,
Michelle Ross [ctb],
Jon Wakefield [aut],
Mikael Moise [aut] | Title: | Methods and Data for Spatial Epidemiology |
|---|---|
| Description: | Methods and data for cluster detection and disease mapping. |
| Authors: | Cici Chen [ctb],
Albert Y. Kim [aut, cre] ,
Michelle Ross [ctb],
Jon Wakefield [aut],
Mikael Moise [aut] |
| Maintainer: | Albert Y. Kim <[email protected]> |
| License: | GPL-2 |
| Version: | 1.2.8.9000 |
| Built: | 2024-11-07 04:12:43 UTC |
| Source: | https://github.com/rudeboybert/spatialepi |
Implementation of the Bayesian Cluster detection model of Wakefield and Kim (2013) for a study region with n areas. The prior and posterior probabilities of each of the n.zones single zones being a cluster/anti-cluster are estimated using Markov chain Monte Carlo. Furthermore, the posterior probability of k clusters/anti-clusters is computed.
bayes_cluster( y, E, population, sp.obj, centroids, max.prop, shape, rate, J, pi0, n.sim.lambda, n.sim.prior, n.sim.post, burnin.prop = 0.1, theta.init = vector(mode = "numeric", length = 0) )bayes_cluster( y, E, population, sp.obj, centroids, max.prop, shape, rate, J, pi0, n.sim.lambda, n.sim.prior, n.sim.post, burnin.prop = 0.1, theta.init = vector(mode = "numeric", length = 0) )
y |
vector of length |
E |
vector of length |
population |
vector of length |
sp.obj |
an object of class SpatialPolygons |
centroids |
|
max.prop |
maximum proportion of the study region's population each single zone can contain |
shape |
vector of length 2 of narrow/wide shape parameter for gamma prior on relative risk |
rate |
vector of length 2 of narrow/wide rate parameter for gamma prior on relative risk |
J |
maximum number of clusters/anti-clusters |
pi0 |
prior probability of no clusters/anti-clusters |
n.sim.lambda |
number of importance sampling iterations to estimate lambda |
n.sim.prior |
number of MCMC iterations to estimate prior probabilities associated with each single zone |
n.sim.post |
number of MCMC iterations to estimate posterior probabilities associated with each single zone |
burnin.prop |
proportion of MCMC samples to use as burn-in |
theta.init |
Initial configuration used for MCMC sampling |
List containing return(list( prior.map=prior.map, post.map=post.map, pk.y=pk.y))
prior.map |
A list containing, for each area: 1) |
post.map |
A list containing, for each area: 1) |
pk.y |
posterior probability of k clusters/anti-clusters given y for k=0,...,J |
Albert Y. Kim
Wakefield J. and Kim A.Y. (2013) A Bayesian model for cluster detection.
## Note for the NYleukemia example, 4 census tracts were completely surrounded ## by another unique census tract; when applying the Bayesian cluster detection ## model in [bayes_cluster()], we merge them with the surrounding ## census tracts yielding `n=277` areas. ## Load data and convert coordinate system from latitude/longitude to grid data(NYleukemia) sp.obj <- NYleukemia$spatial.polygon population <- NYleukemia$data$population cases <- NYleukemia$data$cases centroids <- latlong2grid(NYleukemia$geo[, 2:3]) ## Identify the 4 census tract to be merged into their surrounding census tracts remove <- NYleukemia$surrounded add <- NYleukemia$surrounding ## Merge population and case counts and geographical objects accordingly population[add] <- population[add] + population[remove] population <- population[-remove] cases[add] <- cases[add] + cases[remove] cases <- cases[-remove] sp.obj <- SpatialPolygons(sp.obj@polygons[-remove], proj4string=CRS("+proj=longlat +ellps=WGS84")) centroids <- centroids[-remove, ] ## Set parameters y <- cases E <- expected(population, cases, 1) max.prop <- 0.15 shape <- c(2976.3, 2.31) rate <- c(2977.3, 1.31) J <- 7 pi0 <- 0.95 n.sim.lambda <- 10^4 n.sim.prior <- 10^5 n.sim.post <- 10^5 ## (Uncomment first) Compute output #output <- bayes_cluster(y, E, population, sp.obj, centroids, max.prop, # shape, rate, J, pi0, n.sim.lambda, n.sim.prior, n.sim.post) #plotmap(output$prior.map$high.area, sp.obj) #plotmap(output$post.map$high.area, sp.obj) #plotmap(output$post.map$RR.est.area, sp.obj, log=TRUE) #barplot(output$pk.y, names.arg=0:J, xlab="k", ylab="P(k|y)")## Note for the NYleukemia example, 4 census tracts were completely surrounded ## by another unique census tract; when applying the Bayesian cluster detection ## model in [bayes_cluster()], we merge them with the surrounding ## census tracts yielding `n=277` areas. ## Load data and convert coordinate system from latitude/longitude to grid data(NYleukemia) sp.obj <- NYleukemia$spatial.polygon population <- NYleukemia$data$population cases <- NYleukemia$data$cases centroids <- latlong2grid(NYleukemia$geo[, 2:3]) ## Identify the 4 census tract to be merged into their surrounding census tracts remove <- NYleukemia$surrounded add <- NYleukemia$surrounding ## Merge population and case counts and geographical objects accordingly population[add] <- population[add] + population[remove] population <- population[-remove] cases[add] <- cases[add] + cases[remove] cases <- cases[-remove] sp.obj <- SpatialPolygons(sp.obj@polygons[-remove], proj4string=CRS("+proj=longlat +ellps=WGS84")) centroids <- centroids[-remove, ] ## Set parameters y <- cases E <- expected(population, cases, 1) max.prop <- 0.15 shape <- c(2976.3, 2.31) rate <- c(2977.3, 1.31) J <- 7 pi0 <- 0.95 n.sim.lambda <- 10^4 n.sim.prior <- 10^5 n.sim.post <- 10^5 ## (Uncomment first) Compute output #output <- bayes_cluster(y, E, population, sp.obj, centroids, max.prop, # shape, rate, J, pi0, n.sim.lambda, n.sim.prior, n.sim.post) #plotmap(output$prior.map$high.area, sp.obj) #plotmap(output$post.map$high.area, sp.obj) #plotmap(output$post.map$RR.est.area, sp.obj, log=TRUE) #barplot(output$pk.y, names.arg=0:J, xlab="k", ylab="P(k|y)")
Besag-Newell cluster detection method. There are differences with the original paper and our implementation:
