Small Area Disease Risk Estimation and Visualization Using R
Paula Moraga
Centre for Health Informatics, Computing and Statistics (CHICAS), Lancaster Medical School2018-06-07
Abstract
Small area disease risk estimation is essential for disease prevention and control. In this paper, we demonstrate how R can be used to obtain disease risk estimates and quantify risk factors using areal data. We explain how to define disease risk models and how to perform Bayesian inference using the INLA package. We also show how to make interactive maps of estimates using the leaflet package to better understand the disease spatial patterns and communicate the results. We show an example of lung cancer risk in Pennsylvania, United States, in year 2002, and demonstrate that R represents an excellent tool for disease surveillance by enabling reproducible health data analysis.Introduction
Disease risk mapping analyses can help to better understand the spatial variation of the disease, and allow the identification of important public health determinants. These analyses are essential to inform programmes of disease prevention and control. The increased availability of geospatial disease and population data has enabled to study a number of health outcomes worldwide such as influenza and cancer in developed countries (P. Moraga and Ozonoff 2013; P. Moraga and Kulldorff 2016), and neglected tropical diseases (P. Moraga et al. 2015; Hagan et al. 2016).
Areal disease data often arise when disease outcomes observed at point level locations are aggregated over subareas of the study region due to several reasons such as patient confidentiality. Producing disease risk estimates at areal level is complicated by the fact that raw rates can be very unstable in areas with small populations and for rare diseases, and also by the presence of spatial correlation that may exist due to spatially correlated risk factors (Leroux, Lei, and Breslow 2000). Thus, generalized linear mixed models are often used to obtain disease risk estimates since they enable to improve local estimates by accommodating spatial correlation and the effects of explanatory variables. Bayesian inference in these models may be performed using the Integrated Nested Laplace Approximation (INLA) approach (HRue, Martino, and Chopin 2009) which is a computational alternative to MCMC that allows to do approximate Bayesian inference in latent Gaussian models. This approach is implemented in the R package called INLA (Rue et al. 2017) (http://www.r-inla.org/).
Small area disease estimates can be visualized through maps, greatly facilitating effective communication. R provides excellent tools for visualization including packages for making interactive maps such as leaflet (Cheng, Karambelkar, and Xie 2017). The maps created with leaflet support interactive panning and zooming which is very convenient to examine small areas in detail.
In this paper, we illustrate the use of R for performing disease risk mapping analysis using areal data. First, we introduce disease risk models for areal data and give a brief overview of INLA. In Section 4 we show how to estimate lung cancer risk and quantify risk factors in Pennsylvania, United States, in year 2000. Specifically, we discuss how to compute the observed and expected disease counts in the Pennsylvania counties, how to obtain disease risk estimates by fitting a spatial disease risk model using INLA, and how to build interactive maps showing the risk estimates using leaflet. Finally, the conclusions are presented.
Disease risk models
Disease risk estimates in areas can be obtained by computing the Standardized Incidence Ratios (SIRs). For area \(i\), \(i=1,\ldots,n\), the SIR is obtained as the ratio of the observed to the expected disease counts: \(SIR_i=Y_i/E_i\). The expected counts represent the total number of disease cases that one would expect if the population of the specific area behaved the way the standard (or regional) population behaves. The expected counts can be calculated using indirect standardization as \[E_i=\sum_{j=1}^m r_j^{(s)} n_j,\] where \(r_j^{(s)}\) is the disease rate in stratum \(j\) of the standard population, and \(n_j\) is the population in stratum \(j\) of the specific area. The SIR corresponding to area \(i\), \(SIR_i\), indicates whether the area \(i\) has more (\(SIR_i > 1\)), equal (\(SIR_i = 1\)) or fewer (\(SIR_i < 1\)) cases observed than expected from the standard population. When applied to mortality data, the ratio is commonly known as the Standardized Mortality Ratio or SMR.
