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

Lee, Meng-Chih; Wu, Wei-Ya; Lu, Hung-Yi; Hsieh, Hsin-Neng; Wu, Wei-Hwa

doi:10.1186/s12874-023-01990-w

BMC Medical Research Methodology

Table 7 Under \(\tau_{R} - \tau_{P}\) = 9, 15, and 20, estimate the Bias, MSE and CP of non-inferiority limit by the GPV-based, the Delta, and the empirical bootstrap methods

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

\(\mu_{R} - \mu_{P}\)	\(\tau_{P}\)	\(n\)	Point Estimation Property						Interval Estimation Property
			Bias			MSE			CP
			GP	DM	EB	GP	DM	EB	GP	DM	EB
9	0.5	60	0.0340	0.0865	0.2170	0.1114	5.7267	53.2988	0.9503	0.9999	0.9999
		90	0.0246	0.0407	0.1125	0.0815	1.1064	8.8637	0.9497	0.9999	0.9997
		120	0.0221	0.0295	0.0847	0.0595	0.0712	3.2183	0.9494	0.9998	0.9991
		480	0.0080	0.0080	0.0130	0.0123	0.0123	0.0276	0.9489	0.9984	0.9918
		900	0.0015	0.0015	0.0057	0.0063	0.0063	0.0133	0.9482	0.9962	0.9736
	1.0	60	0.0186	0.0240	0.0133	0.0590	0.5243	15.3224	0.9514	0.9999	0.9985
		90	0.0139	0.0152	0.0400	0.0393	0.0467	1.7485	0.9507	0.9998	0.9982
		120	0.0135	0.0141	0.0266	0.0283	0.0295	0.2401	0.9502	0.9998	0.9955
		480	0.0027	0.0028	0.0022	0.0061	0.0061	0.0129	0.9499	0.9997	0.9682
		900	0.0011	0.0011	0.0013	0.0033	0.0033	0.0067	0.9494	0.9996	0.9564
	2.0	60	0.0098	0.0097	0.0260	0.0300	0.0446	2.4935	0.9512	0.9999	0.9909
		90	0.0067	0.0058	0.0051	0.0196	0.0206	0.1298	0.9501	0.9999	0.9873
		120	0.0058	0.0053	0.0024	0.0143	0.0145	0.0421	0.9496	0.9998	0.9736
		480	0.0012	0.0011	0.0008	0.0033	0.0033	0.0068	0.9494	0.9998	0.9618
		900	0.0011	0.0011	0.0004	0.0018	0.0018	0.0035	0.9489	0.9997	0.9564
15	0.5	60	0.0226	0.0231	0.0465	0.0400	0.0431	0.2712	0.9525	0.9992	0.9982
		90	0.0151	0.0157	0.0306	0.0255	0.0257	0.0691	0.9519	0.9991	0.9945
		120	0.0113	0.0117	0.0177	0.0189	0.0189	0.0897	0.9518	0.9981	0.9909
		480	0.0017	0.0017	0.0034	0.0044	0.0044	0.0087	0.9501	0.9964	0.9727
		900	0.0005	0.0005	0.0025	0.0023	0.0023	0.0045	0.9498	0.9957	0.9636
	1.0	60	0.0124	0.0113	0.0201	0.0192	0.0195	0.0799	0.9507	0.9996	0.9845
		90	0.0078	0.0073	0.0130	0.0126	0.0126	0.0277	0.9499	0.9996	0.9809
		120	0.0045	0.0042	0.0087	0.0093	0.0094	0.0195	0.9495	0.9993	0.9782
		480	0.0011	0.0011	0.0012	0.0022	0.0022	0.0044	0.9492	0.9993	0.9577
		900	0.0008	0.0008	0.0013	0.0012	0.0012	0.0023	0.9486	0.9985	0.9555
	2.0	60	0.0053	0.0041	0.0094	0.0095	0.0095	0.0224	0.9500	0.9999	0.9673
		90	0.0031	0.0028	0.0026	0.0064	0.0064	0.0133	0.9497	0.9998	0.9636
		120	0.0014	0.0009	0.0013	0.0048	0.0048	0.0102	0.9496	0.9998	0.9627
		480	0.0003	0.0003	0.0009	0.0012	0.0012	0.0023	0.9493	0.9997	0.9545
		900	0.0002	0.0002	0.0007	0.0006	0.0006	0.0013	0.9488	0.9996	0.9527
20	0.5	60	0.0145	0.0135	0.0251	0.0221	0.0223	0.0514	0.9505	0.9979	0.9927
		90	0.0074	0.0070	0.0144	0.0139	0.0139	0.0291	0.9497	0.9975	0.9873
		120	0.0044	0.0041	0.0092	0.0099	0.0099	0.0212	0.9489	0.9968	0.9836
		480	0.0010	0.0010	0.0034	0.0024	0.0024	0.0050	0.9486	0.9953	0.9645
		900	0.0006	0.0006	0.0013	0.0012	0.0012	0.0026	0.9484	0.9942	0.9536
	1.0	60	0.0072	0.0063	0.0106	0.0101	0.0101	0.0221	0.9513	0.9994	0.9736
		90	0.0042	0.0038	0.0068	0.0066	0.0066	0.0141	0.9507	0.9990	0.9709
		120	0.0036	0.0034	0.0044	0.0050	0.0050	0.0104	0.9496	0.9990	0.9697
		480	0.0001	0.0001	0.0006	0.0012	0.0012	0.0024	0.9490	0.9988	0.9545
		900	0.0002	0.0002	0.0002	0.0007	0.0007	0.0013	0.9487	0.9985	0.9509
	2.0	60	0.0039	0.0031	0.0019	0.0053	0.0053	0.0112	0.9514	0.9999	0.9582
		90	0.0030	0.0026	0.0014	0.0035	0.0035	0.0072	0.9510	0.9999	0.9564
		120	0.0019	0.0017	0.0012	0.0026	0.0026	0.0054	0.9498	0.9998	0.9555
		480	0.0002	0.0001	0.0005	0.0006	0.0006	0.0013	0.9491	0.9997	0.9536
		900	0.0002	0.0002	0.0003	0.0003	0.0003	0.0007	0.9485	0.9995	0.9523

\(n\) The total sample sizes, GP The GPV-based method, DM The Delta method and EB The empirical bootstrap method, MSE Mean square error, CP coverage probability

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