Modelling Spatio-temporal Patterns of Disease for Spatially Misaligned Data: An Application on Measles Incidence Data in Namibia from 2005-2014

PLoS ONE. 2018, 13(8): e0201700.


Making inferences about measles distribution patterns at small area level is vital for more focal targeted intervention. However, in statistical literature, the analysis of originally collected data on one resolution with the purpose to make inferences on a different level of spatial resolution is referred to as the misalignment problem. In Namibia the measles data were available in aggregated format at regional level for the period 2005 to 2014. This leads to a spatial misalignment problem if the purpose is to make decisions at constituency level. Moreover, although data on risk covariates of measles could be obtained at constituency level, they were not available each year between 2005 and 2014. Thus, assuming that covariates were constant through the study period would induce measurement errors which might have effects on the analysis results. This paper presents a spatio-temporal model through a multi-step approach in order to deal with misalignment and measurement error.


For the period 2005-2014, measles data from the Ministry of Health and Social Services (MoHSS) were analysed in two steps. First, a multi-step approach was applied to correct spatial misalignment in the data. Second, a classical measurement error model was fitted to account for measurement errors. The time effects were specified using a nonparametric formulation for the linear trend through first order random walk. An interaction between area and time was modelled through type I and type II interaction structures.


The study showed that there was high variation in measles risk across constituencies and as well as over the study period (2005-2014). Furthermore, the risk of measles was found to be associated with (i) the number of people aged between 0 and 24 years, (ii) the percentages of women aged 15-49 with an educational level more than secondary, (iii) the percentages of children age 12-23 months who received measles vaccine, (iv) the percentages of malnourished children under 5 years, and (vi) the measles cases for each previous year.


The study showed some of the determinants of measles risk and revealed areas at high risk through disease mapping. Additionally, the study showed a non-linear temporal distribution of measles risk over the study period. Finally, it was shown that ignoring the measurement errors may yield misleading results. It was recommended that group and geographically targeted intervention, prevention and control strategies can be tailored on the basis these findings.

D. Ntirampeba, I. Neema, LN. Kazembe