A spatio-temporal statistical model to analyze COVID-19 spread in the USA

Abstract

Coronavirus pandemic has affected the whole world extensively and it is of immense importance to understand how the disease is spreading. In this work, we provide evidence of spatial dependence in the pandemic data and accordingly develop a new statistical technique that captures the spatio-temporal dependence pattern of the COVID-19 spread appropriately. The proposed model uses a separable Gaussian spatio-temporal process, in conjunction with an additive mean structure and a random error process. The model is implemented through a Bayesian framework, thereby providing a computational advantage over the classical way. We use state-level data from the United States of America in this study. We show that a quadratic trend pattern is most appropriate in this context. Interestingly, the population is found not to affect the numbers significantly, whereas the number of deaths in the previous week positively affects the spread of the disease. Residual diagnostics establish that the model is adequate enough to understand the spatio-temporal dependence pattern in the data. It is also shown to have superior predictive power than other spatial and temporal models. In fact, we show that the proposed approach can predict well for both short term (1 week) and long term (up to three months).

Methods Used in the Spatial and Spatiotemporal Analysis of COVID-19 Epidemiology: A Systematic Review

“…GLMM with Separable Gaussian spatiotemporal process: Rawat et al, 2021 [ 179 ] proposed a model structure that includes a separable Gaussian spatial-temporal process model implemented through a Bayesian framework, in conjunction with an additive mean structure and a random error process to estimate the relative risk of COVID-19. The spatial and temporal trends both follow an exponentially decaying pattern.…”

“…The models with the lowest DIC or WAIC values were chosen as the best-adjusted models. Some of the other model selection criteria used in the studies were the Bayesian cross-validation criterion (BCV) [ 174 ], mean absolute percentage error (MAPE) [ 179 ], Root Mean Squared Error (RMSE) [ 179 ], Continuous Ranked Probability Score (CRPS) [ 179 ], highest probability (HPM) [ 181 ], and best prediction (BPM) [ 181 ] to select the best model ( Table 2 ). Results reported were generally based on the best model selected using these criteria.…”

“…Most of the studies have used a Poisson-based modelling approach where data was assumed to have Poisson distribution. A novel separable Gaussian spatiotemporal model proposed by Rawat et al, 2021 [ 179 ] included an appropriately specified space-time process that provided an advantage of predicting the response variable for any spatial location and at any time point, even if it is unobserved within the data.…”

A Review of Bayesian Spatiotemporal Models in Spatial Epidemiology

“…Bayesian spatiotemporal models have been widely utilized for COVID-19 analysis and forecasting globally, including in the United States [100][101][102], England [103,104], Spain, Italy, Germany, Sweden [87,[105][106][107], Africa [108], and in some regional areas such as the West Java Province, Indonesia [109], and the Greater Seoul Area, Korea [110]. As an illustration, Nazia et al [111] applied a Bayesian hierarchical spatiotemporal model to assess the COVID-19 risk.…”

Reproduction number projection for the COVID-19 pandemic

“…For HI-STR projection, the delay is of less significance. Potential SIPs are recognised by demonstrable distinct regional pandemic characteristics [23,[216][217][218][219] instead.…”