Table 2.

Summary of the important parameters and abbreviations defined

${\tilde{E}}_s,{\tilde{p}}_I,{\tilde{p}}_C$	Effectiveness and prevalences in the intervention and control arm (ignoring contamination)
Δij	Distance of jth household in the ith cluster to nearest discordant household
$\mathcal{S}$	Sigmoid model (allowing for contamination)
${\mathcal{S}}_{\mathit{\text{RE}}}$	Sigmoid random effects model (allowing for contamination and including random effects)
β1, β2, β3	Parameters for $\mathcal{S}$ and ${\mathcal{S}}_{\mathit{\text{RE}}}$, describing the position, height and steepness of the function
${Ê}_s,{\widehat{p}}_I,{\widehat{p}}_C$	Effectiveness and prevalences in the intervention and control arm
	for $\mathcal{S}$ or ${\mathcal{S}}_{\mathit{\text{RE}}}$ (allowing for contamination)
$\widehat{\theta }$	Estimated contamination range from $\mathcal{S}$ or ${\mathcal{S}}_{\mathit{\text{RE}}}$
μ, τ	Hyperparameters for the Bayesian hierarchical model ${\mathcal{S}}_{\mathit{\text{RE}}}$
ω	Percentage of households in core, that is households whose distance to the discordant arm is greater than $\widehat{\theta }$ (ignoring assignment to arms)