Although in some situations SIRs can give a sense of the disease’s spatial variability, very extreme values can occur in areas with small populations owing to the small sample sizes involved. In contrast, disease models are preferred to obtain disease risks estimates because they enable to incorporate covariates and borrow information from neighboring areas to improve local estimates, resulting in the smoothing or shrinking of extreme values based on small sample sizes (Gelfand et al. 2000). A common approach is to model the observed counts \(Y_i\), \(i=1,\ldots,n\), using a Poisson distribution with mean \(E_i \times \theta_i\), where \(E_i\) is the expected counts and \(\theta_i\) is the relative risk in area \(i\). Then, the log risks are modeled with a sum of an intercept to model the overall disease risk level, and random effects that account for extra-Poisson variability in the observed data (Lawson 2009). Areas with relative risks \(\theta > 1\) and \(\theta < 1\) are areas with high and low risks, respectively. Areas with \(\theta = 1\) have the same risk as expected from the standard population.
The general model in disease mapping is expressed as \[Y_i \sim Po(E_i \times \theta_i),\ i=1,\ldots,n,\]
\[\log(\theta_i)= \alpha + u_i + v_i.\] Here, \(\alpha\) denotes the overall risk level, \(u_i\) is a spatial structured random effect that models the spatial dependence between the relative risks, and \(v_i\) is an unstructured exchangeable random effect that models uncorrelated noise. Often, other covariates or random effects are also included to quantify risk factors and deal with other sources of variability.
A model commonly used in disease mapping is the Besag-York-Mollié (BYM) model (Besag, York, and Mollié 1991). In this model, the spatially structured component \(u_i\) is modelled with the conditional autoregressive (CAR) distribution which smoothes the data according to a certain adjacency structure given by a neighborhood matrix that specifies two areas are neighbours if they have a common boundary. The CAR distribution is expressed as \[u_i| \mathbf{u_{-i}} \sim N\left(\bar u_{\delta_i}, \frac{\sigma^2_u}{n_{\delta_i}}\right),\] where \(\bar u_{\delta_i}= n_{\delta_i}^{-1} \sum_{j \in \delta_i} u_j\), and \(\delta_i\) and \(n_{\delta_i}\) represent, respectively, the set of neighbours and the number of neighbours of area \(i\). The unstructured component \(v_i\) is modelled using independent and identically distributed normal variables with zero-mean and variance equal to \(\sigma_v^2\).
INLA
Traditionally, Bayesian inference has been implemented via MCMC methods which make inference tractable for complex models but may present convergence and computation time problems. Integrated Nested Laplace Approximation (INLA) is a computational less-intensive alternative to MCMC designed to perform approximate Bayesian inference in latent Gaussian models (HRue, Martino, and Chopin 2009). These models include a very wide and flexible class of models ranging from generalized linear mixed to spatial and spatio-temporal models. Specifically, models are of the form \[y_i|\mathbf{x}, \boldsymbol{\theta} \sim \pi(y_i|x_i, \boldsymbol{\theta}),\]
\[\mathbf{x}|\boldsymbol{\theta} \sim N(\mathbf{0}, \boldsymbol{Q(\theta)}^{-1}),\]
\[\boldsymbol{\theta} \sim \pi(\boldsymbol{\theta}),\] where \(\mathbf{y}\) are the observed data, \(\mathbf{x}\) represents a Gaussian field, and \(\boldsymbol{\theta}\) are hyperparameters. Observations \(y_i\) are assumed to belong to an exponential family with mean \(\mu_i = g^{-1}(\eta_i)\). The linear predictor \(\eta_i\) accounts for effects of various covariates in an additive way, \[\eta_i = \alpha + \sum_{k=1}^{n_{\beta}} \beta_k z_{ki} + \sum_{j=1}^{n_f} f^{(j)}(u_{ji}).\] Here, \(\alpha\) is the intercept, \(\{ \beta_k \}\)’s quantify the linear effects of covariates \(\{ z_{ki} \}\) on the response, and \(\{ f^{(j)}(\cdot) \}\)’s are a set of non-linear or smooth functions defined in terms of some covariates \(\{ u_{ji}\}\). This formulation permits to accommodate a wide range of models thanks to the very different forms that the functions \(\{f^{(j)}\}\) can take including the disease risk models previously introduced. INLA uses a combination of analytical approximation and numerical integration to obtain approximated posterior distributions of the parameters that can then be post-processed to compute quantities of interest like posterior expectations and quantiles.
