Table 2.

Optimal allocation matrices for cohort designs with D = 2. The optimal allocation matrices in the case $\mathfrak{I}=\{6\}$, $\mathfrak{C}=\{{\mathfrak{C}}_6\}=\{10\}$, $\mathfrak{M}={\mathfrak{M}}_{10,6}=\{10\}$, and σ ² = 1, with w = 0 and β = 1 are shown for a range of possible combinations of ρ ₀, ρ ₁, and ρ ₂. Restrictions are placed on $\mathfrak{X}$ such that Equation (1) is identifiable and that each cluster must start in the control intervention (arm 0) and conclude in the experimental intervention (arm 1). Each allocation matrix was identified via our exhaustive search method

Factor		Results
ρ 0		0.050	0.050	0.050	0.050
ρ 1		0.001	0.001	0.002	0.002
ρ 2		0.250	0.500	0.250	0.500
X		$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\end{array}\right)$	$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\end{array}\right)$	$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\end{array}\right)$	$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\end{array}\right)$
${\mathit{p}}_{\text{th}}^{\top }$		(0.30,0.08,0.08,0.08,0.30)	(0.24,0.10,0.10,0.10,0.24)	(0.29,0.08,0.08,0.08,0.29)	(0.24,0.10,0.10,0.10,0.24)
${\mathit{p}}_{\text{emp}}^{\top }$		(0.4,0.1,0.1,0.1,0.3)	(0.3,0.1,0.2,0.1,0.3)	(0.4,0.1,0.1,0.1,0.3)	(0.3,0.1,0.2,0.1,0.3)
ρ 0		0.100	0.100	0.100	0.100
ρ 1		0.001	0.001	0.002	0.002
ρ 2		0.250	0.500	0.250	0.500
X		$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\end{array}\right)$	$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\end{array}\right)$	$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\end{array}\right)$	$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 1& 1& 1\\ 0& 0& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1\end{array}\right)$
${\mathit{p}}_{\text{th}}^{\top }$		(0.32,0.07,0.07,0.07,0.32)	(0.26,0.10,0.10,0.10,0.26)	(0.31,0.07,0.07,0.07,0.31)	(0.26,0.10,0.10,0.10,0.26)
${\mathit{p}}_{\text{emp}}^{\top }$		(0.4,0.1,0,0.1,0.4)	(0.3,0.1,0.2,0.1,0.3)	(0.4,0.1,0,0.1,0.4)	(0.3,0.1,0.2,0.1,0.3)