Table 5.

Optimal design (OD) at unknown parameter value ρ in working correlation matrix for two-sample study with B = 15,000$, c = 100, and s = 20

ρ	nLOD	mLOD	(1 − β)LOD	$n_{\mathit{min}}^{\ast }$	$m_{\mathit{min}}^{\ast }$	${(1-\beta )}_{\mathit{min}}^{\ast }$	$n_{\mathit{max}}^{\ast }$	$m_{\mathit{max}}^{\ast }$	${(1-\beta )}_{\mathit{max}}^{\ast }$	$n_{\text{LOD}}^{\prime }$	$m_{\text{LOD}}^{\prime }$	${(1-\beta )}_{\text{LOD}}^{\prime }$
0.05	9.7	50.9	0.998	10	50	0.998	9	53	0.997	10	50	0.998
0.1	6.7	64.1	0.990	7	62	0.989	6	68	0.989	6	68	0.989
0.15	5.3	72.7	0.977	6	68	0.976	5	75	0.977	5	75	0.977
0.2	4.5	79.2	0.962	5	75	0.961	4	83	0.961	5	75	0.961
0.25	3.9	84.5	0.946	145	5	0.207	4	80	0.937	4	80	0.937
0.3	3.4	89.1	0.929	145	5	0.180	4	80	0.918	4	80	0.918
0.35	3.0	93.2	0.913	145	5	0.161	4	80	0.897	4	80	0.897

(ρ_min, ρ_max) = (0.05, 0.35) and (m_min, m_max) = (5, 80).

For m_LOD ∈ (m_min, m_max), $n_{\mathit{min}}^{\ast }=n_{\text{up}},m_{\mathit{min}}^{\ast }=m_{\text{up}},n_{\mathit{max}}^{\ast }=n_{\text{down}}$ and $m_{\mathit{max}}^{\ast }=m_{\text{down}};n_{\mathit{min}}^{\ast }=n_{min},m_{\mathit{min}}^{\ast }=m_{min},n_{\mathit{max}}^{\ast }=n_{max}$ and $m_{\mathit{max}}^{\ast }=m_{max}$.