Re-formulating Gehan’s design as a flexible two-stage single-arm trial

Grayling, Michael J.; Mander, Adrian P.

doi:10.1186/s12874-019-0659-2

BMC Medical Research Methodology

Table 1 Optimal hypothesis tests in Gehan designs using f_G

From: Re-formulating Gehan’s design as a flexible two-stage single-arm trial

β ₁	γ	π ₁	Method	P(π₀)	P(π₁)	ESS(π₀)	ESS(π₁)	D(1)	…	D(7)	D(8)	D(9)	D(10)	D(11)	D(12)	D(13)	D(14)
0.050	0.050	0.200	Original	0.011	0.918	37.595	79.781	0.011	…	0.341	0.433	0.498	0.558	0.623	1	1	1
0.050	0.050	0.200	Conservative	0.038	0.952	46.420	87.837	0.069	…	0.260	0.411	0.431	0.431	0.591	0.722	0.793	0.825
0.100	0.050	0.200	Original	0.006	0.884	35.709	78.604	0.013	…	0.125	0.201	0.337	1	1
0.100	0.050	0.200	Conservative	0.049	0.913	43.429	86.933	0.068	…	0.638	0.656	0.804	0.881	0.910
0.050	0.100	0.200	Original	0.790	0.148	27.484	22.238	0	…	0.008	0.044	0.143	1	1	1	1	1
0.050	0.100	0.200	Conservative	0.0001	0.093	16.726	22.438	0.00001	…	0.002	0.002	0.002	0.002	0.012	0.057	0.185	1
0.100	0.100	0.200	Original	0.001	0.188	13.813	20.689	0.001	…	0.226	1	1	1	1
0.100	0.100	0.200	Conservative	0.001	0.219	15.633	22.557	0.001	…	0.004	0.004	0.025	0.086	0.185
0.050	0.050	0.250	Original	0.049	0.937	54.563	85.193	0.013	…	0.125	0.201	0.337	1	1
0.050	0.050	0.250	Conservative	0.050	0.948	64.667	92.219	0.068	…	0.638	0.656	0.804	0.881	0.910
0.100	0.050	0.250	Original	0.049	0.909	52.961	83.088	0.037	…	0.537	1	1
0.100	0.050	0.250	Conservative	0.050	0.918	61.160	90.499	0.116	…	0.839	0.921	0.946
0.050	0.100	0.250	Original	0.011	0.376	16.512	21.979	0.001	…	0.226	1	1	1	1
0.050	0.100	0.250	Conservative	0.016	0.403	18.859	23.531	0.001	…	0.004	0.004	0.025	0.086	0.185
0.100	0.100	0.250	Original	0.035	0.517	15.904	21.446	0.001	…	1	1	1
0.100	0.100	0.250	Conservative	0.040	0.607	18.026	23.348	0.030	…	0.043	0.153	0.337
0.050	0.050	0.300	Original	0.050	0.926	66.975	86.330	0.064	…	0.277	0.376	0.570	1	1
0.050	0.050	0.300	Conservative	0.050	0.938	75.364	94.102	0.053	…	0.878	0.950	0.975	0.979	0.993
0.100	0.050	0.300	Original	0.049	0.890	62.925	81.433	0.047	…	0.794	1	1
0.100	0.050	0.300	Conservative	0.050	0.901	68.827	90.501	0.063	…	0.984	0.991	0.998
0.050	0.100	0.300	Original	0.040	0.524	18.393	22.065	0.009	…	0.410	1	1	1	1
0.050	0.100	0.300	Conservative	0.048	0.571	20.558	24.042	0.013	…	0.044	0.044	0.134	0.264	0.344
0.100	0.100	0.300	Original	0.021	0.404	17.416	20.829	0.053	…	1	1	1
0.100	0.100	0.300	Conservative	0.049	0.572	19.230	23.517	0.044	…	0.211	0.415	0.570

A summary of the optimal choices of the D(s₁), along with the associated type-I error-rate, P(π₀), and power, P(π₁), are shown for a range of values of β₁,γ, and π₁. In all cases, π₀=π₁−0.15. Note that D(0) is not listed as it is zero in all instances. All values D(s₁)∈(0,1) are given to 4 decimal places

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ISSN: 1471-2288

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