Small Area Estimation of Child Mortality in the Absence of Vital Registration

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. Conventional hierarchical models are not immediately applicable since one must account for the survey weights in order to alleviate bias due to non-random sampling and non-response. The application that motivated this work is estimation of child mortality rates in five-year time intervals in regions of Tanzania. Data come from Demographic and Health Surveys (DHS) conducted over the period 1980–2010 and two demographic surveillance system sites. We derive a variance estimator that accounts for the complex survey weighting, and a simulation study examines the properties of our estimator, with a comparison to a jackknife alternative. For our application, the hierarchical models we consider include random effects for area, time and survey and we compare models using the conditional predictive ordinate (CPO). The method we propose is implemented via the fast and accurate integrated nested Laplace approximation (INLA).