Spatially varying auto-regressive models for prediction of new human immunodeficiency virus diagnoses

Modeling geostatistical incomplete spatially correlated survival data with applications to COVID-19 mortality in Ghana

Survival models which incorporate frailties are common in time-to-event data collected over distinct spatial regions. While incomplete data are unavoidable and a common complication in statistical analysis of spatial survival research, most researchers still ignore the missing data problem. In this paper, we propose a geostatistical modeling approach for incomplete spatially correlated survival data. We achieve this by exploring missingness in outcome, covariates, and spatial locations. In the process, we analyze incomplete spatially-referenced survival data using a Weibull model for the baseline hazard function and correlated log-Gaussian frailties to model spatial correlation. We illustrate the proposed method with simulated data and an application to geo-referenced COVID-19 data from Ghana. There are several disagreements between parameter estimates and credible intervals widths obtained using our proposed approach and complete case analysis. Based on these findings, we argue that our approach provides more reliable parameter estimates and has higher predictive accuracy.

Asynchronous Changepoint Estimation for Spatially Correlated Functional Time Series

We propose a new solution under the Bayesian framework to simultaneously estimate mean-based asynchronous changepoints in spatially correlated functional time series. Unlike previous methods that assume a shared changepoint at all spatial locations or ignore spatial correlation, our method treats changepoints as a spatial process. This allows our model to respect spatial heterogeneity and exploit spatial correlations to improve estimation. Our method is derived from the ubiquitous cumulative sum (CUSUM) statistic that dominates changepoint detection in functional time series. However, instead of directly searching for the maximum of the CUSUM-based processes, we build spatially correlated two-piece linear models with appropriate variance structure to locate all changepoints at once. The proposed linear model approach increases the robustness of our method to variability in the CUSUM process, which, combined with our spatial correlation model, improves changepoint estimation near the edges. We demonstrate through extensive simulation studies that our method outperforms existing functional changepoint estimators in terms of both estimation accuracy and uncertainty quantification, under either weak or strong spatial correlation, and weak or strong change signals. Finally, we demonstrate our method using a temperature data set and a coronavirus disease 2019 (COVID-19) study. Supplementary materials accompanying this paper appear online. Supplementary materials for this article are available at 10.1007/s13253-022-00519-w.

A Model for Highly Fluctuating Spatio-Temporal Infection Data, with Applications to the COVID Epidemic

Spatio-temporal models need to address specific features of spatio-temporal infection data, such as periods of stable infection levels (endemicity), followed by epidemic phases, as well as infection spread from neighbouring areas. In this paper, we consider a mixture-link model for infection counts that allows alternation between epidemic phases (possibly multiple) and stable endemicity, with higher AR1 coefficients in epidemic phases. This is a form of regime-switching, allowing for non-stationarity in infection levels. We adopt a generalised Poisson model appropriate to the infection count data and avoid transformations (e.g., differencing) to alternative metrics, which have been adopted in many studies. We allow for neighbourhood spillover in infection, which is also governed by adaptive regime-switching. Compared to existing models, the observational (in-sample) model is expected to better reflect the balance between epidemic and endemic tendencies, and short-term extrapolations are likely to be improved. Two case study applications involve COVID area-time data, one for 32 London boroughs (and 96 weeks) since the start of the COVID epidemic, the other for a shorter time span focusing on the epidemic phase in 144 areas of Southeast England associated with the Alpha variant. In both applications, the proposed methods produce a better in-sample fit and out-of-sample short term predictions. The spatial dynamic implications are highlighted in the case studies.

A spatio-temporal autoregressive model for monitoring and predicting COVID infection rates

The COVID-19 epidemic has raised major issues with regard to modelling and forecasting outcomes such as cases, deaths and hospitalisations. In particular, the forecasting of area-specific counts of infectious disease poses problems when counts are changing rapidly and there are infection hotspots, as in epidemic situations. Such forecasts are of central importance for prioritizing interventions or making severity designations for different areas. In this paper, we consider different specifications of autoregressive dependence in incidence counts as these may considerably impact on adaptivity in epidemic situations. In particular, we introduce parameters to allow temporal adaptivity in autoregressive dependence. A case study considers COVID-19 data for 144 English local authorities during the UK epidemic second wave in late 2020 and early 2021, which demonstrate geographical clustering in new cases-linked to the then emergent alpha variant. The model allows for both spatial and time variation in autoregressive effects. We assess sensitivity in short-term predictions and fit to specification (spatial vs space-time autoregression, linear vs log-linear, and form of space decay), and show improved one-step ahead and in-sample prediction using space-time autoregression including temporal adaptivity.

Are spatial models advantageous for predicting county-level HIV epidemiology across the United States?

Predicting human immunodeficiency virus (HIV) epidemiology is vital for achieving public health milestones. Incorporating spatial dependence when data varies by region can often provide better prediction results, at the cost of computational efficiency. However, with the growing number of covariates available that capture the data variability, the benefit of a spatial model could be less crucial. We investigate this conjecture by considering both non-spatial and spatial models for county-level HIV prediction over the US. Due to many counties with zero HIV incidences, we utilize a two-part model, with one part estimating the probability of positive HIV rates and the other estimating HIV rates of counties not classified as zero. Based on our data, the compound of logistic regression and a generalized estimating equation outperforms the candidate models in making predictions. The results suggest that considering spatial correlation for our data is not necessarily advantageous when the purpose is making predictions.