Spatiotemporal Bayesian modeling of West Nile virus: Identifying risk of infection in mosquitoes with local-scale predictors

Abstract

Monitoring and control of West Nile virus (WNV) presents a challenge to state and local vector control managers. Models of mosquito presence and viral incidence have revealed that variations in mosquito autecology and land use patterns introduce unique dynamics of disease at the scale of a county or city, and that effective prediction requires locally parameterized models. We applied Bayesian spatiotemporal modeling to West Nile surveillance data from 49 mosquito trap sites in Nassau County, New York, from 2001 to 2015 and evaluated environmental and sociological predictors of West Nile virus incidence in Culex pipiens-restuans. A Bayesian spike-and-slab variable selection algorithm was used to help select influential independent variables. This method can be used to identify locally-important predictors.

The best model predicted West Nile positives well, with an Area Under Curve (AUC) of 0.83 on holdout data. The temporal trend was nonlinear and increased throughout the year. The spatial component identified increased West Nile incidence odds in the northwestern portion of the county, with lower odds in wetlands on the south shore of Long Island. High Normalized Difference Vegetation Index (NDVI) areas, wetlands, and areas of high urban development had negative associations with WNV incidence.

In this study we demonstrate a method for improving spatiotemporal models of West Nile virus incidence for decision making at the county and community scale, which empowers disease and vector control organizations to prioritize and evaluate prevention efforts.

GRAPHICAL ABSTRACT

1. Introduction

1.1. West Nile virus

West Nile Virus (WNV) is a mosquito-borne pathogen in the genus Flavivirus that has become endemic in the United States and surrounding North American countries since its accidental introduction in 1999 (Edward et al., 2005). The associated disease, West Nile fever, is usually asymptomatic or mild, but approximately 1 in 150 cases become neuroinvasive and can cause encephalitis and death (CDC (Centers for Disease Control and Prevention), 2017). From 1999 to 2016, there were 46,086 reported cases of West Nile fever in the United States, resulting in 2017 deaths (CDC (Centers for Disease Control and Prevention), 2016). The elderly are particularly vulnerable to the disease.

WNV is maintained in an enzootic cycle between mosquitoes and infected birds, primarily corvids such as jays and crows (Bernard et al., 2001). These birds serve as reservoir species for the virus, allowing it to replicate without killing the host and subsequently infect new hosts through mosquitoes taking blood meals. The main human vectors of WNV are Culex spp. mosquitoes, which are highly susceptible to infection and feed on both humans and birds (Andreadis et al., 2004; Apperson et al., 2004). While other human-biting mosquitoes such as Aedes and Anopheles spp. have been found to transmit the virus when inoculated under laboratory conditions, they are not thought to be major vectors (Turell et al., 2000).

1.2. WNV modeling

Several methods have been used to model and predict WNV infection and populations of competent WNV vector mosquitoes. Non-spatial models have focused on linear, logistic or Poisson regression to identify large-scale environmental predictors (Trawinski and Mackay, 2010; Brown et al., 2008; Tran et al., 2014). Time-lagged meteorological predictors, most prominently precipitation and air temperature, have been identified as reliable predictors worldwide (Paz, 2015), on a subcontinental scale (Tran et al., 2014; Paz, 2015; Hahn et al., 2015), regional scale (Roiz et al., 2014; Cotar et al., 2016), and at the county level (Little et al., 2016). Notably, while climate variables are consistently significant predictors, the direction and magnitude of individual effects vary among study areas (Wimberly et al., 2014). Other factors that influence West Nile incidence in the United States include land use type, socioeconomic factors such as poverty and housing quality, and degree of urbanization (Liu and Weng, 2009), with effects that vary among subregions of the study area (Degroote and Sugumaran, 2012). A prior study examined West Nile surveillance in Suffolk County, New York, which neighbors Nassau County to the east and is less developed, with greater coverage of forests, wetlands, and cropland. That study identified the presence of septic systems and wetland land cover as important predictors of West Nile infection in mosquitoes in rural and exurban areas (Myer et al., 2017). A model for WNV in Suffolk County predicted human cases based on the number of observed mosquito, bird, and human infections, but that study indicated that inclusion of local predictors may improve the utility of WNV prediction in the area (DeFelice et al., 2017).

Improvements in statistical software and affordable computing power have led to wide use of spatiotemporal modeling. Because mosquito vector surveillance relies on repeated sampling from traps spread across a study area, the results are inherently correlated across space and time. Studies have demonstrated improved performance from the inclusion of spatial and temporal effects in WNV modeling, using statistical methods such as geographically weighted regression, ecological niche modeling, and generalized linear mixed modeling (Kala et al., 2017; Sallam et al., 2017; Yoo, 2013). Fitting a model that includes spatial and temporal effects is generally computationally expensive, requiring substantial processing power due to the “big n problem” common to datasets replicated in space and time (Jona Lasinio et al., 2013). Solutions to this problem have been proposed, including the use of agent- based models for disease spread (Perez and Dragicevic, 2009; Manore et al., 2015). Such models have been used to simulate the spread of WNV on a regional scale (Bouden et al., 2008) but require prior knowledge of the dynamics of disease spread in the study area. They are also parameterized at the level of individual organisms or “agents” rather than at a larger environmental scale such as a landscape (Sukumar and Nutaro, 2012). A modeling solution can be found in the use of Gaussian Markov random fields in Bayesian models for spatial effects, with fast approximate solutions via the INLA (Rue et al., 2009) SPDE (Lindgren and Rue, 2015) (integrated nested Laplace approximations, continuous domain stochastic partial differential equations) method. INLA SPDE is a modeling framework implemented in the statistical software R (R Development Core Team, 2008) that allows many types of models, including spatiotemporal analyses, to be treated as hierarchical Bayesian models with spatial, temporal, and regression components. A key advantage of INLA SPDE is that it is generalizable to any spatial and temporal scale. Because the influence of WNV predictors is known to vary among areas, an effective model must incorporate the most relevant covariates for that study area. In this study, we present a new approach to creating location-specific WNV models by including spatial and temporally correlated effects, gathering predictor variables at a local scale, and fitting a Bayesian spatiotemporal model that predicts West Nile infection in mosquito traps.

