Distance sampling for epidemiology: an interactive tool for estimating under-reporting of cases from clinic data

Distance sampling methods are widely used in ecology to estimate and map the abundance of animal and plant populations from spatial survey data. The key underlying concept in distance sampling is the detection function, the probability of detecting the occurrence of an event as a function of its distance from the observer, as well as other covariates that may influence detection. In epidemiology, the burden and distribution of infectious disease is often inferred from cases that are reported at clinics and hospitals. In areas with few public health facilities and low accessibility, the probability of detecting a case is also a function of the distance between an infected person and the "observer" (e.g. a health centre). While the problem of distance-related under-reporting is acknowledged in public health; there are few quantitative methods for assessing and correcting for this bias when mapping disease incidence. Here, we develop a modified version of distance sampling for prediction of infectious disease incidence by relaxing some of the framework's fundamental assumptions. We illustrate the utility of this approach using as our example malaria distribution in rural Burkina Faso, where there is a large population at risk but relatively low accessibility of health facilities.

The modified distance-sampling framework was used to predict the probability of reporting malaria infection at 8 rural clinics, based on road-travel distances from villages. The rate at which reporting probability dropped with distance varied between clinics, depending on road and clinic positions. The probability of case detection was estimated as 0.3-1 in the immediate vicinity of the clinic, dropping to 0.1-0.6 at a travel distance of 10 km, and effectively zero at distances > 30-40 km.

To enhance the method's strategic impact, we provide an interactive mapping tool (as a self-contained R Shiny app) that can be used by non-specialists to interrogate model outputs and visualize how the overall probability of under-reporting and the catchment area of each clinic is influenced by changing the number and spatial allocation of health centres.