The INLA approach is implemented in the R package
INLA. This package is not on CRAN because it
uses some external C libraries that make difficult to build the
binaries. Therefore, when we install the package we need to use
install.packages() adding the URL of the
INLA repository:
install.packages("INLA", repos = "https://inla.r-inla-download.org/R/stable",
dep = TRUE)To fit a model using INLA we need to take
two steps. First, we need to write the linear predictor of the model as
a formula object in R. Then, we run the model calling the
inla() function where we specify the formula, the family,
the data and other options. Results can be inspected with the
summary() function and the posterior distributions can be
post-processed using a set of specific functions provided by
INLA. Further details about how to use all
these functions will be given in the disease mapping example in next
Section.
Example: lung cancer risk in Pennsylvania
In this Section we present an example of small area disease mapping study where we estimate the risk of lung cancer in Pennsylvania counties in year 2002. We use the data contained in the R package SpatialEpi (Kim and Wakefield 2016). The data contain the counties population which was obtained from the 2000 decennial census, and the lung cancer and smoking proportions which were obtained from the Pennsylvania Department of Health. We show how to calculate the observed and expected disease cases, and the the SIRs in each of the counties. We also obtain disease risk estimates and quantify risk factors by fitting a Bayesian model using INLA. Finally, we show how to make interactive maps of the risk estimates using leaflet.
Data
We start by loading the SpatialEpi package
and attaching the pennLC data.
library(SpatialEpi)
data(pennLC)By typing ?pennLC we see pennLC is a list
with the following elements:
geo: a data frame of county ids, and longitude and latitude of the geographic centroid of each county,data: a data frame of county ids, number of cases, population and strata information,smoking: a data frame of county ids and proportion of smokers,spatial.polygon: aSpatialPolygonsobject with the map of Pennsylvania.
pennLC$data contains the number of lung cancer cases and
the population at county level, stratified on race (white and
non-white), gender (female and male) and age group (under 40, 40-59,
60-69 and 70+).
We now create a data frame called d with columns
containing the counties ids, the observed and expected number of cases,
the smoking proportions and the SIRs. Specifically, d will
contain the following columns:
id: id of each county,Y: observed number of cases in each county,E: expected number of cases in each county,smoking: smoking proportion in each county,SIR: SIR of each county.
Observed cases
pennLC$data contains the cases in each county stratified
by race, gender and age. We can obtain the number of cases in each
county, Y, by aggregating the rows of
pennLC$data by county and adding up the observed number of
cases.
d <- aggregate(x = pennLC$data$cases, by = list(county = pennLC$data$county),
FUN = sum)aggregate() returns a data frame where the first row is
the county and the second column is the observed number of cases in each
of the counties. We set the column names of the returned object equal to
id and Y.
names(d) <- c("id", "Y")Expected cases
Now we calculate the indirectly standardized expected number of cases
in each county as explained in Section 2. That is, we use the strata-specific
rates from the the Pennsylvania population (standard population), and
apply them to the population distribution of the county. The expected
counts represent the total number of disease cases one would expect if
the population in the county behaved the way the Pennsylvania population
behaves. We can do this by using the expected() function of
SpatialEpi. This function has three arguments,
namely,
population: a vector of population counts for each strata in each area,cases: a vector with the number of cases for each strata in each area,n.strata: number of strata considered.
Vectors population and cases have to be
sorted by area first and then, within each area, the counts for all
strata need to be listed in the same order. All strata need to be
included in the vectors, including strata with 0 cases. Hence, to get
the expected counts we first sort the data using the
order() function where we specify the order as county,
race, gender and finally age.
pennLC$data <- pennLC$data[order(pennLC$data$county, pennLC$data$race,
pennLC$data$gender, pennLC$data$age), ]Then we call the expected() function to obtain the
expected counts E in each county. In the function we set
population equal to pennLC$data$population and
cases equal to pennLC$data$cases. There are 2
races, 2 genders and 4 age groups for each county, so number of strata
is set to 2 x 2 x 4 = 16.
population <- pennLC$data$population
cases <- pennLC$data$cases
n.strata <- 16
E <- expected(population, cases, n.strata)Now we add the vector E to the data frame d
which contains the counties ids (id) and the observed
counts (Y), making sure the E elements
correspond to the counties in d$id in the same order. To do
that, we use match() to calculate the vector of the
positions that match d$id in
unique(pennLC$data$county) which are the corresponding
counties of E. Then we rearrange E using that
vector.