2. Material and methods

2.1. Study area

The study was conducted in Nassau County, New York, USA, located on Long Island to the east of the New York City borough of Queens, and to the west of Suffolk County. It spans 1173 km², including 438 km² of ocean area, and is densely populated with approximately 1160 inhabitants per square kilometer (U.S. Census Bureau Population Division, 2016). Developed land, as classified by the 2011 National Land Cover Database, comprises 79.8% of Nassau County (Homer et al., 2015). The southern half of the county below U.S. Highway 495 is more highly developed and residential, with wetlands and barrier islands on the south shore abutting the Atlantic Ocean. Less dense development extends north of Hwy 495, with deciduous and evergreen forests surrounding residential areas terminating in the south shore of the Long Island Sound. Nassau County is affluent relative to the rest of the United States, with a median household income of $102,044 (U.S. Census Bureau, 2016).

2.2. Mosquito surveillance, trapping, and testing

Due to the rapid spread of WNV and the potentially deadly effects of West Nile fever, municipalities in affected areas have created mosquito surveillance networks or adapted existing ones to monitor for mosquito-borne disease. Nassau County, New York, has an extensive system of Centers for Disease Control (CDC) gravid and light traps and has monitored for WNV since 2001 due to the county’s proximity to New York City, the original location of the virus’ introduction to the United States (Asnis et al., 2001).

CDC gravid and light traps were placed at 49 locations (Fig. 1) across Nassau County, representing a cross-section of habitat types including dense urban development, coastal wetlands, forests, and residential suburban development. Trap sites were chosen based on physical and legal accessibility and the need to sample diverse environments. Sampling was undertaken on a rotating biweekly schedule from May through September, corresponding with the breeding season for Culex mosquitoes (Ecology and Environment Inc., 2009). Due to funding, personnel, time, and weather constraints, some mosquito traps were sampled at a different frequency than biweekly. All mosquito traps were left in the dataset because our analysis method, hierarchical mixed-effects modeling, is robust to unbalanced data (Laird and Ware, 1982). Mosquito trap contents (pools) were collected by the Nassau County Department of Public Works and captured mosquitoes were identified to species, separated, and counted. Species-separated pools were then sent to the New York State Department of Health Wadsworth Center for DNA extraction, automated nucleic acid purification, and arboviral testing using qRT-PCR (quantitative reverse transcriptase PCR) (Zink et al., 2013). West Nile surveillance results from Culex pipiens-restuans mosquitoes were used in this study because Cx. pipiens-restuans is the primary vector of WNV to humans in New York (Turell et al., 2000).

Fig. 1.

Location of mosquito trap sites within boundary of Nassau County, New York, USA.

2.3. Variable collection and data preparation

The variables collected for consideration in the model are listed in Table 1. All variables were summarized in 1-kilometer-radius buffers around each trap site based on the flight range of Culex mosquitoes, which can range up to 2 km in search of blood meals, and from a study examining buffer size choices for environmental modeling of Culex mosquito abundance (Trawinski and Mackay, 2010). Additionally, the coarsest-resolution variables considered were DAYMET weather data, which are available at a 1-kilometer resolution, and all other variables were summarized at the same resolution to avoid considering variables at differing resolutions.

Table 1.

Variables considered for inclusion in Nassau County WNV incidence model.

Variable name	Abbreviation	Units
DAYMET
Precipitation, no lag	Prcp	Millimeters rainfall (mm)
Precipitation, 1 week lag	L1Prcp	Millimeters rainfall (mm)
Precipitation, 2 weeks lag	L2Prcp	Millimeters rainfall (mm)
Temperature, no lag	Temp	Degrees celsius (°C)
Temperature, 1 week lag	L1Temp	Degrees celsius (°C)
Temperature, 2 weeks lag	L2Temp	Degrees celsius (°C)
NLCD 2011
Developed open space	DevOpen	Square meters (m2)
Low intensity development	DevLo	Square meters (m2)
Medium intensity development	DevMed	Square meters (m2)
High intensity development	DevHi	Square meters (m2)
Deciduous forest	DecFor	Square meters (m2)
Evergreen forest	EvFor	Square meters (m2)
Mixed forest	MixFor	Square meters (m2)
Woody wetlands	WoWet	Square meters (m2)
Emergent herbaceous wetlands	EmHerb	Square meters (m2)
Open water	OpWat	Square meters (m2)
Barren land	Barren	Square meters (m2)
Shrub and scrubland	ShrScr	Square meters (m2)
Grassland	Grass	Square meters (m2)
Pastureland	Pasture	Square meters (m2)
Cropland	Crops	Square meters (m2)
Landsat 8
Normalized Difference Vegetation Index	NDVI	Unitless index (0–10,000)
Provided by county
Catch basin count	BasinCount	Number of catch basins
Catch basin area	BasinArea	Square meters (m2)
Number of mosquitoes in pool	NumlnPool	Number of mosquitoes
U.S. 2000 census
Houses built before 1950	Builtb41950	Percentage of houses (%)
Houses built 1950–1969	Built50to69	Percentage of houses (%)
Houses built 1970–1989	Built70to89	Percentage of houses (%)
Houses built 1990–2000	Built90to00	Percentage of houses (%)

Climatological variables were obtained from the DAYMET 1 -km resolution North American gridded climactic variable dataset, maintained by Oak Ridge National Laboratory (Kala et al., 2017). DAYMET is a public dataset of modeled daily weather parameters. Daily precipitation and temperature maxima and minima were downloaded for the 1-km grid containing each trap site for the entirety of the monitoring period, 2001–2015. A synthetic variable for approximate mean temperature was created by taking the mean of the daily maximum and minimum temperature. Weekly precipitation and temperature variables were calculated by taking the mean of the daily observations aggregated by the ordinal week (1 through 52). For each mosquito trap observation, weather variables on the week of observation were extracted from the dataset along with variables lagged at 1 week and 2 weeks.

