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) |