Table 1.

Locally optimal design (LOD) at known parameter value ρ in working correlation matrix for two-sample study with c = 100, and s = 50

ρ	nLOD	mLOD	(1 − β)LOD	nup	mup	(1 − β)up	Bup	ndown	mdown	(1 − β)down	Bdown
B = 15,000$; p0 = 0.1, p1 = 0.3
0.1	4.2	48.1	0.893	5	42	0.885	14700	4	50	0.893	15000
0.2	2.8	62.1	0.834	3	60	0.833	15000	2	75	0.823	15000
0.3	2.2	72.1	0.793	3	60	0.782	15000	2	75	0.792	15000
0.4	1.7	80.4	0.764	2	75	0.762	15000	1	100	0.733	15000
0.5	1.4	87.9	0.745	2	75	0.733	15000	1	100	0.733	15000
0.6	1.2	95.1	0.735	2	75	0.705	15000	1	100	0.733	15000
0.7	0.9	102.5	0.734	1	100	0.733	15000	NA
0.8	0.7	110.8	0.743	1	100	0.733	15000	NA
0.9	0.5	121.4	0.770	1	100	0.733	15000	NA
B = 20,000$; p0 = 0.1, p1 = 0.3
0.1	4.2	64.1	0.959	5	57	0.958	19950	4	66	0.957	19800
0.2	2.8	82.8	0.923	3	80	0.922	20000	2	100	0.915	20000
0.3	2.2	96.1	0.893	3	80	0.885	20000	2	100	0.893	20000
0.4	1.7	107.2	0.872	2	100	0.870	20000	1	133	0.846	19950
0.5	1.4	117.2	0.857	2	100	0.846	20000	1	133	0.846	19950
0.6	1.2	126.8	0.848	2	100	0.823	20000	1	133	0.846	19950
0.7	0.9	136.7	0.847	1	133	0.846	19950	NA
0.8	0.7	147.8	0.855	1	133	0.846	19950	NA
0.9	0.5	161.9	0.876	1	133	0.846	19950	NA

n_up = int(n_LOD) + 1, $m_{\text{up}}=int(\frac{B}{c+s{n}_{\text{up}}})$; n_down = int(n_LOD), $m_{\text{down}}=int(\frac{B}{c+s{n}_{\text{down}}})$; int=an integer part of a number; (1 − β)_up and B_up, (1 − β)_down and B_down are actual power and needed budget based on (n_up, m_up) and (n_down, m_down), respectively; Bold refers to the proposed optimal sample size and number of repeated measures with larger power between (n_up, m_up) and (n_down, m_down); NA = Not Applicable.