  Multiple diagnostic tests are often used due to limited resources or because
they provide complementary information on the epidemiology of a disease under
investigation. Existing statistical methods to combine prevalence data from
multiple diagnostics ignore the potential over-dispersion induced by the
spatial correlations in the data. To address this issue, we develop a
geostatistical framework that allows for joint modelling of data from multiple
diagnostics by considering two main classes of inferential problems: (1) to
predict prevalence for a gold-standard diagnostic using low-cost and
potentially biased alternative tests; (2) to carry out joint prediction of
prevalence from multiple tests. We apply the proposed framework to two case
studies: mapping Loa loa prevalence in Central and West Africa, using
miscroscopy and a questionnaire-based test called RAPLOA; mapping Plasmodium
falciparum malaria prevalence in the highlands of Western Kenya using
polymerase chain reaction and a rapid diagnostic test. We also develop a Monte
Carlo procedure based on the variogram in order to identify parsimonious
geostatistical models that are compatible with the data. Our study highlights
(i) the importance of accounting for diagnostic-specific residual spatial
variation and (ii) the benefits accrued from joint geostatistical modelling so
as to deliver more reliable and precise inferences on disease prevalence.