we base our analysis on cases, rather than other cases as prescribed in the paper.
we do not subtract 1 from the accumulated numbers of other cases and accumulated numbers of others at risk, as was prescribed in the paper to discount selection bias
M is the total number of areas included, not the number of additional areas included. i.e. starts at 1, not 0.
p-values are not based on the original value of , rather the actual number of cases observed until we view or more cases. Ex: if , but as we consider neighbors we encounter 1, 2, 9 then 12 cases, we base our -values on
we do not provide a Monte-Carlo simulated : the number of tests that attain significance at a fixed level
The first two and last differences are because we view the testing on an area-by-area level, rather than a case-by-case level.
besag_newell(geo, population, cases, expected.cases = NULL, k, alpha.level)besag_newell(geo, population, cases, expected.cases = NULL, k, alpha.level)
geo |
an |
population |
aggregated population counts for all |
cases |
aggregated case counts for all |
expected.cases |
expected numbers of disease for all |
k |
number of cases to consider |
alpha.level |
alpha-level threshold used to declare significance |
For the population and cases tables, the rows are bunched by areas first, and then for each area, the counts for each strata are listed. It is important that the tables are balanced: the strata information are in the same order for each area, and counts for each area/strata combination appear exactly once (even if zero).
List containing
clusters |
information on all clusters that are |
p.values |
for each of the |
m.values |
for each of the |
observed.k.values |
based on |
The clusters list elements are themselves lists reporting:
location.IDs.included |
ID's of areas in cluster, in order of distance |
population |
population of cluster |
number.of.cases |
number of cases in cluster |
expected.cases |
expected number of cases in cluster |
SMR |
estimated SMR of cluster |
p.value |
|
Albert Y. Kim
Besag J. and Newell J. (1991) The Detection of Clusters in Rare Diseases Journal of the Royal Statistical Society. Series A (Statistics in Society), 154, 143–155
## Load Pennsylvania Lung Cancer Data data(pennLC) data <- pennLC$data ## Process geographical information and convert to grid geo <- pennLC$geo[,2:3] geo <- latlong2grid(geo) ## Get aggregated counts of population and cases for each county population <- tapply(data$population,data$county,sum) cases <- tapply(data$cases,data$county,sum) ## Based on the 16 strata levels, computed expected numbers of disease n.strata <- 16 expected.cases <- expected(data$population, data$cases, n.strata) ## Set Parameters k <- 1250 alpha.level <- 0.05 # not controlling for stratas results <- besag_newell(geo, population, cases, expected.cases=NULL, k, alpha.level) # controlling for stratas results <- besag_newell(geo, population, cases, expected.cases, k, alpha.level)## Load Pennsylvania Lung Cancer Data data(pennLC) data <- pennLC$data ## Process geographical information and convert to grid geo <- pennLC$geo[,2:3] geo <- latlong2grid(geo) ## Get aggregated counts of population and cases for each county population <- tapply(data$population,data$county,sum) cases <- tapply(data$cases,data$county,sum) ## Based on the 16 strata levels, computed expected numbers of disease n.strata <- 16 expected.cases <- expected(data$population, data$cases, n.strata) ## Set Parameters k <- 1250 alpha.level <- 0.05 # not controlling for stratas results <- besag_newell(geo, population, cases, expected.cases=NULL, k, alpha.level) # controlling for stratas results <- besag_newell(geo, population, cases, expected.cases, k, alpha.level)
This function is used for plotting purposes
circle(geo, cluster.center, cluster.end)circle(geo, cluster.center, cluster.end)
geo |
A |
cluster.center |
The area index (an integer between |
cluster.end |
The area index (an integer between |
cluster.radius |
A data frame that you can plot |
Albert Y. Kim
data(pennLC) geo <- pennLC$geo[,2:3] plot(geo,type='n') text(geo,labels=1:nrow(geo)) lines( circle(geo, 23, 46), col = "red" )data(pennLC) geo <- pennLC$geo[,2:3] plot(geo,type='n') text(geo,labels=1:nrow(geo)) lines( circle(geo, 23, 46), col = "red" )
This internal function creates the geographical objects needed to run the Bayesian cluster detection method in bayes_cluster(). Specifically it creates all single zones based data objects, where single zones are the zones defined by Kulldorff (1997).