d$E <- E[match(d$id, unique(pennLC$data$county))]Smokers proportions
We also add to d the variable smoking which
represents the proportion of smokers in each county. We add this
variable using the merge() function where we specify the
columns for merging as id in d and
county in pennLC$smoking.
d <- merge(d, pennLC$smoking, by.x = "id", by.y = "county")SIRs
Finally, we compute the vector of SIRs as the ratio of the observed
to the expected counts, and add it to the data frame d.
d$SIR <- d$Y/d$EAdd data to map
The map of Pennsylvania counties is given by the
SpatialPolygons object called
pennLC$spatial.polygon. Using this object and the data
frame d we can create a
SpatialPolygonsDataFrame called map, that will
allow us to make maps of the variables in d. In order to do
that, we first set the row names of the data frame d equal
to d$id. Then we merge pennLC$spatial.polygon
and d matching the SpatialPolygons member
Polygons ID slot values with the data frame row names.
library(sp)
rownames(d) <- d$id
map <- SpatialPolygonsDataFrame(pennLC$spatial.polygon, d, match.ID = TRUE)
head(map@data)
## id Y E smoking SIR
## adams adams 55 69.62730 0.234 0.7899200
## allegheny allegheny 1275 1182.42804 0.245 1.0782897
## armstrong armstrong 49 67.61012 0.250 0.7247435
## beaver beaver 172 172.55806 0.276 0.9967660
## bedford bedford 37 44.19013 0.228 0.8372910
## berks berks 308 300.70598 0.249 1.0242563Mapping variables
We can visualize the observed and expected disease counts, the SIRs,
as well as the smokers proportions in an interactive chropleth map using
the leaflet package. We create the map by
first calling leaflet() and adding the default
OpenStreetMap map tiles to the map with addTiles(). Then we
add the Pennsylvania counties with addPolygons() where we
specify the areas boundaries color (color) and the stroke
width (weight). We fill the areas with the colours given by
the color palette function generated with colorNumeric(),
and set fillOpacity to a value less than 1 to be able to
see the background map. We use colorNumeric() to create a
color palette function that maps data values to colors according to a
given palette. We create the function using the parameters
palette with the color function that values will be mapped
to, and domain with the possible values that can be mapped.
Finally, we add the legend by specifying the color palette function
(pal) and the values used to generate colors from the
palette function (values). We set opacity to
the same value as the opacity in the areas, and specify a title and a
position for the legend.
library(leaflet)
l <- leaflet(map) %>% addTiles()
pal <- colorNumeric(palette = "YlOrRd", domain = map$SIR)
l %>% addPolygons(color = "grey", weight = 1, fillColor = ~pal(SIR),
fillOpacity = 0.5) %>%
addLegend(pal = pal, values = ~SIR, opacity = 0.5, title = "SIR",
position = "bottomright")We can improve the map by highlighting the counties when the mouse
hovers over them, and showing information about the observed and
expected counts, SIRs, and smoking proportions. We do this by adding the
arguments highlightOptions, label and
labelOptions to addPolygons(). We choose to
highlight the areas using a bigger stroke width
(highlightOptions(weight = 4)). We create the labels using
HTML syntax. First, we create the text to be shown using the function
sprintf() which returns a character vector containing a
formatted combination of text and variable values and then applying
htmltools::HTML() which marks the text as HTML. In
labelOptions we specify the labels style,
textsize, and direction. Possible values for
direction are left, right and
auto and this specifies the direction the label displays in
relation to the marker. We choose auto so the optimal
direction will be chosen depending on the position of the marker.
labels <- sprintf("<strong> %s </strong> <br/> Observed: %s <br/> Expected: %s <br/>
Smokers proportion: %s <br/> SIR: %s",
map$id, map$Y, round(map$E, 2), map$smoking, round(map$SIR, 2)) %>%
lapply(htmltools::HTML)
l %>% addPolygons(color = "grey", weight = 1, fillColor = ~pal(SIR), fillOpacity = 0.5,
highlightOptions = highlightOptions(weight = 4), label = labels,
labelOptions = labelOptions(style = list("font-weight" = "normal",
padding = "3px 8px"),
textsize = "15px",
direction = "auto")) %>%
addLegend(pal = pal, values = ~SIR, opacity = 0.5, title = "SIR",
position = "bottomright")Figure 1 shows a snapshot of the
interactive map created using leaflet showing the SIRs in
the Pennsylvania counties. We can examine the map and see which counties
have SIR equal to 1 indicating observed counts are the same as expected
counts, and which counties have SIR greater (or smaller) than 1,
indicating observed counts are greater (or smaller) than expected
counts.