Ecological and urban land use/land cover (LULC) data were obtained from the National Land Cover Database (NLCD) 2011 (Homer et al., 2015). The dataset contains LULC data at a 30-meter resolution, based on a decision-tree classification of remote sensed images. Because the WNV dataset spans 2001 through 2015, we compared the land cover pixels that changed between the 2001 and 2011 NLCD products (Fig. A.1). Less than 1% of pixels changed classification between 2001 and 2011, and among those that changed, approximately 95% were ‘Developed’ pixels increasing to a higher category of development intensity. For example, medium intensity development (impervious surfaces account for 50 to 79% of ground cover) increased to high intensity development (impervious surfaces account for >80% of ground cover). Because few pixels changed between the two NLCD years available, we decided to use the 2011 NLCD for all observations. A 1- kilometer circular buffer was drawn around each trap site, and the fraction of cover represented by each land classification was calculated. Due to the minor discrepancies involved in fitting a circular buffer to a raster dataset made up of 30-meter pixels, each 1 -kilometer buffer zone represented 3,141,592 ± 300 m².

Normalized Difference Vegetation Index (NDVI) data were obtained from eMODlS (EROS Moderate Resolution Imaging Spectroradiometer) satellite monthly scenes at 250-meter resolution (USGS Long Term Archive, 2017). The NDVI is a relative measure of greenness, calculated from satellite imagery. lt is used as a proxy measurement for plant biomass and vegetation phenology (Reed et al., 1994). Our use of NDVI as a peak annual summer value was as a proxy for green, undeveloped areas such as forests, croplands, or parks. For each year of observation, an eMODlS image with <10% cloud cover was obtained between mid-July and mid-August (ordinal weeks 29–32), representing the yearly peak vegetative coverage. NDVl values were summarized by taking the mean value in a 1-kilometer buffer around each trap site.

Housing age was included as a potential predictor variable. Several studies have found that older suburban housing, especially housing constructed before 1960, correlates with higher populations of mosquitoes, higher rates of WNV incidence, and higher odds of WNV infection in humans (Labeaud et al., 2008; Ruiz et al., 2007; Ruiz et al., 2004). These studies suggest several potential causes, including poor drainage and construction characteristics. Data on the age of housing in metropolitan and suburban New York City was downloaded as a 30-arcsecond resolution grid (approximately 250 m²) from the 2000 U.S. Census (Seirup and Yetman, 2006). Housing age was summarized by percentage of total housing within 1-kilometer circular buffer zones of trap sites represented in the following categories: pre-1950, 1950–1969,1970–1989, and 1990–2000.

The locations of water recharge catch basins were provided by the Nassau County Department of Public Works, as an additional variable of local interest (Fig. A.2). These basins are constructed to hold stormwater runoff and allow it to slowly seep into the ground and remain inundated long after rain events, creating areas of standing fresh water that are potential mosquito breeding sites. Basin locations and their area were obtained as ArcGIS polygon files, and within each 1km circular buffer, the number of basins and their total area were calculated.

2.4. Statistical analysis

The response variable, WNV incidence in mosquito traps, was coded as a binary response (0/1). We used zero-inflated binomial regression to account for the rarity of WNV infection, and the possibility that some of the negative responses were structural zeros, or traps that had no chance of testing positive for WNV. We can define the model as a general hierarchical model for zero-inflated binomial observations with spatial and temporal correlated random effects. Let y(s, t) represent the binary presence or absence of WNV in the trap sampled at location s on week t (t = 1 T = 22), with the weeks standardized to begin at 1 by subtracting 18 from each value because the mosquito trapping season for Nassau County’s vector control agency begins on ordinal week 19 in early-mid May. The observational model can be written as follows:

$$y(s,t)|\eta (s,t)~zero-inflatedBinomial(1,\mathrm{\pi }(s,t))$$ (1)

where η(s, t) is a vector of linear predictors and π(s, t) is the vector of occurrence probabilities. The details of the zero-inflated binomial likelihood model used are provided in the R-INLA zero-inflated model documentation (R-INLA Project, 2016), with likelihood defined as:

$$y(s,t)=p\times \mathrm{\delta }(y)+(1-p)\times Binomial(1,\mathrm{\pi }(s,t))$$ (2)

where δ(y)is the Dirac delta function and p, the zero-inflation parameter, represents the probability of a structural zero response and is specified by a hyperparameter θ_p:

$$p=\frac{\exp \left({\theta }_p\right)}{1+\exp \left({\theta }_p\right)}$$ (3)

where the prior distribution is given for θ_p. The process model has the generalized form:

$$\eta (s,t)={\beta }_1{X}_1+\dots +{\beta }_n{X}_n+u(s)+\mu (t)$$ (4)

where parameters ${\beta }_1,\dots ,{\beta }_n$ are the regression coefficients for the independent variables X₁,….,X_n, u(s) is the spatially correlated random effect, $\mu (t)$ is the temporally correlated random effect, and the relationship between the linear predictor $\eta (s,t)$ and the occurrence probability $\pi (s,t)$ is the logit link function:

$$\pi (s,t)=\log \frac{\eta (s,t)}{1-\eta (s,t)}$$ (5)

