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

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.