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The COVID-19 pandemic has caused severe public health consequences in theUnited States. In this study, we use a hierarchical Bayesian model to estimatethe 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-rankGaussian Process (GP) projected by regularised B-splines. We show that thisprojection defines a new GP with attractive smoothness and computationalefficiency properties, derive its kernel function, and discuss the penaltyterms induced by the projected GP. Simulation analyses and benchmark resultsshow that the spatial approach performs better than standard B-splines andBayesian P-splines and equivalently well as a standard GP, for considerablylower runtimes. The B-splines projected GP priors that we develop are likely anappealing addition to the arsenal of Bayesian regularising priors. We apply themodel to weekly, age-stratified COVID-19 attributable deaths reported by the USCenters for Disease Control, which are subject to censoring and reportingbiases. Using the B-splines projected GP, we can estimate longitudinal trendsin COVID-19 associated deaths across the US by 1-year age bands. Theseestimates are instrumental to calculate age-specific mortality rates, describevariation in age-specific deaths across the US, and for fitting epidemicmodels. Here, we couple the model with age-specific vaccination rates to showthat lower vaccination rates in younger adults aged 18-64 are associated withsignificantly stronger resurgences in COVID-19 deaths, especially in Floridaand Texas. These results underscore the critical importance of medically ableindividuals of all ages to be vaccinated against COVID-19 in order to limitfatal outcomes.

Regularised B-splines projected Gaussian Process priors to estimate time-trends of age-specific COVID-19 deaths related to vaccine roll-out