The spatially correlated random effect u(s) was investigated using the INLA SPDE method. INLA SPDE evaluates spatial covariance by modeling spatial variation conditional on all other model parameters as a Gaussian Markov random field (GMRF) with mean 0 and covariance defined by a Matern correlation function, using estimates of the values of that field at vertices of an adjacency matrix constructed across the study area (Fig. A.3), as in the equations:

$$u_{ij}~GMRF\left(0,\mathrm{cov}\left(u_i,u_j\right)\right)$$ (6)

and

$$\mathrm{cov}\left(u_i,u_j\right)=\frac{2^{1-v}}{\Gamma (v)}\times {\left(\kappa \times \Vert u_i-u_j\Vert \right)}^v\times K_v\left(\kappa \times \Vert u_i-u_j\Vert \right)\times {\sigma }_u^2$$ (7)

where v and $K$ are parameters of the Matern function, $\Gamma (v)$ is the Gamma function, $\Vert u_i-u_j\Vert$ is the distance between u_i and U_j, K_v is the modified Bessel function of the second kind, and ${\sigma }_u^2$ is the solution to an SPDE for the Matérn function. The priors are given for the hyperparameter ${\sigma }_u$ and the range parameter r. The relationship between the range parameter and the parameters v and k of the Matern function is as follows:

$$r=\frac{\sqrt{8\times v}}{\kappa }$$ (8)

In R-INLA, the parameter v is set to 1, which simplifies Eqs. (7) and (8) considerably, and the prior distribution of k is derived from r as in Eq. (8). Details of the SPDE and the Matern correlation function can be found in the foundational SPDE paper by Lindgren et al. (Lindgren et al., 2011). To summarize Eq. (7), the covariance in the WNV mosquito incidence response between two sites i and j remaining after considering all other model parameters including fixed effects is modeled as a Matern correlation function multiplied by a variance term ${\sigma }_u^2$ and the spatial variance between observations is from a Gaussian Markov random field, which is Gaussian because its values vary according to a multivariate normal distribution and is Markov because the values of the field are correlated only with adjacent values. The mathematical underpinnings of INLA SPDE can be found in Cosandey-Godin et al. (Cosandey-Godin et al., 2014) and a further explanation of spatiotemporal zero-inflated modeling in INLA can be found in Musenge et al. (Musenge et al., 2013). An overview of Bayesian hierarchical approaches to spatial disease modeling can be found in Lawson (Lawson, 2009) and Best et al. (Best et al., 2005). Temporal correlation $\mu (t)$ was investigated by fitting an autoregressive order 1 (AR1) model to the data by ordinal week, where:

$$\begin{gathered} t=1;\mu (t)=N\left(0,{\left(\tau \left(1-{\rho }^2\right)\right)}^{-1}\right) \\ \mu (t)=\rho \times \mu (t-1)+ϵ(t),ϵ(t)~N\left(0,{\tau }^{-1}\right) \end{gathered}$$ (9)

To summarize Eq. (9), the temporally correlated trend at time t is equal to the trend at time t — 1 multiplied by the autoregressive parameter p, plus a normally distributed innovation term with precision $\tau$ $\tau$. The priors are given for the internal parameters ${\theta }_{1}and{\theta }_2,$ which represent the precision and the autoregressive parameter respectively according to the following equations:

$$\begin{gathered} {\theta }_1=\log \left(\tau \left(1-{\rho }^2\right)\right) \\ {\theta }_2=\log \left(\frac{1+\rho }{1-\rho }\right) \end{gathered}$$ (10)

Penalized-complexity priors (PC-priors) were chosen for all hyperparameters (Table 2) to avoid subjectivity in assigning prior distributions (Simpson et al., 2017).

Table 2.

Priors for hyperparameters of the INLA SPDE model^a.

Parameter	Prior specification	Initial values
Mean for spatial range r	(Mean, p<)b	(10, 0.5)
σu for spatial effect	(Mean, p>)c	(1,0.5)
θ1 for precision of AR1	(τ, p>)d	(0.5, 0.5)
θ2 for autoregressive parameter	(ρ, p>)e	(0.5, 0.9)
θp for zero-inflation probability	(Mean,S.D.)	(1,0.5)

^aAll priors used are penalized-complexity priors.

^bThe prior is defined on the probability that the mean posterior marginal range of the spatial effect will be less than the initial value. The range is defined as the distance at which correlation declines to approximately 0.13.

^cThe prior is defined on the probability that the mean posterior marginal standard deviation of the spatial effect will exceed the initial value.

^dThe prior is defined on the probability the precision of the AR1 innovation is greater than the initial value.

^eThe prior is defined on the probability that the autoregressive parameter is greater than the initial value.

Independent variables, which were treated as fixed effects (Table 1), were selected in a multi-step process involving both algorithmic selection and consideration of mosquito ecology, West Nile epidemiology, and the geography of the study area. A correlation matrix between all 28 collected variables was created by using the R function cor() to obtain Spearman’s rank correlation coefficients for all variable pairs (Data B.1). A literature search identified several Bayesian variable selection techniques appropriate for logistic models, including the Bayesian Lasso (Xu and Ghosh, 2015), stochastic search variable selection (Cantoni and Auda, 2017), and spike-and-slab regression based on the work of George and McCulloch (George and McCulloch, 1997). An adaptation of the George and McCulloch technique for logistic models was used to select variables, implemented in the R package ‘BoomSpikeSlab’ (Scott, 2018). Default priors were used for all variables, giving each an equal chance of inclusion in the model. The expected number of chosen variables was set to 6, and the prior information weight was set to 0.01, the default value. Of the variables with inclusion probabilities higher than 0.5, the 6 with the highest inclusion probabilities were selected. The number of mosquitoes captured in each pool was included in the final model as a control variable, because we expected that more trapped mosquitoes would lead to a higher chance of a pool containing WNV-positive mosquitoes. The area of stormwater catch basins within 1 km of the observation site was also retained as a control variable of interest to Nassau County vector control.