create_geo_objects(max.prop, population, centroids, sp.obj)create_geo_objects(max.prop, population, centroids, sp.obj)
max.prop |
maximum proportion of study region's population each single zone can contain |
population |
vector of length |
centroids |
|
sp.obj |
object of class SpatialPolygons (See SpatialPolygons-class) representing the study region |
overlap |
list with two elements: |
cluster.coords |
|
Albert Y. Kim
Wakefield J. and Kim A.Y. (2013) A Bayesian model for cluster detection.Biostatistics, 14, 752–765.
data(pennLC) max.prop <- 0.15 population <- tapply(pennLC$data$population, pennLC$data$county, sum) centroids <- latlong2grid(pennLC$geo[, 2:3]) sp.obj <- pennLC$spatial.polygon output <- create_geo_objects(max.prop, population, centroids, sp.obj) ## number of single zones nrow(output$cluster.coords)data(pennLC) max.prop <- 0.15 population <- tapply(pennLC$data$population, pennLC$data$county, sum) centroids <- latlong2grid(pennLC$geo[, 2:3]) sp.obj <- pennLC$spatial.polygon output <- create_geo_objects(max.prop, population, centroids, sp.obj) ## number of single zones nrow(output$cluster.coords)
The computes empirical Bayes estimates of relative risk of study region with n areas, given observed and expected numbers of counts of disease and covariate information.
eBayes(Y, E, Xmat = NULL)eBayes(Y, E, Xmat = NULL)
Y |
a length |
E |
a length |
Xmat |
|
A list with 5 elements:
RR |
the ecological relative risk posterior mean estimates |
RRmed |
the ecological relative risk posterior median estimates |
beta |
the MLE's of the regression coefficients |
alpha |
the MLE of negative binomial dispersion parameter |
SMR |
the standardized mortality/morbidity ratio Y/E |
Clayton D. and Kaldor J. (1987) Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43, 671–681
data(scotland) data <- scotland$data x <- data$AFF Xmat <- cbind(x,x^2) results <- eBayes(data$cases,data$expected,Xmat) scotland.map <- scotland$spatial.polygon mapvariable(results$RR, scotland.map)data(scotland) data <- scotland$data x <- data$AFF Xmat <- cbind(x,x^2) results <- eBayes(data$cases,data$expected,Xmat) scotland.map <- scotland$spatial.polygon mapvariable(results$RR, scotland.map)
This function produces plots of empirical Bayes posterior densities which are gamma distributions with parameters (alpha+Y, (alpha+E*mu)/mu) where mu = exp(x beta). The SMRs are drawn on for comparison.
EBpostdens( Y, E, alpha, beta, Xrow = NULL, lower = NULL, upper = NULL, main = "" )EBpostdens( Y, E, alpha, beta, Xrow = NULL, lower = NULL, upper = NULL, main = "" )
Y |
observed disease counts |
E |
expected disease counts |
alpha |
x |
beta |
x |
Xrow |
x |
lower |
x |
upper |
x |
main |
x |
A plot containing the gamma posterior distribution
Jon Wakefield
data(scotland) Y <- scotland$data$cases E <- scotland$data$expected ebresults <- eBayes(Y,E) EBpostdens(Y[1], E[1], ebresults$alpha, ebresults$beta, lower=0, upper=15, main="Area 1")data(scotland) Y <- scotland$data$cases E <- scotland$data$expected ebresults <- eBayes(Y,E) EBpostdens(Y[1], E[1], ebresults$alpha, ebresults$beta, lower=0, upper=15, main="Area 1")
This function produces the posterior probabilities of exceeding a threshold given a gamma distributions with parameters (alpha+Y, (alpha+E*mu)/mu) where mu = exp(x beta). This model arises from Y being Poisson with mean theta times E where theta is the relative risk and E are the expected numbers. The prior on theta is gamma with parameters alpha and beta. The parameters alpha and beta may be estimated using empirical Bayes.
