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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)