leaflet showing the lung cancer SIRs in
Pennsylvania counties in 2002.This map gives a sense of the disease risk across Pennsylvania. However, SIRs are misleading and insufficiently reliable in counties with small populations. In contrast, model-based approaches enable to incorporate covariates and borrow information from neighboring counties to improve local estimates, resulting in the smoothing of extreme values based on small sample sizes. In the next section we will show how to obtain disease risk estimates using a Bayesian model using INLA.
Modeling
In this Section we specify the model for the data, and detail the required steps to fit the model and obtain the disease risk estimates using INLA.
Model
We specify a model assuming that the observed counts \(Y_i\) are conditionally independently Poisson distributed, \[Y_i|\theta_i \sim Po(E_i \times \theta_i),\ i=1,\ldots,n,\] where \(E_i\) is the expected count and \(\theta_i\) is the relative risk in area \(i\). The logarithm of \(\theta_i\) is expressed as follows: \[\log(\theta_i) = \beta_0 + \beta_1 \times smoking_i + u_i + v_i,\] where \(\beta_0\) is the intercept, \(\beta_1\) is the coefficient of the smokers proportion covariate, \(u_i\) is an structured spatial effect, \(u_i|\mathbf{u_{-i}} \sim N(\bar{u}_{\delta_i}, \frac{\sigma_u^2}{n_{\delta_i}})\), and \(v_i\) is an unstructured spatial effect, \(v_i \sim N(0, \sigma_v^2)\).
Neighbourhood matrix
We create the neighbourhood matrix needed to define the spatial
random effect using the poly2nb() and the
nb2INLA() functions of the spdep
package (Bivand 2017). First, we use
poly2nb() to create a neighbours list based on areas with
contiguous boundaries. Then, we use nb2INLA() to convert
this list into a file with the representation of the neighbourhood
matrix as required by INLA that is saved in
the working directory. Then we read the file using the
inla.read.graph() function of
INLA, and store it in the object
g which we will later use for specifying the spatial
disease model with INLA.
library(spdep)
library(INLA)
nb <- poly2nb(map)
head(nb)
## [[1]]
## [1] 21 28 67
##
## [[2]]
## [1] 3 4 10 63 65
##
## [[3]]
## [1] 2 10 16 32 33 65
##
## [[4]]
## [1] 2 10 37 63
##
## [[5]]
## [1] 7 11 29 31 56
##
## [[6]]
## [1] 15 36 38 39 46 54
nb2INLA("map.adj", nb)
g <- inla.read.graph(filename = "map.adj")Inference using INLA
As stated in Section 4.3.1, the model
includes two random effects, namely, \(u_i\) for modeling spatial residual
variation, and \(v_i\) for modeling
unstructured noise. We need to include two vectors in the data that
denote the indices of these random effects. We call re_u
the vector denoting \(u_i\), and
re_v the vector denoting \(v_i\). We set both re_u and
re_v equal to \(1,\ldots,n\), where \(n\) is the number of counties. In our
example, \(n=67\) and this can be
obtained with the number of rows in the data
(nrow(map@data)).
map$re_u <- 1:nrow(map@data)
map$re_v <- 1:nrow(map@data)We specify the model formula by including the response in the
left-hand side, and the fixed and random effects in the right-hand side.
Random effects are set using f() with parameters equal to
the name of the variable and the chosen model. For \(u_i\), we use model = "besag"
with neighbourhood matrix given by g. For \(v_i\) we choose
model = "iid".
formula <- Y ~ smoking + f(re_u, model = "besag", graph = g) + f(re_v, model = "iid")We fit the model by calling the inla() function. We
specify the formula, family, data, and the expected counts, and set
control.predictor equal to
list(compute = TRUE) to compute the posterior means of the
linear predictors.
res <- inla(formula, family = "poisson", data = map@data, E = E,
control.predictor = list(compute = TRUE))Results
We can inspect the results object res using
summary().