EBpostthresh(Y, E, alpha, beta, Xrow = NULL, rrthresh)EBpostthresh(Y, E, alpha, beta, Xrow = NULL, rrthresh)
Y |
observed disease counts |
E |
expected disease counts |
alpha |
x |
beta |
x |
Xrow |
x |
rrthresh |
x |
Posterior probabilities of exceedence are returned.
Jon Wakefield
data(scotland) Y <- scotland$data$cases E <- scotland$data$expected ebresults <- eBayes(Y,E) #Find probabilities of exceedence of 3 thresh3 <- EBpostthresh(Y, E, alpha=ebresults$alpha, beta=ebresults$beta, rrthresh=3) mapvariable(thresh3, scotland$spatial.polygon)data(scotland) Y <- scotland$data$cases E <- scotland$data$expected ebresults <- eBayes(Y,E) #Find probabilities of exceedence of 3 thresh3 <- EBpostthresh(Y, E, alpha=ebresults$alpha, beta=ebresults$beta, rrthresh=3) mapvariable(thresh3, scotland$spatial.polygon)
Internal function to estimate values of lambda needed for MCMC_simulation and prior probability of k clusters/anti-clusters for k=0,...,J
estimate_lambda(n.sim, J, prior.z, overlap, pi0)estimate_lambda(n.sim, J, prior.z, overlap, pi0)
n.sim |
number of importance sampling iterations |
J |
maximum number of clusters/anti-clusters to consider |
prior.z |
prior probability of each single zone |
overlap |
output of |
pi0 |
prior probability of no clusters |
estimates of lambda and prior.j
Wakefield J. and Kim A.Y. (2013) A Bayesian model for cluster detection. Biostatistics, 14, 752–765.
Compute the internally indirect standardized expected numbers of disease.
expected(population, cases, n.strata)expected(population, cases, n.strata)
population |
a vector of population counts for each strata in each area |
cases |
a vector of the corresponding number of cases |
n.strata |
number of strata considered |
The population and cases vectors must be balanced: all counts are sorted by area first, and then within each area the counts for all strata are listed (even if 0 count) in the same order.
expected.cases |
a vector of the expected numbers of disease for each area |
Albert Y. Kim
Elliot, P. et al. (2000) Spatial Epidemiology: Methods and Applications. Oxford Medical Publications.
data(pennLC) population <- pennLC$data$population cases <- pennLC$data$cases ## In each county in Pennsylvania, there are 2 races, gender and 4 age bands ## considered = 16 strata levels pennLC$data[1:16,] expected(population, cases, 16)data(pennLC) population <- pennLC$data$population cases <- pennLC$data$cases ## In each county in Pennsylvania, there are 2 races, gender and 4 age bands ## considered = 16 strata levels pennLC$data[1:16,] expected(population, cases, 16)
Compute parameters to calibrate the prior distribution of a relative risk that has a gamma distribution.
GammaPriorCh(theta, prob, d)GammaPriorCh(theta, prob, d)
theta |
upper quantile |
prob |
upper quantile |
d |
degrees of freedom |
List containing
a |
shape parameter |
b |
rate parameter |
Jon Wakefield
LogNormalPriorCh
param <- GammaPriorCh(5, 0.975,1) curve(dgamma(x,shape=param$a,rate=param$b),from=0,to=6,n=1000,ylab="density")param <- GammaPriorCh(5, 0.975,1) curve(dgamma(x,shape=param$a,rate=param$b),from=0,to=6,n=1000,ylab="density")
Convert geographic coordinates from Universal Transverse Mercator system to Latitude/Longitude.
grid2latlong(input)grid2latlong(input)
input |
A data frame with columns named |
Longitude/latitudes are not a grid-based coordinate system: latitudes are equidistant but the distance between longitudes varies.
Either a data frame with the corresponding longitude and latitude, or a SpatialPolygons object with the coordinates changed.
Rough conversion of US lat/long to km (used by GeoBUGS): (see also forum.swarthmore.edu/dr.math/problems/longandlat.html). Radius of earth: r = 3963.34 (equatorial) or 3949.99 (polar) mi = 6378.2 or 6356.7 km, which implies: km per mile = 1.609299 or 1.609295 a change of 1 degree of latitude corresponds to the same number of km, regardless of longitude. arclength=rtheta, so the multiplier for coord y should probably be just the radius of earth. On the other hand, a change of 1 degree in longitude corresponds to a different distance, depending on latitude. (at N pole, the change is essentially 0. at the equator, use equatorial radius. Perhaps for U.S., might use an "average" latitude, 30 deg is roughly Houston, 49deg is most of N bdry of continental 48 states. 0.5(30+49)=39.5 deg. so use r approx 6378.2sin(51.5)
Lance A. Waller
coord <- data.frame(rbind( # Montreal, QC c(-6414.30, 5052.849), # Vancouver, BC c(-122.6042, 45.6605) )) grid2latlong(coord)coord <- data.frame(rbind( # Montreal, QC c(-6414.30, 5052.849), # Vancouver, BC c(-122.6042, 45.6605) )) grid2latlong(coord)
Kulldorff spatial cluster detection method for a study region with n areas. The method constructs zones by consecutively aggregating nearest-neighboring areas until a proportion of the total study population is included. Given the observed number of cases, the likelihood of each zone is computed using either binomial or poisson likelihoods. The procedure reports the zone that is the most likely cluster and generates significance measures via Monte Carlo sampling. Further, secondary clusters, whose Monte Carlo p-values are below the -threshold, are reported as well.
