Child mortality estimation incorporating summary birth history data

The United Nations' Sustainable Development Goal 3.2 aims to reduce under-five child mortality to 25 deaths per 1000 live births by 2030. Child mortality tends to be concentrated in developing regions where information needed to assess achievement of this goal often comes from surveys and censuses. In both, women are asked about their birth histories, but with varying degrees of detail. Full birth history (FBH) data contain the reported dates of births and deaths of every surveyed mother's children. In contrast, summary birth history (SBH) data contain only the total number of children born and total number of children who died for each mother. Specialized methods are needed to accommodate this type of data into analyses of child mortality trends. We develop a data augmentation scheme within a Bayesian framework where for SBH data, birth and death dates are introduced as auxiliary variables. Since we specify a full probability model for the data, many of the well-known biases that exist in this data can be accommodated, along with space-time smoothing on the underlying mortality rates. We illustrate our approach in a simulation, showing robustness to model misspecification and that uncertainty is reduced when incorporating SBH data over simply analyzing all available FBH data. We also apply our approach to data from the Central region of Malawi and compare with the well-known Brass method.