Variability in mosquito density and protective efficacy across houses and weeks: an arbitrary house-week analysis
The interval estimates presented above refer to an average situation, corresponding to a hypothetical house and week being the average over all the houses and weeks seen in the trial (average house-week). For a very large field study such average estimates would be very narrow (assuming the model to be well specified), which might mistakenly be interpreted as a uniform effect across houses and weeks. However, the hierarchical, multilevel Bayesian analysis also provides predictions of the mosquito density and the protective efficacy that is expected for an arbitrary house and week in the field (arbitrary house-week), based on the variability over houses and weeks seen in the field trial. The interval estimate for an arbitrary house-week will always show considerable uncertainty no matter how big the study is, reflecting the high variability of mosquito densities and of intervention effectiveness in reality. In other words, if potential users of the intervention ask how much it will reduce the mosquito density at their house, they should be communicated the interval estimates (HDI) for an arbitrary house-week (given no specific relevant information about them or their house is available), and not the interval estimate (HDI) for an average house-week (which may not even exist in the field). Interval estimates with respect to an arbitrary house-week are graphically displayed in Figs. As shown by the left-hand side graphs in Figs. As shown by the right-hand side charts in Figs. 