Table 1.

A summary of types of common spatial analytical tools and their purpose.

	Purpose	Measure	Commonly used techniques	D*	References
T1: Visualization and descriptive analysis	Transformation of locational information into geographic coordinates	Geocoding/georeferencing	GIS based geocoding of street address, postal code, or administrative divisions	pp, pr, ar	(29–31)
T2: Spatial/Spatiotemporal dependence and pattern recognition	Visualization and description of the size and shape of the spatial distribution	Exploratory spatial data analysis	Mean center	pp, pr, ar	(32)
			Median center		(32)
			Convex hull		(33)
			Standard deviation (weighted by attributes)		(32)
			Directional mean and variance		(34)
			Moran scatter plot		(35)
		Characterize nearby features	Features with in a distance band/buffer zone	pr, ar	(31, 36)
			Distance to feature		(31)
			Overlaying features		(31)
	Test whether there is spatial dependence in the event data	Spatial autocorrelation	Global Moran's I	pr, ar	(37)
			Geary's C		(38)
			Mantel test		(39)
			Geti's ord		(40, 41)
		Spatial autocorrelation among regression residuals	Moran's I test	pr, ar	(42, 43)
			Kelejian–Robinson test		(44, 45)
		Distance analysis	Nearest neighbor analysis		(46)
			Ripley's K		(47, 48)
			Distance matrices		(31)
	Measure the uneven distribution of the populations and risk factors	Local or stratified spatial heterogeneity	Getis Ord Gi*	pr, ar	(40, 41)
			K-means clustering		(49)
			Anselin's local Moran's I (L-Moran)		(50)
			Spatial stratified heterogeneity test		(51)
	Measure the spatial dependence while accounting for background population		Oden's Ipop	ar	[(52, 53); https://www.biomedware.com]
	Test whether there is any spatial trends	Testing for first-order effects	Trend analysis	pr, ar	(18, 54, 55)
	Test whether there is any spatial clustering in the data	Global cluster detection	Nearest neighbor test	pp, pr, ar	(46)
			Cuzick and Edward's test (case-control data)		(56)
			Local indicators of spatial association (LISA)		(50)
	Locate the clusters and the statistical significance of the clustering	Purely spatial local cluster detection	Spatial scan statistics Flexscan	ar	(57–59) (60)
			Turnbull's test	pr, ar	(61)
			Besag and Newell's test		(62)
	Test whether there is space and time clustering in the data	Spatiotemporal cluster detection	Knox test	pp, pr, ar	(63)
			Mantel test		(39)
			Barton's test		(64)
			kth nearest neighbor test for time-space interaction		(65)
			Space-time permutation scan statistic		(66, 67)
			Edrer-Myers-Mantel test		(68, 69)
	Detect the direction of progression of an event over time	Spatiotemporal directionality	Spatiotemporal directionality test	pr, ar	[(53, 70); https://www.biomedware.com]
			Spatiotemporal anisotropy parameter		(71, 72)
T3: Spatial smoothing and interpolation	Quantifying spatial variations in event intensity: spatial point pattern (SPP) intensity	Density based point pattern recognition	Univariate Kernel density estimation (KDE)	pr	(73–75)
			Multidimensional KDE		(76, 77)
			Empirical Bayes smoothing (EBS)	ar	(78, 79)
	Smoothing and interpolation	Deterministic spatial interpolation	Thiessen (Voronoi) polygons	pr	(80)
			Neighborhood matrices		(31)
			Inverse Distance Estimation (IDW)		(32, 81, 82)
			Triangulated Irregular Network (TIN)		(83, 84)
			Headbang smoothing		(85–87)
		Spatial modeling with stochastic partial differential equations (SPDE)		pr	(88, 89)
		Geostatistical interpolation and spatial regression	Kriging	pr	(32, 90, 91) (92) (93–96)
			Spline regression models
			Trend Surface Interpolation
		Multivariate spatial interpolation	Co-kriging	pr	(32, 91, 97) (98–100)
			Regression kriging
		Spatiotemporal interpolation	Space-time kriging	pr	(101, 102) (103)
			Autoregressive spatial smoothing and temporal Spline smoothing
T4: Geographic correlation studies: modeling and regression	Estimate the probability of disease spread using explanatory variables	Regression at spatial units	Ordinary least square regression and test for spatial autocorrelation of residuals	pp, pr, ar	(42, 43, 45)
			Spatial lag model with independent variable representing neighbors		(104, 105)
		Spatial and spatiotemporal error autoregression models for areal data (When regression residuals have spatial autocorrelation)	Simultaneous autoregressive (SAR) models	pr, ar	(19, 24, 106)
			Geographically weighted regression (GWR)		(107, 108)
			Purely spatial: Conditional autoregressive (CAR) models		(19, 109, 110)
			Spatiotemporal CAR models		(111, 112)
			Two-stage space-time mixture modeling		(113)
			Latent structure models		(113–115)
		Spatial and spatiotemporal models for point-level data	Point process models with weighted sum approximation	pp	(116, 117)
			Conditional logistic model	pp, pr	(118, 119)
			Separable models for spatiotemporal data		(19)
			Non-separable models for spatiotemporal		(19)
	Measure the gravitation of adverse effects and the risk factors based on distance	Estimate most probable spatial interactions between entities	Gravity models	pr, ar	(120–123)
	Analysis of spatially explicit time-to-event data	Spatial survival models	Spatial cure rate model	pr	(124)
			Frailty models		(124)
	Estimate the probability of disease when the disease occurrence is correlated with environmental variables	Environmental/Ecological niche modeling	Maximum Entropy Ecological Niche modeling (Maxent)	pr	(125–127)
			Genetic Algorithm for Rule Set Production (GARP)		(128–130)
		Machine/statistical learning techniques	Random forest	pr	(131, 132)
			Generalized additive models (GAMs)		(133–135)
			Artificial neural networks (ANN)		(136, 137)

D* Column represents the type of data primarily applicable on the set of tools, where, pp, point-pattern; pr, point-referenced; ar, areal data.