Joint spatial Bayesian modeling for studies combining longitudinal and cross-sectional data.

Design for intervention studies may combine longitudinal data collected from sampled locations over several survey rounds and cross-sectional data from other locations in the study area. In this case, modeling the impact of the intervention requires an approach that can accommodate both types of data, accounting for the dependence between individuals followed up over time. Inadequate modeling can mask intervention effects, with serious implications for policy making. In this paper we use data from a large-scale larviciding intervention for malaria control implemented in Dar es Salaam, United Republic of Tanzania, collected over a period of almost 5 years. We apply a longitudinal Bayesian spatial model to the Dar es Salaam data, combining follow-up and cross-sectional data, treating the correlation in longitudinal observations separately, and controlling for potential confounders. An innovative feature of this modeling is the use of Ornstein-Uhlenbeck process to model random time effects. We contrast the results with other Bayesian modeling formulations, including cross-sectional approaches that consider individual-level random effects to account for subjects followed up in two or more surveys. The longitudinal modeling approach indicates that the intervention significantly reduced the prevalence of malaria infection in Dar es Salaam by 20% whereas the joint model did not suggest significance within the results. Our results suggest that the longitudinal model is to be preferred when longitudinal information is available at the individual level.