kulldorff( geo, cases, population, expected.cases = NULL, pop.upper.bound, n.simulations, alpha.level, plot = TRUE )kulldorff( geo, cases, population, expected.cases = NULL, pop.upper.bound, n.simulations, alpha.level, plot = TRUE )
geo |
an |
cases |
aggregated case counts for all |
population |
aggregated population counts for all |
expected.cases |
expected numbers of disease for all |
pop.upper.bound |
the upper bound on the proportion of the total population each zone can include |
n.simulations |
number of Monte Carlo samples used for significance measures |
alpha.level |
alpha-level threshold used to declare significance |
plot |
flag for whether to plot histogram of Monte Carlo samples of the log-likelihood of the most likely cluster |
If expected.cases is specified to be NULL, then the binomial likelihood is used. Otherwise, a Poisson model is assumed. Typical values of n.simulations are 99, 999, 9999
List containing:
most.likely.cluster |
information on the most likely cluster |
secondary.clusters |
information on secondary clusters, if none |
type |
type of likelihood |
log.lkhd |
log-likelihood of each zone considered |
simulated.log.lkhd |
|
The most.likely.cluster and secondary.clusters list elements are themselves lists reporting:
location.IDs.included |
ID's of areas in cluster, in order of distance |
population |
population of cluster |
number.of.cases |
number of cases in cluster |
expected.cases |
expected number of cases in cluster |
SMR |
estimated SMR of cluster |
log.likelihood.ratio |
log-likelihood of cluster |
monte.carlo.rank |
rank of lkhd of cluster within Monte Carlo simulated values |
p.value |
Monte Carlo |
Albert Y. Kim
SatScan: Software for the spatial, temporal, and space-time scan statistics https://www.satscan.org/ Kulldorff, M. (1997) A spatial scan statistic. Communications in Statistics: Theory and Methods, 26, 1481–1496. Kulldorff M. and Nagarwalla N. (1995) Spatial disease clusters: Detection and Inference. Statistics in Medicine, 14, 799–810.
## Load Pennsylvania Lung Cancer Data data(pennLC) data <- pennLC$data ## Process geographical information and convert to grid geo <- pennLC$geo[,2:3] geo <- latlong2grid(geo) ## Get aggregated counts of population and cases for each county population <- tapply(data$population,data$county,sum) cases <- tapply(data$cases,data$county,sum) ## Based on the 16 strata levels, computed expected numbers of disease n.strata <- 16 expected.cases <- expected(data$population, data$cases, n.strata) ## Set Parameters pop.upper.bound <- 0.5 n.simulations <- 999 alpha.level <- 0.05 plot <- TRUE ## Kulldorff using Binomial likelihoods binomial <- kulldorff(geo, cases, population, NULL, pop.upper.bound, n.simulations, alpha.level, plot) cluster <- binomial$most.likely.cluster$location.IDs.included ## plot plot(pennLC$spatial.polygon,axes=TRUE) plot(pennLC$spatial.polygon[cluster],add=TRUE,col="red") title("Most Likely Cluster") ## Kulldorff using Poisson likelihoods poisson <- kulldorff(geo, cases, population, expected.cases, pop.upper.bound, n.simulations, alpha.level, plot) cluster <- poisson$most.likely.cluster$location.IDs.included ## plot plot(pennLC$spatial.polygon,axes=TRUE) plot(pennLC$spatial.polygon[cluster],add=TRUE,col="red") title("Most Likely Cluster Controlling for Strata")## Load Pennsylvania Lung Cancer Data data(pennLC) data <- pennLC$data ## Process geographical information and convert to grid geo <- pennLC$geo[,2:3] geo <- latlong2grid(geo) ## Get aggregated counts of population and cases for each county population <- tapply(data$population,data$county,sum) cases <- tapply(data$cases,data$county,sum) ## Based on the 16 strata levels, computed expected numbers of disease n.strata <- 16 expected.cases <- expected(data$population, data$cases, n.strata) ## Set Parameters pop.upper.bound <- 0.5 n.simulations <- 999 alpha.level <- 0.05 plot <- TRUE ## Kulldorff using Binomial likelihoods binomial <- kulldorff(geo, cases, population, NULL, pop.upper.bound, n.simulations, alpha.level, plot) cluster <- binomial$most.likely.cluster$location.IDs.included ## plot plot(pennLC$spatial.polygon,axes=TRUE) plot(pennLC$spatial.polygon[cluster],add=TRUE,col="red") title("Most Likely Cluster") ## Kulldorff using Poisson likelihoods poisson <- kulldorff(geo, cases, population, expected.cases, pop.upper.bound, n.simulations, alpha.level, plot) cluster <- poisson$most.likely.cluster$location.IDs.included ## plot plot(pennLC$spatial.polygon,axes=TRUE) plot(pennLC$spatial.polygon[cluster],add=TRUE,col="red") title("Most Likely Cluster Controlling for Strata")
Convert geographic latitude/longitude coordinates to kilometer-based grid coordinates.