summary(res)
##
## Call:
## c("inla(formula = formula, family = \"poisson\", data = map@data, ", " E = E,
## control.predictor = list(compute = TRUE))")
##
## Time used:
## Pre-processing Running inla Post-processing Total
## 0.3179 1.1198 0.2155 1.6531
##
## Fixed effects:
## mean sd 0.025quant 0.5quant 0.975quant mode kld
## (Intercept) -0.3236 0.1503 -0.6212 -0.3234 -0.0279 -0.3231 0
## smoking 1.1567 0.6247 -0.0809 1.1582 2.3853 1.1619 0
##
## Random effects:
## Name Model
## re_u Besags ICAR model
## re_v IID model
##
## Model hyperparameters:
## mean sd 0.025quant 0.5quant 0.975quant
## Precision for re_u 93.05 49.95 30.95 81.84 220.42
## Precision for re_v 17956.92 18118.49 1155.86 12549.06 65967.91
## mode
## Precision for re_u 63.63
## Precision for re_v 3103.11
##
## Expected number of effective parameters(std dev): 18.61(4.366)
## Number of equivalent replicates : 3.60
##
## Marginal log-Likelihood: -320.53
## Posterior marginals for linear predictor and fitted values computedWe see the intercept \(\hat
\beta_0\)= -0.3236 with a 95% credible interval equal to
(-0.6212, -0.0279), and the coefficient of smoking is \(\hat \beta_1=\) 1.1567 with a 95% credible
interval equal to (-0.0810, 2.3853). This indicates that the smokers
proportion has a positive although non significant effect on disease
risk. We can plot the posterior distribution of the smoking coefficient.
We do this by calculating a spline smoothing of the marginal
distribution of the coefficient with inla.smarginal() and
then plot it with ggplot() of ggplot2
package (Wickham and Chang 2016) (see
Figure 2).
library(ggplot2)
marginal <- inla.smarginal(res$marginals.fixed$smoking)
marginal <- data.frame(marginal)
ggplot(marginal, aes(x = x, y = y)) + geom_line() +
labs(x = expression(beta[1]), y = "Density") +
geom_vline(xintercept = 0, col = "blue") + theme_bw()
The disease risk estimates and uncertainty for each of the counties
are given by the mean posterior and the 95% credible intervals of \(\theta_i\), \(i=1,\ldots,n\) which are in the data frame
res$summary.fitted.values. Here, column mean
is the mean posterior and 0.025quant and
0.975quant are the 2.5 and 97.5 percentiles, respectively.
We add these data to map to be able to make maps of these
variables. We assign column mean to the estimate of the
relative risk, and columns 0.025quant and
0.975quant to the lower and upper limits of 95% credible
intervals of the risks.
head(res$summary.fitted.values)
## mean sd 0.025quant 0.5quant 0.975quant
## fitted.Predictor.01 0.8793912 0.05856462 0.7633052 0.8797123 0.9943822
## fitted.Predictor.02 1.0597516 0.02768817 1.0067707 1.0592960 1.1153106
## fitted.Predictor.03 0.9632142 0.05186119 0.8555748 0.9649813 1.0612639
## fitted.Predictor.04 1.0270184 0.05121187 0.9270286 1.0267054 1.1289998
## fitted.Predictor.05 0.9076782 0.05497745 0.7978867 0.9081541 1.0156557
## fitted.Predictor.06 0.9951907 0.04023105 0.9184425 0.9943119 1.0770673
## mode
## fitted.Predictor.01 0.8808707
## fitted.Predictor.02 1.0583769
## fitted.Predictor.03 0.9685918
## fitted.Predictor.04 1.0262831
## fitted.Predictor.05 0.9096874
## fitted.Predictor.06 0.9927333
map$RR <- res$summary.fitted.values[, "mean"]
map$LL <- res$summary.fitted.values[, "0.025quant"]
map$UL <- res$summary.fitted.values[, "0.975quant"]Mapping disease risk
We show the estimated disease risk in an interactive map using
leaflet. In the map, we add labels that appear when mouse
hovers over the counties showing information about observed and expected
counts, SIRs, smokers proportions, RRs, and lower and upper limits of
95% credible intervals.