The usefulness of the spatial and temporal random effects was determined by fitting a model without random effects, referred to hereafter as the restricted model, and examining the deviance residuals for spatial and temporal correlation. A variogram was used to evaluate spatial correlation among restricted model residuals. A horizontal line on a variogram indicates that the residuals are not spatially correlated, and a deviation from a straight line is evidence that the inclusion of a spatial effect may improve model fit (Ecker and Gelfand, 1997). Temporal correlation was assessed using a plot of the autocorrelation function (ACF) for each trap site, which shows correlation among residuals at increasing time lags. 95% confidence intervals are shown, and ACF values that exceed this value are considered indicative of significant temporal correlation and considered evidence that inclusion of a temporal effect may improve model fit. The relative contributions of the spatial and temporal effects to the model were assessed by computing the intraclass correlation (ICC) for their variance, using the equation

$$IC{C}_{uv}=\frac{{\sigma }_u^2+{\sigma }_v^2}{{\sigma }_u^2+{\sigma }_v^2+{\sigma }^2}$$ (11)

where ${\sigma }_u^{2}and{\sigma }_v^2$ are the variance of the spatial and temporal random effects, respectively, and ${\sigma }^2$ is the variance of the logistic distribution, or $\frac{{\pi }^2}{3}$ (Goldstein et al., 2002). The ICC is interpreted as the correlation between observations in the same group, spatial or temporal, after all fixed effects are considered. For example, the ICC_U represents the correlation between any two mosquito pool observations at the same spatial coordinate but from different time points and with all fixed effects held constant. The restricted and full models were compared by DIC to determine whether the inclusion of spatial and temporal effects improved fit.

Model performance was evaluated by setting aside 20% of the data (1043 observations) at random as a holdout dataset and fitting the model on the remaining 4169 observations. The model was then used to predict the responses of the holdout dataset. Predictive performance was evaluated by plotting the Receiver Operating Characteristic (ROC) curve, which is a plot of sensitivity (true positives) vs. 1 — specificity (false positives), across all possible cutoff points for classification of a binary outcome. The integrated area under the ROC curve is referred to as the Area Under Curve (AUC) value and is the probability that a randomly-chosen WNV-positive observation will have a higher predicted value than a randomly-chosen WNV-negative observation. An AUC value that is far from 0.5 indicates that the model is better than random chance at classifying the response. An optimized cutoff point for classification was determined by finding the point along the ROC curve that maximizes Youden’s index, or theJ statistic, calculated by

$$J=sensitivity+specificity-1$$ (12)

which is a measure of performance for a dichotomous classifier. This cutoff point balances maximizing the number of true positives correctly identified by the model and minimizing the number of true negatives that the model misclassifies, which was considered optimal for our application of creating a well-fit and balanced model. The ROC curve can aid in choosing a different cutoff value for a particular model application if an increased sensitivity and a decrease in specificity is desired.

Analyses were conducted using R 3.5.1 on a Dell Precision T3600 workstation with an Intel Xeon e5–1629 processor and 32 GB of RAM, running Windows 10 Enterprise. R code for conducting the analysis and recreating the figures is presented in Data B.2.

3. Results

3.1. Variable selection and summary statistics

After applying the spike-and-slab regression for variable selection, 6 variables remained for consideration in the final model (Table 3). All variables were then scaled by subtracting the mean and dividing by the standard deviation prior to model fitting so that regression coefficients could be directly compared.

Table 3.

Descriptive statistics for variables considered in final model.

Variable	Mean ± SD	Range (min:max)
LIPrcp	3.5 ± 4.0 mm	0:42.9
L2Temp	22.7 ± 3.0 °C	8.8:29.4
NDVI	6430 ± 1252	2770:9231
DevHi	294,183 ± 274,843 m2	0:1,086,300
EmHerb	82,872 ± 219,103 m2	0:1,163,700
OpWat	150,285 ± 326,147 m2	0:1,418,992
BasinArea	31,450 ± 32,635 m2	0:106,200
NumInPool	27 ± 17	4:60

Summary statistics for mosquito trapping and WNV testing are presented in Fig. 2. The number of trap sites sampled per year ranged between 37 and 49, and 269 ± 50 pools were collected per year. The percentage of mosquito pools that tested positive for WNV ranged from 5.1% in 2004 to 40.3% in 2010. The maximum WNV positive pools were observed in 2010, both in absolute number and as a fraction of the total (Fig. A.4). The maximum number of observed positives in 2010 did not coincide with the maximum number of trap sites sampled or the maximum number of mosquito pools collected, both in 2012, nor with the number of mosquitoes trapped per pool, total mosquitoes trapped, or the mean mosquitoes trapped per week which had their maxima in 2014.

Fig. 2.

Descriptive barplots for Nassau county mosquito traps. (A) Number of mosquito trap sites per year. (B) Total number of mosquito pools collected per year. (C) Number of pools testing positive for West Nile Virus per year. (D) The mean number of mosquitoes trapped per pool collected per year. (E) The total number of C. pipiens-restuans mosquitoes trapped per year. (F) The mean number of C. pipiens-restuans mosquitoes trapped per week per year.

3.2. Fixed effects

The mean posterior coefficients of the fixed effect predictors that were included in the final model are presented in log odds and represent the expected effect of a 1 standard deviation change in the predictor due to the scaling applied to all fixed effects (Table 4). The 95% credible interval (CI) represents coverage of 95% of the posterior distribution for the fixed effect, and its interpretation is extremely intuitive: we are 95% certain that the true parameter value lies within the indicated range given the data. A fixed effect with a 95% CI that does not encompass zero is interpreted as an important variable. Mean precipitation lagged at 1 week, high intensity development, emergent herbaceous wetlands, open water, and NDVI had a negative effect on WNV incidence in mosquito pools. NDVI had the largest negative effect in magnitude. The number of mosquitoes trapped and mean temperature lagged at 2 weeks had a positive effect, with the number of mosquitoes trapped having the largest positive effect. The area of catch basins near trap sites had a 95% CI that eclipsed zero and small coefficient relative to other predictors and was thus considered a less important predictor. Less important predictors were not removed from the model because our a priori modeling approach did not permit post-hoc removal, and because they provide insight into the local drivers of WNV presence in Nassau County despite their lack of contribution to predictive power.