latlong2grid(input)latlong2grid(input)
input |
either an |
Longitude/latitudes are not a grid-based coordinate system: latitudes are equidistant but the distance between longitudes varies.
Either a data frame with the corresponding (x,y) kilometer-based grid coordinates, or a SpatialPolygons object with the coordinates changed.
Rough conversion of US lat/long to km (used by GeoBUGS): (see also forum.swarthmore.edu/dr.math/problems/longandlat.html). Radius of earth: r = 3963.34 (equatorial) or 3949.99 (polar) mi = 6378.2 or 6356.7 km, which implies: km per mile = 1.609299 or 1.609295 a change of 1 degree of latitude corresponds to the same number of km, regardless of longitude. arclength=r*theta, so the multiplier for coord y should probably be just the radius of earth. On the other hand, a change of 1 degree in longitude corresponds to a different distance, depending on latitude. (at N pole, the change is essentially 0. at the equator, use equatorial radius.
Lance A. Waller
## Convert coordinates coord <- data.frame(rbind( # Montreal, QC: Latitude: 45deg 28' 0" N (deg min sec), Longitude: 73deg 45' 0" W c(-73.7500, 45.4667), # Vancouver, BC: Latitude: 45deg 39' 38" N (deg min sec), Longitude: 122deg 36' 15" W c(-122.6042, 45.6605) )) latlong2grid(coord) ## Convert SpatialPolygon data(pennLC) new <- latlong2grid(pennLC$spatial.polygon) par(mfrow=c(1,2)) plot(pennLC$spatial.polygon,axes=TRUE) title("Lat/Long") plot(new,axes=TRUE) title("Grid (in km)")## Convert coordinates coord <- data.frame(rbind( # Montreal, QC: Latitude: 45deg 28' 0" N (deg min sec), Longitude: 73deg 45' 0" W c(-73.7500, 45.4667), # Vancouver, BC: Latitude: 45deg 39' 38" N (deg min sec), Longitude: 122deg 36' 15" W c(-122.6042, 45.6605) )) latlong2grid(coord) ## Convert SpatialPolygon data(pennLC) new <- latlong2grid(pennLC$spatial.polygon) par(mfrow=c(1,2)) plot(pennLC$spatial.polygon,axes=TRUE) title("Lat/Long") plot(new,axes=TRUE) title("Grid (in km)")
leglabs makes character strings from the same break points. This function was copied from the soon-to-be
deprecated maptools package with permission from author Roger Bivand
leglabs(vec, under = "under", over = "over", between = "-", reverse = FALSE)leglabs(vec, under = "under", over = "over", between = "-", reverse = FALSE)
vec |
vector of break values |
under |
character value for under |
over |
character value for over |
between |
character value for between |
reverse |
flag to reverse order of values, you will also need to reorder colours, see example |
Roger Bivand, Nick Bearman, Nicholas Lewin-Koh
Compute parameters to calibrate the prior distribution of a relative risk that has a log-normal distribution.
LogNormalPriorCh(theta1, theta2, prob1, prob2)LogNormalPriorCh(theta1, theta2, prob1, prob2)
theta1 |
lower quantile |
theta2 |
upper quantile |
prob1 |
lower probability |
prob2 |
upper probability |
A list containing
mu |
mean of log-normal distribution |
sigma |
variance of log-normal distribution |
Jon Wakefield
# Calibrate the log-normal distribution s.t. the 95% confidence interval is [0.2, 5] param <- LogNormalPriorCh(0.2, 5, 0.025, 0.975) curve(dlnorm(x,param$mu,param$sigma), from=0, to=6, ylab="density")# Calibrate the log-normal distribution s.t. the 95% confidence interval is [0.2, 5] param <- LogNormalPriorCh(0.2, 5, 0.025, 0.975) curve(dlnorm(x,param$mu,param$sigma), from=0, to=6, ylab="density")
Plot levels of a variable in a colour-coded map along with a legend.
