  The COVID-19 pandemic has caused severe public health consequences in the
United States. In this study, we use a hierarchical Bayesian model to estimate
the age-specific COVID-19 attributable deaths over time in the United States.
The model is specified by a novel non-parametric spatial approach, a low-rank
Gaussian Process (GP) projected by regularised B-splines. We show that this
projection defines a new GP with attractive smoothness and computational
efficiency properties, derive its kernel function, and discuss the penalty
terms induced by the projected GP. Simulation analyses and benchmark results
show that the spatial approach performs better than standard B-splines and
Bayesian P-splines and equivalently well as a standard GP, for considerably
lower runtimes. The B-splines projected GP priors that we develop are likely an
appealing addition to the arsenal of Bayesian regularising priors. We apply the
model to weekly, age-stratified COVID-19 attributable deaths reported by the US
Centers for Disease Control, which are subject to censoring and reporting
biases. Using the B-splines projected GP, we can estimate longitudinal trends
in COVID-19 associated deaths across the US by 1-year age bands. These
estimates are instrumental to calculate age-specific mortality rates, describe
variation in age-specific deaths across the US, and for fitting epidemic
models. Here, we couple the model with age-specific vaccination rates to show
that lower vaccination rates in younger adults aged 18-64 are associated with
significantly stronger resurgences in COVID-19 deaths, especially in Florida
and Texas. These results underscore the critical importance of medically able
individuals of all ages to be vaccinated against COVID-19 in order to limit
fatal outcomes.