Table 4.

Fixed effect and hyperparameter posterior mean values for modeled WNV incidence in mosquito traps. Important fixed effects (95% CI does not encompass 0) are in bold.

Fixed effect	Log odds	95% CI
L1Prcp	−0.21	−0.33:−0.09
L2Tavg	0.62	0.41:0.86
DevHi	−0.51	−0.73:−0.29
NDV1	−0.80	−1.07:−0.55
EmHerb	−0.47	−0.88:−0.07
OpWat	−0.50	−0.82:−0.19
BasinArea	−0.04	−0.37:0.22
NumlnPool	0.70	0.55:0.89
Hyperparameter	Posterior mean	95% CI
p for zero-inflation	0.24	0.10:0.40
Spatial range	27.9	0.91:136.20
σu for spatial effect	0.46	0.16:0.97
ρ for AR1	0.97	0.92:0.99
τ for AR1	0.21	0.05:0.55

3.3. Random effects and hyperparameters

Comparing the fit of the reduced model without spatial or temporal random effects to the full model, the DIC of the reduced model was 2974.3,while the DIC of the full model was 2583.5, resulting in a $\Delta$ DIC value of 390.8 which indicates that the model with spatial and temporal effects is a better fit to the data. The variogram of deviance residuals of the reduced model showed a non-flat relationship between distance and semivariance (Fig. A.5), supporting the inclusion of a spatial random effect in the full model. The ACF plots of the deviance residuals of the reduced model indicated temporal relationships among residuals in 22 out of 49 trap sites (Fig. A.6), supporting the inclusion of a temporal random effect.

The zero-inflation parameter p had a mean posterior value of 0.24, with a 95% CI from 0.10 to 0.40, indicating that zero-inflation was present in the response. This result indicates that around one-fourth of the WNV testing results were structural zeros in the zero-inflated model, meaning that unlike zeroes due to chance, those traps never had a chance of testing positive in the first place.

The posterior mean value of the spatial effect was mapped across the Nassau County study area at 1 km² resolution (Fig. 3A). The basis function weights for the spatial effect at the vertex points, or nodes, of the adjacency matrix (Fig. A.3) were projected onto a map of Nassau County using INLA’s built-in ‘inla.mesh.projector’ function. The function then interpolates and extrapolates the values of the random field at the locations of our user-defined 1 km² grid (Lindgren and Rue, 2015). Level plots of the spatial random effect were plotted using functions from the R package ‘lattice’ (Sarkar, 2008). The relevant code can be found in Data B.2. There was a gradient of increasing odds from south to north, with the greatest spatial effect in the northwestern corner of the county and a lower spatial effect in the southern half of the county. The expected spatially correlated random effect for the odds of finding a WNV positive was higher than the overall mean in the northwest, while it was lower than the mean in the central southern portion of the county. The spatial range was 28 km, indicating that the data have a spatial correlation that decreases slowly with distance. The variability of the spatial effect (Fig. 3B) was generally greater in areas that had fewer WNV positive observations, which led to fewer data available to the model to estimate the effect.

Fig. 3.

Spatially correlated random effect mean (A) and standard deviation (B) mapped across Nassau County, New York. Areas of relatively lower WNV odds are near barrier islands to the south, while the northwest corner has relatively higher odds of WNV incidence. Open circles represent mosquito trap sites. Each pixel represents 1 km².

The temporal effect measures variation of WNV responses in time that are not captured by the fixed effects. The temporal effect by week had an increasing trend throughout the year and a generally sigmoid shape with small fluctuations near the end of the sampling period in early September (Fig. 4). The temporal effect is strongly negative until the middle of June, when it begins to rise. The maximum temporal trend value is reached in the third week of August and declines slightly before rising again in October. The autocorrelation parameter $\rho ,$ which represents the correlation between the current and previous week’s temporal effect, was 0.97. This indicates that the temporal effect changes slowly with time, each new realization is similar to the previous one. The correlation between sequential effects is, of course, not precisely 0.97 because the AR1 model contains an innovation term The prior and posterior distributions for the hyperparameters of the model can be found in Fig. 5.

Fig. 4.

AR(1) temporal trend by week. The data have the general shape of a sigmoidal curve, reaching a maximum in the third week in August. The shaded area represents a 95% credible interval.

Fig 5.

Prior (dotted) and posterior (solid) distributions for hyperparameters. A. Zero-probability parameter p. B. Standard deviation σ_u of the spatially correlated random effect. C. Spatial range r, in kilometers, where spatial correlation becomes negligible. D. Precision τ of the temporally correlated random effect. E. Autocorrelation parameter p for the AR1 effect.

Comparing the spatial and temporal random effects by intraclass correlation, we found that for the spatial and temporal effects ICC_uv=0.17, which is interpreted as the expected correlation between two mosquito pool WNV observations at the same trap site during the same week after all fixed effects are considered. For the spatial effect ICC_u = 0.05, which is the correlation expected between two observations at the same site during different weeks. For the temporal effect ICC_v = 0.11, which is the correlation between two observations in the same week at different sites.