pal <- colorNumeric(palette = "YlOrRd", domain = map$RR)
labels <- sprintf("<strong> %s </strong> <br/> Observed: %s <br/> Expected: %s <br/>
Smokers proportion: %s <br/> SIR: %s <br/> RR: %s (%s, %s)",
map$id, map$Y, round(map$E, 2), map$smoking, round(map$SIR, 2),
round(map$RR, 2), round(map$LL, 2), round(map$UL, 2)) %>%
lapply(htmltools::HTML)
leaflet(map) %>% addTiles() %>%
addPolygons(color = "grey", weight = 1, fillColor = ~pal(RR), fillOpacity = 0.5,
highlightOptions = highlightOptions(weight = 4), label = labels,
labelOptions = labelOptions(style = list("font-weight" = "normal",
padding = "3px 8px"),
textsize = "15px", direction = "auto")) %>%
addLegend(pal = pal, values = ~RR, opacity = 0.5, title = "RR",
position = "bottomright")A snapshot of the interactive map created is shown in Figure 3. We observe counties with greater disease risk are located in the west and south east of Pennsylvania, and counties with lower risk are located in the center. The 95% credible intervals give a measure of the uncertainty in the risk estimates.
leaflet showing the lung cancer RRs in
Pennsylvania counties in 2002.By typing range(map@data$SIR) and
range(map@data$RR) we see that the range of SIRs is much
wider about 1 compared to the range of RRs: (0.32 to 1.37) versus (0.85
to 1.15). We can also see the shrinkage of the RRs toward 1 by comparing
maps of SIRs and RRs created using the same scale on the SIR gradient
legend (see Figure 4). For
example, in the SIRs map, in the central, less populated part of the
state, there are 3 counties with extreme high values (dark colour) and 3
counties with extreme low values (light colour). In the RRs map, these
extreme values shrink toward values closer to 1.
pal <- colorNumeric(palette = "YlOrRd", domain = map$SIR)
leaflet(map) %>% addTiles() %>%
addPolygons(color = "grey", weight = 1, fillColor = ~pal(RR), fillOpacity = 0.5,
highlightOptions = highlightOptions(weight = 4), label = labels,
labelOptions = labelOptions(style = list("font-weight" = "normal",
padding = "3px 8px"),
textsize = "15px", direction = "auto")) %>%
addLegend(pal = pal, values = ~RR, opacity = 0.5, title = "RR",
position = "bottomright")
leaflet showing the lung cancer SIRs (left) and RRs (right)
in Pennsylvania counties in 2002 using the same scale.
Summary
In this article we have shown how to obtain small area disease risk estimates, and generate interactive maps that help the understanding and interpretation of the results. First, we have introduced disease risk models using areal data, and have given an overview of the INLA package for performing Bayesian inference. Then, we have given a practical example where we have estimated lung cancer risk in Pennsylvania in 2002. We have conducted the analyses using several R packages such as spdep for spatial data manipulation, SpatialEpi for calculating the expected disease counts in the Pennsylvania counties, INLA for performing Bayesian inference, and leaflet and ggplot2 for visualization of the results.
One limitation of disease models based on areal data is that they are often subject to ecological bias. This bias occurs when associations obtained from analyses that use variables at an aggregated level lead to conclusions different from analyses that use the same variables measured at an individual level (Robinson 1950). Therefore, whenever point data are available, it is preferable to use disease models without aggregating data and predict disease risk in a continuous surface (Paula Moraga et al. 2017; Diggle et al. 2013).
It is also possible to use R to build tools to better communicate the results to stakeholders and the general public. For instance, summaries and maps of disease risk estimates can be presented in interactive dashboards using flexdashboard (Allaire 2017), and web applications using shiny (Chang et al. 2017). One example of such web application is the SpatialEpiApp package (Paula Moraga 2017a, 2017b) which is useful for disease risk mapping and the detection of clusters. This is an easy to use application where users simply need to upload their data and click several buttons that execute the tasks and process the outputs, making spatial analysis methods accessible to multiple disciplines. SpatialEpiApp creates interactive visualizations by using the packages leaflet for rendering maps, dygraphs (Vanderkam et al. 2017) for plotting time series, and DT (Xie 2016) for displaying data tables, and enables the generation of reports by using rmarkdown (Allaire et al. 2017). In conclusion, R represents an excellent tool for disease surveillance by enabling reproducible health data analysis.