  Many people living in low- and middle-income countries are not covered by
civil registration and vital statistics systems. Consequently, a wide variety
of other types of data, including many household sample surveys, are used to
estimate health and population indicators. In this paper we combine data from
sample surveys and demographic surveillance systems to produce small area
estimates of child mortality through time. Small area estimates are necessary
to understand geographical heterogeneity in health indicators when
full-coverage vital statistics are not available. For this endeavor
spatio-temporal smoothing is beneficial to alleviate problems of data sparsity.
The use of conventional hierarchical models requires careful thought since the
survey weights may need to be considered to alleviate bias due to nonrandom
sampling and nonresponse. The application that motivated this work is an
estimation of child mortality rates in five-year time intervals in regions of
Tanzania. Data come from Demographic and Health Surveys conducted over the
period 1991-2010 and two demographic surveillance system sites. We derive a
variance estimator of under five years child mortality that accounts for the
complex survey weighting. For our application, the hierarchical models we
consider include random effects for area, time and survey and we compare models
using a variety of measures including the conditional predictive ordinate
(CPO). The method we propose is implemented via the fast and accurate
integrated nested Laplace approximation (INLA).
