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Table 2 Summary of the important parameters and abbreviations defined

From: Analysis of contamination in cluster randomized trials of malaria interventions

\(\tilde {E}_{s},\,\tilde {p}_{I},\,\tilde {p}_{C}\)

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)

\(\mathcal {S}_{RE}\)

Sigmoid random effects model (allowing for contamination and including random effects)

β1, β2, β3

Parameters for \(\mathcal {S}\) and \(\mathcal {S}_{RE}\), describing the position, height and steepness of the function

\(\hat {E}_{s},\,\hat {p}_{I},\,\hat {p}_{C}\)

Effectiveness and prevalences in the intervention and control arm

 

for \(\mathcal {S}\) or \(\mathcal {S}_{RE}\) (allowing for contamination)

\(\hat {\theta }\)

Estimated contamination range from \(\mathcal {S}\) or \(\mathcal {S}_{RE}\)

μ, τ

Hyperparameters for the Bayesian hierarchical model \(\mathcal {S}_{RE}\)

ω

Percentage of households in core, that is households whose distance to the discordant arm is greater than \(\hat {\theta }\) (ignoring assignment to arms)