3.4. Model performance

To test model performance, 20% of the data were randomly set aside before model fitting. The final model was used to predict the responses of the holdout dataset, and an ROC curve with a corresponding AUC value was calculated. Because the binomial model output is a probability of a positive response while WNV detection in mosquito pools is a binary process, a cutoff point must be chosen for classifying the response. Youden’s index was maximized to find an optimized cutoff value. The ROC curve (Fig. 6) shows the trade-off between sensitivity and specificity for all potential cutoff values. The AUC was 0.83, indicating that the model was better than chance at classifying WNV detections. The Youden-optimized cutoff point was 0.22, at which the sensitivity was 0.78, while the specificity was 0.73.

Fig. 6.

ROC curve showing trade-offs between sensitivity and specificity. The diagonal represents the theoretical performance of a random binomial classifier (e.g. a coin toss). The dot represents the cutoff value of 0.25, at which Youden’s index (sensitivity + specificity − 1) is maximized.

4. Discussion & conclusions

Predicting at-risk locations for West Nile virus is important in targeting vector control and public health resources. Regional and national models are insufficient to predict local hotspots of WNV activity because of variation in the ecology of mosquito populations, reservoir species, ecosystem types, human influences on the environment, and the interactions between them. To develop models that predict WNV incidence at a county or city scale, variable selection techniques can be applied that help identify the local factors that influence WNV dissemination. In this study, we identified locally influential predictors, determined the optimal lag for weather predictors, developed a model that incorporates spatial and temporal correlation, and accurately classified WNV positives in Nassau County on holdout data. Highly developed areas, emergent herbaceous wetlands, open water, and green spaces were indicative of lowered incidence of WNV. The number of mosquitoes trapped at each observation was an important control variable. Rainwater catch basin area, which was a predictor of interest to local vector-control, had no significant effect on WNV incidence.

Our results confirm relationships found in the WNV modeling literature with respect to temperature and precipitation in the eastern United States, with higher temperature and lower precipitation associated with increased WNV incidence (Hahn et al., 2015). Higher temperatures result in greater fecundity, faster time-to-development, and increased taking of blood meals in the Culexpipiens mosquitoes that transmit WNV in New York (Ciota et al., 2014). Increased adult mosquito populations and more aggressive feeding behavior on reservoir species both increase the probability of detecting WNV at a trap site. Precipitation amount had an inverse relationship with WNV incidence, echoing a study conducted in Illinois (Ruiz et al., 2010). Culex larvae and pupae are particularly susceptible to being flushed out of the containers they inhabit and easily killed by rainfall events (Gardner et al., 2012; Koenraadt and Harrington, 2008).

Decreased WNV incidence was estimated for areas that had higher NDVI values. The reduced incidence of WNV in green areas measured by NDVI may be related to the life history of the primary vector of WNV, Culex mosquitoes, which are container breeders whose larvae thrive in artificial pools of water where they have few predators (Horsfall, 1955). Culex larvae are outcompeted by other mosquitoes such as Aedes spp. (Carrieri et al., 2003) whose abundance correlates with NDVI (Britch et al., 2008). Urban areas are more often associated with Culex mosquito abundance, yet our model found a negative association between high intensity urban development and WNV incidence. The NLCD classifies high intensity urban development as “highly developed areas where people reside or work in high numbers. Examples include apartment complexes, row houses and commercial/industrial. Impervious surfaces account for 80% to 100% of the total cover” (Homer et al., 2004). While Culex mosquito abundance may be high in these areas due to availability of artificial containers and lack of drainage, the risk of WNV is dependent on the enzootic cycle between mosquitoes and reservoirs. Corvid birds such as crows, jays, and magpies can live in a wide variety of habitats including urban centers but typically prefer areas with grass and trees. Suburban areas in New York are particularly hospitable to crows (McGowan, 2001), which are used as a sentinel species in WNV surveillance because they are reservoirs for the disease. Both highly urban areas with almost no greenspace and highly green areas with little development are likely to have fewer interactions between Culex mosquitoes and reservoir birds that lead to WNV transmission, meaning that suburban and exurban areas may be at greater risk.

We controlled for the presence of stormwater catch basins and found no significant effect. Nassau County conducts larvicide treatments (Bacillus thuringiensis, B. sphaericus, methoprene, and BASF Agnique® MMF (Poly (oxy 1,2 ethanediyl), a (C16 20 branched and linear alkyl) m hydroxy)) on persistently wet stormwater catch basins and has a surveillance program to monitor intermittently wet basins for mosquito larva development and apply larvicide if necessary (Ecology and Environment Inc., 2009). Our results provide evidence that mosquito larvicide treatment as conducted in Nassau County is effective in stormwater catch basins.

Emergent herbaceous wetlands and open water areas had a negative association with WNV incidence. A negative association with open water is likely related to larval habitat suitability, as the permanent bodies of water in the study area are either stormwater catch basins and municipal ponds, which are treated with larvicide, or brackish and salt water that is not suitable for Culex mosquito development. The negative association between wetlands and WNV incidence may be linked to avian biodiversity and wetland health. It is hypothesized that wetlands that support a diverse avian population reduce the density of competent reservoir hosts for WNV (Ezenwa et al., 2007; Chen et al., 2013). In urban wetlands in the northeastern United States, the proportion of WNV-competent Culex species and avian reservoir species were shown to be lower than in adjacent residential areas (Johnson et al., 2012). Whether the observed effect of wetlands on lowered WNV incidence is related to avian community composition is a matter of some controversy, as a prominent study failed to find an association between avian biodiversity and WNV, and instead attributed the effect to other factors such as mosquito blood meal preference and other environmental variables (Loss et al., 2009). Wetland characteristics including the degree of human modification and inundation surface can affect the distribution of Culex pipiens and other vector mosquitoes (Roiz et al., 2015), and in a study of associations between land cover types and WNV human incidence across the United States, wetlands were found to have regionally variable effects (Bowden et al., 2011 ). We therefore treat the generalizability of this result with caution and emphasize the importance of choosing locally-important variables for models of WNV on a case-by-case basis.

