  Estimates of the under-five mortality rate (U5MR) are used to track progress
in reducing child mortality and to evaluate countries' performance related to
Millennium Development Goal 4. However, for the great majority of developing
countries without well-functioning vital registration systems, estimating the
U5MR is challenging due to limited data availability and data quality issues.
We describe a Bayesian penalized B-spline regression model for assessing levels
and trends in the U5MR for all countries in the world, whereby biases in data
series are estimated through the inclusion of a multilevel model to improve
upon the limitations of current methods. B-spline smoothing parameters are also
estimated through a multilevel model. Improved spline extrapolations are
obtained through logarithmic pooling of the posterior predictive distribution
of country-specific changes in spline coefficients with observed changes on the
global level. The proposed model is able to flexibly capture changes in U5MR
over time, gives point estimates and credible intervals reflecting potential
biases in data series and performs reasonably well in out-of-sample validation
exercises. It has been accepted by the United Nations Inter-agency Group for
Child Mortality Estimation to generate estimates for all member countries.
