Exploratory Analysis For Spatio-Temporal Epidemiological Data Web App (Spatial)

Abstract

This online application implements statistical methods to analyse spatio-temporal data considering lattice data to describe the space. It allows the user to create the data for analysis based on spatial files (shape files zipped), which could contain potential information on risk factors/covariates, temporal information based for example on, outbreak data or surveillance reports as well as data containing potential risk factors that have been recorded. Once the different data sources have been merged within the application using specific index variables that identifies space and temporal resolution to be used in the analysis and for which information have been recorded, an exploratory analysis using descriptive statistics over space and time can be performed. The exploratory analyses provide the user the possibility to estimate local statistics such as: Moran's I and Geary's C, which could aid to recognize potential clusters and hotspots. Smoothed predictions over space and time can be calculated and visualized using ordinary kriging. Furthermore, two models have been also implemented, considering the binomial nature of the response (Logistic regression models). These models allow the user to include spatial and temporal effects, spatio-temporal interactions as well as potential covariates. The implemented models are, the Bayesian hierarchical models and generalized additive models considering several model structures that could be compared using model diagnostics. The Bayesian Hierarchical Model deals with data that is collected across space and time, taking into account the spatial andtemporal dependence of the observations. The linear component of the spatio-temporal model for the binary data is written including a random effect accommodating temporal dependence, and another one to account for spatial dependence, as well as the possibility to include potential interactions between space and time. The implementation considers the model structure proposed by Besag, York and Mollie's (BYM). The BYM model takes into account not only the spatial auto-correlation present in the data, but it also assumes that the estimates obtained between areas are dependent of each other. The spatial effect of the BYM model assumes that the expected value of each area depends on the values of the neighbouring areas (areas sharing boundaries). Thus, areas close together are considered to be more similar than areas that are far apart. In this application, it was assumed that the structured and unstructured effects are not independent of each other as it is described by Riebler et al, 2016. Thus, the model was written considering a mixture formulation in which it reduces to pure over dispersion (spatially unstructured), if the mixture parameter is estimated to be 0, or to the intrinsic conditionally autoregressive (ICAR)/Besag model when the mixture parameter is equal to 1. Thus, the proportion of the marginal variance explained by the spatial effect is given by the mixture parameter. The Generalized Additive Model (GAM) is a linear model that allows for response distributions other than normal and whose linear predictor involves a sum of smooth functions. In that way, the model allows for rather flexible specification of the dependence between response and non-responses. The GAM spatio-temporal model includes a term that models the space as well as time patterns (considering several possibilities, such as linear, saturated, smoothed, etc.). The model could include covariates as linear, saturated or smoothed effects. The spatial correlation implemented is approximated by a Markov random field (MRF) smoother. This smoother was defined by lattice regions and a neighborhood structure defined within the application. A full rank MRF, with a coefficient for each lattice region is constructed and used in the model. The R-package mgcv was used where estimation is based on quadratically penalized (possibly quasi-)likelihood maximization. More information on the GAM models can be found in Wood (2006). Summary measures for the estimated response values can be visualized over space and time. An interactive component guides the user in uploading data, performing an exploratory analysis and fitting spatio-temporal models.