Spatial and temporal dynamics of WNV incidence were examined in our model to capture variation not explained by the fixed effects. Comparison of the restricted non-spatiotemporal model to the full model by DIC showed that the inclusion of the spatial and temporal effects resulted in improved model fit, as expected after examination of the variogram and ACF plots for the restricted residuals. Intraclass correlations revealed that trap location and sampling time explained approximately 17% of the variation in observed WNV incidence, with a greater contribution from the temporal effect. The spatial effect correlation range was long, approximately 28 km. To aid in visualization of the spatial correlation range, Nassau County is approximately 29 km longitudinally, and 38 km latitudinally. This can indicate one or more unmeasured covariates influencing WNV incidence that vary gradually on a large spatial extent, such as the community composition of mosquitoes, their predators, or reservoirs. Interspecific competition between mosquito larvae favors invasive Aedes albopictus over Culex pipiens (Costanzo et al., 2005), which may account for some of the variability in spatial effects. Avian community composition also affects the transmission rate of WNV, due to dilution or amplification effects from the prevalence of competent reservoir species (Levine et al., 2017; McKenzie and Goulet, 2010). The barrier islands and wetlands on the south coast of Nassau County had the lowest spatial coefficient and are considered global-priority Important Bird Areas by the Audubon Society (Audubon Society, 2018), which may indicate that biodiversity promotes a dilution effect, or a lowered fraction of competent WNV reservoir birds among the avian population. The temporal effect was sigmoid in shape, beginning to increase in mid-June and reaching a peak in the third week of August. We interpreted this effect as capturing seasonality and other temporally-varying unmeasured trends in mosquito WNV infection, with the peak in New York occurring in late summer. This seasonality stems from interactions between temperature, precipitation, mosquito populations, and mosquito feeding behavior (Spielman, 2001), with seasonal changes in avian blood meal preferences influencing WNV infection (Balenghien et al., 2006).

This study differs in key ways from previous work on WNV incidence in neighboring Suffolk County (Myer et al., 2017), highlighting the need to tailor WNV models to individual areas. Some variables were common predictors of WNV in both counties, including the influence of weather, and a negative effect from higher NDVl and open water. However, the effect of land cover and urban development differed. In Suffolk County, which is less densely built and contains more undeveloped land, developed areas did not influence WNV incidence, while in Nassau there was a negative effect of high intensity development. Woody wetlands had a negative effect on WNV incidence in Suffolk County, while emergent herbaceous wetlands had a negative effect in the present study. This may be due to differences in wetland flora or fauna because of greater urbanization in Nassau county. Woody wetlands are akin to a forested or shrubland swamp, with larger hard-stemmed flora, while emergent herbaceous wetlands are characterized by soft-stemmed perennial plants (Homer et al., 2004). Removal of woody wetlands with subsequent regeneration leads to the conversion of woody wetlands to herbaceous wetlands. Comparing neighboring areas with differing construction and development characteristics but a similar climate and mosquito population allowed us to examine human-mediated differences in predictors of WNV incidence.

The INLA SPDE spatiotemporal modeling approach used in this study is robust to uneven sampling, which is common in disease surveillance data. Because of the empirical variable selection we employed, the methodology is objective and repeatable in new areas to determine local variables of importance. By using a Bayesian approach, previously-known information can be incorporated into subsequent models as prior distributions, although we did not do so in this study because it was the first Bayesian model for WNV conducted in the study area. If the model was used for targeting vector control or estimating the risk of WNV in a municipal context, we would recommend recalibrating the model each year as new surveillance data becomes available, using the previous year’s results to inform prior distributions. Our model can capture spatial and temporal correlation by using the INLA SPDE, which allows us to make inferences about spatial and temporal variability even without directly measuring the variables with which they are associated.

Although our model generates predictions for WNV incidence in mosquitoes and does not explicitly address human spillover, we consider the approach useful for public health decision making, because WNV detection in mosquito traps has been shown to be predictive of human cases (DeFelice et al., 2017; Kilpatrick and Pape, 2013). Privacy concerns related to spatial data on human infections meant we were unable to include them in our model.

While modeling WNV is not by itself novel, researchers must create new models and use new approaches for each new locality to solve the problem of local applicability. The differences in important WNV mosquito incidence predictors between neighboring counties on Long lsland highlights the heterogeneity of the dynamics that influence the spread of vector-borne disease and provide evidence for the importance of tailoring models to local conditions. Furthermore, DeFelice et al. developed a recent model for WNV using a compartmental epidemiological Bayesian approach to simulate spillover (DeFelice et al., 2017). This model forecast WNV spillover in Long Island and Chicago with good accuracy and can estimate human infections, but the authors noted that future models should include ecological covariates and a spatial component. Our model complements this approach and reduces uncertainty, facilitating the ability to make spatial predictions and draw inferences about local influences on WNV. By applying a consistent and repeatable variable selection and modeling approach in Nassau County, we demonstrated that a spatiotemporal model with good predictive power can be adapted to local conditions in modeling WNV incidence. The results allow inferences to be made about the unique characteristics that influence dynamics of WNV in different areas. For example, in Nassau County, both high intensity development and dense plant growth had a negative effect on WNV incidence, pointing to areas with intermediate levels of development and greenspace as potential concerns. By revealing the important predictors influencing WNV dynamics in specific local areas, our model provides a solution to prioritize vector control and public health resources.

HIGHLIGHTS.

• 49 mosquito trap locations tested for West Nile virus over a 15-year span

• Bayesian zero-inflated binomial model with spatial and temporal correlated random effects developed using R-INLA

• Model predicted 75% of all WNV outcomes correctly on holdout data, with 72% of positives correctly classified.

• Spatial and temporal trends mapped across the study area highlighted areas and times of concern for WNV incidence.

• Areas with lower vegetation and less- dense development, such as suburbs, were at highest risk.