mapvariable( y, spatial.polygon, ncut = 1000, nlevels = 10, lower = NULL, upper = NULL, main = NULL, xlab = NULL, ylab = NULL )mapvariable( y, spatial.polygon, ncut = 1000, nlevels = 10, lower = NULL, upper = NULL, main = NULL, xlab = NULL, ylab = NULL )
y |
variable to plot |
spatial.polygon |
an object of class SpatialPolygons (See SpatialPolygons-class) |
ncut |
number of cuts in colour levels to plot |
nlevels |
number of levels to include in legend |
lower |
lower bound of levels |
upper |
upper bound of levels |
main |
an overall title for the plot |
xlab |
a title for the x axis |
ylab |
a title for the y axis |
A map colour-coded to indicate the different levels of y
Jon Wakefield, Nicky Best, Sebastien Haneuse, and Albert Y. Kim
Bivand, R. S., Pebesma E. J., and Gomez-Rubio V. (2008) Applied Spatial Data Analysis with R. Springer Series in Statistics. E. J. Pebesma and R. S. Bivand. (2005) Classes and methods for spatial data in R. R News, 5, 9–13.
data(scotland) map <- scotland$spatial.polygon y <- scotland$data$cases E <- scotland$data$expected SMR <- y/E mapvariable(SMR,map,main="Scotland",xlab="Eastings (km)",ylab="Northings (km)")data(scotland) map <- scotland$spatial.polygon y <- scotland$data$cases E <- scotland$data$expected SMR <- y/E mapvariable(SMR,map,main="Scotland",xlab="Eastings (km)",ylab="Northings (km)")
Census tract level (n=281) leukemia data for the 8 counties in upstate New York from 1978-1982, paired with population data from the 1980 census.
Note that 4 census tracts were completely surrounded by another unique census tract;
when applying the Bayesian cluster detection model in bayes_cluster(),
we merge them with the surrounding census tracts yielding n=277 areas.
NYleukemiaNYleukemia
List with 5 items:
table of the FIPS code, longitude, and latitude of the geographic centroid of each census tract
table of the FIPS code, number of cases, and population of each census tract
bject of class SpatialPolygons
row IDs of the 4 census tracts that are completely surrounded by the
census tracts
Turnbull, B. W. et al (1990) Monitoring for clusters of disease: application to leukemia incidence in upstate New York American Journal of Epidemiology, 132, 136–143
## Load data and convert coordinate system from latitude/longitude to grid data(NYleukemia) map <- NYleukemia$spatial.polygon population <- NYleukemia$data$population cases <- NYleukemia$data$cases centroids <- latlong2grid(NYleukemia$geo[, 2:3]) ## Identify the 4 census tract to be merged into their surrounding census tracts. remove <- NYleukemia$surrounded add <- NYleukemia$surrounding ## Merge population and case counts population[add] <- population[add] + population[remove] population <- population[-remove] cases[add] <- cases[add] + cases[remove] cases <- cases[-remove] ## Modify geographical objects accordingly map <- SpatialPolygons(map@polygons[-remove], proj4string=CRS("+proj=longlat +ellps=WGS84")) centroids <- centroids[-remove, ] ## Plot incidence in latitude/longitude plotmap(cases/population, map, log=TRUE, nclr=5) points(grid2latlong(centroids), pch=4)## Load data and convert coordinate system from latitude/longitude to grid data(NYleukemia) map <- NYleukemia$spatial.polygon population <- NYleukemia$data$population cases <- NYleukemia$data$cases centroids <- latlong2grid(NYleukemia$geo[, 2:3]) ## Identify the 4 census tract to be merged into their surrounding census tracts. remove <- NYleukemia$surrounded add <- NYleukemia$surrounding ## Merge population and case counts population[add] <- population[add] + population[remove] population <- population[-remove] cases[add] <- cases[add] + cases[remove] cases <- cases[-remove] ## Modify geographical objects accordingly map <- SpatialPolygons(map@polygons[-remove], proj4string=CRS("+proj=longlat +ellps=WGS84")) centroids <- centroids[-remove, ] ## Plot incidence in latitude/longitude plotmap(cases/population, map, log=TRUE, nclr=5) points(grid2latlong(centroids), pch=4)
Census tract level (n=281) leukemia data for the 8 counties in upstate New York from 1978-1982, paired with population data from the 1980 census.
Note that 4 census tracts were completely surrounded by another unique census tract;
when applying the Bayesian cluster detection model in bayes_cluster(),
we merge them with the surrounding census tracts yielding n=277 areas.
