sparr: Analyzing Spatial Relative Risk Using Fixed and Adaptive Kernel Density Estimation in R

The estimation of kernel-smoothed relative risk functions is a useful approach to examining the spatial variation of disease risk. Though there exist several options for performing kernel density estimation in statistical software packages, there have been very few contributions to date that have focused on estimation of a relative risk function per se . Use of a variable or adaptive smoothing parameter for estimation of the individual densities has been shown to provide additional benefits in estimating relative risk and specific computational tools for this approach are essentially absent. Furthermore, little attention has been given to providing methods in available software for any kind of subsequent analysis with respect to an estimated risk function. To facilitate analyses in the field, the R package sparr is introduced, providing the ability to construct both fixed and adaptive kernel-smoothed densities and risk functions, identify statistically significant fluctuations in an estimated risk function through the use of asymptotic tolerance contours, and visualize these objects in flexible and attractive ways.

sparr: Analyzing Spatial Relative Risk Using Fixed and Adaptive Kernel Density Estimation in R

The estimation of kernel-smoothed relative risk functions is a useful approach to examining the spatial variation of disease risk. Though there exist several options for performing kernel density estimation in statistical software packages, there have been very few contributions to date that have focused on estimation of a relative risk function per se. Use of a variable or adaptive smoothing parameter for estimation of the individual densities has been shown to provide additional benefits in estimating relative risk and specific computational tools for this approach are essentially absent. Furthermore, little attention has been given to providing methods in available software for any kind of subsequent analysis with respect to an estimated risk function. To facilitate analyses in the field, the R package sparr is introduced, providing the ability to construct both fixed and adaptive kernel-smoothed densities and risk functions, identify statistically significant fluctuations in an estimated risk function through the use of asymptotic tolerance contours, and visualize these objects in flexible and attractive ways

Application of kernel smoothing to estimate the spatio-temporal variation in risk of STEC O157 in England

Identifying geographical areas with significantly higher or lower rates of infectious diseases can provide important aetiological clues to inform the development of public health policy and interventions designed to reduce morbidity. We applied kernel smoothing to estimate the spatial and spatio-temporal variation in risk of STEC O157 infection in England between 2009 and 2015, and to explore differences between the residential locations of cases reporting travel and those not reporting travel. We provide evidence that the distribution of STEC O157 infection in England is non-uniform with respect to the distribution of the at-risk population; that the spatial distribution of the three main genetic lineages infecting humans (I, II and I/II) differs significantly and that the spatio-temporal risk is highly dynamic. Our results also indicate that cases of STEC O157 reporting travel within or outside the UK are more likely to live in the south/south-east of the country, meaning that their residential location may not reflect the location of exposure that led to their infection. We suggest that the observed variation in risk reflects exposure to sources of STEC O157 that are geographically prescribed. These differences may be related to a combination of changes in the strains circulating in the ruminant reservoir, animal movements (livestock, birds or wildlife) or the behavior of individuals prior to infection. Further work to identify the importance of behaviours and exposures reported by cases relative to residential location is needed

Testing similarity between first-order intensities of spatial point processes. A comparative study

Testing whether two spatial point processes have the same spatial distribution is an important task that can be addressed from different perspectives. A Kolmogorov-Smirnov test with asymptotic calibration and a Cramer von Mises type test with bootstrap calibration have recently been developed to compare the first-order intensity of two observed patterns. Motivated by common practice in epidemiological studies, we introduce a regression test based on the relative risk function with two alternative bootstrap calibrations. This paper compares the performance of these nonparametric tests through both an intensive simulation study, and the application to wildfire and crime data. The three tests provide good calibrations of the null hypothesis for simulated Poisson and non-Poisson spatial point processes, but the Cramer von Mises and regression tests outperform the cost-efficient Kolmogorov-Smirnov test in terms of power. In the real data analysis we have seen that the Kolmogorov-Smirnov test does not detect differences between spatial point patterns when dealing with sparse data. In view of these results, it would be preferable using the Cramer von Mises or regression tests despite their higher computational demand

Exploring the Spatial Relative Risk of COVID-19 in Berlin-Neukölln

Identifying areas with high and low infection rates can provide important etiological clues. Usually, areas with high and low infection rates are identified by aggregating epidemiological data into geographical units, such as administrative areas. This assumes that the distribution of population numbers, infection rates, and resulting risks is constant across space. This assumption is, however, often false and is commonly known as the modifiable area unit problem. This article develops a spatial relative risk surface by using kernel density estimation to identify statistically significant areas of high risk by comparing the spatial distribution of address-level COVID-19 cases and the underlying population at risk in Berlin-Neukölln. Our findings show that there are varying areas of statistically significant high and low risk that straddle administrative boundaries. The findings of this exploratory analysis further highlight topics such as, e.g., Why were mostly affluent areas affected during the first wave? What lessons can be learned from areas with low infection rates? How important are built structures as drivers of COVID-19? How large is the effect of the socio-economic situation on COVID-19 infections? We conclude that it is of great importance to provide access to and analyse fine-resolution data to be able to understand the spread of the disease and address tailored health measures in urban settings.Deutsche ForschungsgemeinschaftPeer Reviewe

