424
			900	0.0509	0.0002	0.0451
	15	0.5	60	0.0483	0.0008	0.0027
			90	0.0499	0.0009	0.0036
			120	0.0496	0.0019	0.0082
			480	0.0510	0.0030	0.0300
			900	0.0513	0.0048	0.0364
		1.0	60	0.0485	0.0005	0.0145
			90	0.0499	0.0006	0.0173
			120	0.0502	0.0006	0.0273
			480	0.0509	0.0008	0.0409
			900	0.0514	0.0009	0.0418
		2.0	60	0.0495	0.0001	0.0282
			90	0.0496	0.0001	0.0318
			120	0.0506	0.0001	0.0427
			480	0.0511	0.0002	0.0433
			900	0.0516	0.0003	0.0472
	20	0.5	60	0.0482	0.0027	0.0073
			90	0.0500	0.0036	0.0164
			120	0.0505	0.0034	0.0191
			480	0.0508	0.0042	0.0305
			900	0.0509	0.0056	0.0436
		1.0	60	0.0487	0.0004	0.0200
			90	0.0500	0.0009	0.0227
			120	0.0501	0.0010	0.0400
			480	0.0508	0.0011	0.0418
			900	0.0515	0.0015	0.0482
		2.0	60	0.0484	0.0001	0.0318
			90	0.0486	0.0002	0.0409
			120	0.0500	0.0004	0.0415
			480	0.0509	0.0006	0.0435
			900	0.0515	0.0011	0.0484

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

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