  The United Nations' Sustainable Development Goal 3.2 aims to reduce under-5
child mortality to 25 deaths per 1,000 live births by 2030. Child mortality
tends to be concentrated in developing regions where much of the information
needed to assess achievement of this goal 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 that uncertainty is reduced when incorporating SBH data over simply
analyzing all available FBH data. We also apply our approach to data in the
Central region of Malawi. We compare with the well-known Brass method.