The spatio-temporal distribution of COVID-19 infection in England between January and June 2020

The spatio-temporal dynamics of an outbreak provide important insights to help direct public health resources intended to control transmission. They also provide a focus for detailed epidemiological studies and allow the timing and impact of interventions to be assessed.A common approach is to aggregate case data to administrative regions. Whilst providing a good visual impression of change over space, this method masks spatial variation and assumes that disease risk is constant across space. Risk factors for COVID-19 (e.g. population density, deprivation and ethnicity) vary from place to place across England so it follows that risk will also vary spatially. Kernel density estimation compares the spatial distribution of cases relative to the underlying population, unfettered by arbitrary geographical boundaries, to produce a continuous estimate of spatially varying risk.Using test results from healthcare settings in England (Pillar 1 of the UK Government testing strategy) and freely available methods and software, we estimated the spatial and spatio-temporal risk of COVID-19 infection across England for the first 6 months of 2020. Widespread transmission was underway when partial lockdown measures were introduced on 23 March 2020 and the greatest risk erred towards large urban areas. The rapid growth phase of the outbreak coincided with multiple introductions to England from the European mainland. The spatio-temporal risk was highly labile throughout.In terms of controlling transmission, the most important practical application of our results is the accurate identification of areas within regions that may require tailored intervention strategies. We recommend that this approach is absorbed into routine surveillance outputs in England. Further risk characterisation using widespread community testing (Pillar 2) data is needed as is the increased use of predictive spatial models at fine spatial scales

Resample-smoothing of Voronoi intensity estimators

Voronoi estimators are non-parametric and adaptive estimators of the intensity of a point process. The intensity estimate at a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing that location. Their major drawback is that they tend to paradoxically under-smooth the data in regions where the point density of the observed point pattern is high, and over-smooth where the point density is low. To remedy this behaviour, we propose to apply an additional smoothing operation to the Voronoi estimator, based on resampling the point pattern by independent random thinning. Through a simulation study we show that our resample-smoothing technique improves the estimation substantially. In addition, we study statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validation approach to choose the amount of smoothing to apply. Finally we apply our proposed intensity estimation scheme to two datasets: locations of pine saplings (planar point pattern) and motor vehicle traffic accidents (linear network point pattern)

Estimation of relative risk for events on a linear network

Motivated by the study of traffic accidents on a road network, we discuss the estimation of the relative risk, the ratio of rates of occurrence of different types of events occurring on a network of lines. Methods developed for two-dimensional spatial point patterns can be adapted to a linear network, but their requirements and performance are very different on a network. Computation is slow and we introduce new techniques to accelerate it. Intensities (occurrence rates) are estimated by kernel smoothing using the heat kernel on the network. The main methodological problem is bandwidth selection. Binary regression methods, such as likelihood cross-validation and least squares cross-validation, perform tolerably well in our simulation experiments, but the Kelsall–Diggle density-ratio cross-validation method does not. We find a theoretical explanation, and propose a modification of the Kelsall–Diggle method which has better performance. The methods are applied to traffic accidents in a regional city, and to protrusions on the dendritic tree of a neuron

Spatial and spatio-temporal point patterns on linear networks

A thesis submitted in partial fulfillment of the requirements for the degree of Doctor in Information Management, specialization in Geographic Information SystemsThe last decade witnessed an extraordinary increase in interest in the analysis of network related data and trajectories. This pervasive interest is partly caused by a strongly expanded availability of such datasets. In the spatial statistics field, there are numerous real examples such as the locations of traffic accidents and geo-coded locations of crimes in the streets of cities that need to restrict the support of the underlying process over such linear networks to set and define a more realistic scenario. Examples of trajectories are the path taken by moving objects such as taxis, human beings, animals, etc. Intensity estimation on a network of lines, such as a road network, seems to be a surprisingly complicated task. Several techniques published in the literature, in geography and computer science, have turned out to be erroneous. We propose several adaptive and non-adaptive intensity estimators, based on kernel smoothing and Voronoi tessellation. Theoretical properties such as bias, variance, asymptotics, bandwidth selection, variance estimation, relative risk estimation, and adaptive smoothing are discussed. Moreover, their statistical performance is studied through simulation studies and is compared with existing methods. Adding the temporal component, we also consider spatio-temporal point patterns with spatial locations restricted to a linear network. We present a nonparametric kernel-based intensity estimator and develop second-order characteristics of spatio-temporal point processes on linear networks such as K-function and pair correlation function to analyse the type of interaction between points. In terms of trajectories, we introduce the R package trajectories that contains different classes and methods to handle, summarise and analyse trajectory data. Simulation and model fitting, intensity estimation, distance analysis, movement smoothing, Chi maps and second-order summary statistics are discussed. Moreover, we analyse different real datasets such as a crime data from Chicago (US), anti-social behaviour in Castell´on (Spain), traffic accidents in Medell´ın (Colombia), traffic accidents in Western Australia, motor vehicle traffic accidents in an area of Houston (US), locations of pine saplings in a Finnish forest, traffic accidents in Eastbourne (UK) and one week taxi movements in Beijing (China)