  Data from multiple prevalence surveys can provide information on common
parameters of interest, which can therefore be estimated more precisely in a
joint analysis than by separate analyses of the data from each survey. However,
fitting a single model to the combined data from multiple surveys is
inadvisable without testing the implicit assumption that all of the surveys are
directed at the same inferential target. In this paper we propose a
multivariate generalized linear geostatistical model that accommodates two
sources of heterogeneity across surveys so as to correct for spatially
structured bias in non-randomised surveys and to allow for temporal variation
in the underlying prevalence surface between consecutive survey-periods. We
describe a Monte Carlo maximum likelihood procedure for parameter estimation,
and show through simulation experiments how accounting for the different
sources of heterogeneity among surveys in a joint model leads to more precise
inferences. We describe an application to multiple surveys of malaria
prevalence conducted in Chikhwawa District, Southern Malawi, and discuss how
this approach could inform hybrid sampling strategies that combine data from
randomised and non-randomised surveys so as to make the most efficient use of
all available data.