NYleukemia_sfNYleukemia_sf
An sf 'POLYGON' data frame with 281 rows and 4 variables:
Geometric representation of 8 counties in upstate New York
Number of cases per county
Population of each census tract
11-digit Federal Information Processing System identification number for each county
Turnbull, B. W. et al (1990) Monitoring for clusters of disease: application to leukemia incidence in upstate New York American Journal of Epidemiology, 132, 136–143
# Static map of NY Leukemia rate per county library(ggplot2) ## Not run: ggplot(NYleukemia_sf) + geom_sf(aes(fill= cases/population)) + scale_fill_gradient(low = "white", high = "red") ## End(Not run)# Static map of NY Leukemia rate per county library(ggplot2) ## Not run: ggplot(NYleukemia_sf) + geom_sf(aes(fill= cases/population)) + scale_fill_gradient(low = "white", high = "red") ## End(Not run)
County-level (n=67) population/case data for lung cancer in Pennsylvania in 2002, stratified on race (white vs non-white), gender and age (Under 40, 40-59, 60-69 and 70+). Additionally, county-specific smoking rates.
pennLCpennLC
List of 3 items
a table of county IDs, longitude/latitude of the geographic centroid of each county
a table of county IDs, number of cases, population and strata information
a table of county IDs and proportion of smokers
an object of class SpatialPolygons
Population data was obtained from the 2000 decennial census, lung cancer and smoking data were obtained from the Pennsylvania Department of Health website: https://www.health.pa.gov/Pages/default.aspx
data(pennLC) pennLC$geo pennLC$data pennLC$smoking # Map smoking rates in Pennsylvania mapvariable(pennLC$smoking[,2], pennLC$spatial.polygon)data(pennLC) pennLC$geo pennLC$data pennLC$smoking # Map smoking rates in Pennsylvania mapvariable(pennLC$smoking[,2], pennLC$spatial.polygon)
County-level (n=67) population/case data for lung cancer in Pennsylvania in 2002, stratified on race (white vs non-white), gender and age (Under 40, 40-59, 60-69 and 70+). Additionally, county-specific smoking rates.
pennLC_sfpennLC_sf
An sf POLYGON data frame with 1072 rows = 67 counties x 2 race
x 2 gender x 4 age bands
Pennsylvania county
Number of cases per county split by strata
Population per county split by strata
Race (w = white and o = non-white)
Gender (f = female and m = male)
Age (4 bands)
Overall county smoking rate (not broken down by strata)
Geometric representation of counties in Pennsylvania
Population data was obtained from the 2000 decennial census, lung cancer and smoking data were obtained from the Pennsylvania Department of Health website:https://www.health.pa.gov/Pages/default.aspx.
library(ggplot2) library(dplyr) # Sum cases & population for each county lung_cancer_rate <- pennLC_sf %>% group_by(county) %>% summarize(cases = sum(cases), population = sum(population)) %>% mutate(rate = cases/population) # Static map of Pennsylvania lung cancer rates for each county ## Not run: ggplot() + geom_sf(data = lung_cancer_rate, aes(fill = rate)) ## End(Not run)library(ggplot2) library(dplyr) # Sum cases & population for each county lung_cancer_rate <- pennLC_sf %>% group_by(county) %>% summarize(cases = sum(cases), population = sum(population)) %>% mutate(rate = cases/population) # Static map of Pennsylvania lung cancer rates for each county ## Not run: ggplot() + geom_sf(data = lung_cancer_rate, aes(fill = rate)) ## End(Not run)
Plot levels of a variable in a colour-coded map.
plotmap( values, map, log = FALSE, nclr = 7, include.legend = TRUE, lwd = 0.5, round = 3, brks = NULL, legend = NULL, location = "topright", rev = FALSE )plotmap( values, map, log = FALSE, nclr = 7, include.legend = TRUE, lwd = 0.5, round = 3, brks = NULL, legend = NULL, location = "topright", rev = FALSE )
values |
variable to plot |
map |
an object of class SpatialPolygons (See SpatialPolygons-class) |
log |
boolean of whether to plot values on log scale |
nclr |
number of colour-levels to use |
include.legend |
boolean of whether to include legend |
lwd |
line width of borders of areas |
round |
number of digits to round to in legend |
brks |
if desired, pre-specified breaks for legend |
legend |
if desired, a pre-specified legend |
location |
location of legend |
rev |
boolean of whether to reverse colour scheme (darker colours for smaller values) |
A map colour-coded to indicate the different levels of values.
Albert Y. Kim
## Load data data(scotland) map <- scotland$spatial.polygon y <- scotland$data$cases E <- scotland$data$expected SMR <- y/E ## Plot SMR plotmap(SMR, map, nclr=9, location="topleft")## Load data data(scotland) map <- scotland$spatial.polygon y <- scotland$data$cases E <- scotland$data$expected SMR <- y/E ## Plot SMR plotmap(SMR, map, nclr=9, location="topleft")
Converts a polygon (a matrix of coordinates with NA values to separate subpolygons) into a Spatial Polygons object.
polygon2spatial_polygon( poly, coordinate.system, area.names = NULL, nrepeats = NULL )polygon2spatial_polygon( poly, coordinate.system, area.names = NULL, nrepeats = NULL )
poly |
a 2-column matrix of coordinates, where each complete subpolygon is separated by NA's |
coordinate.system |
the coordinate system to use |
area.names |
names of all areas |
nrepeats |
number of sub polygons for each area |
Just as when plotting with the graphics::polygon() function, it is assumed that each subpolygon is to be closed by joining the last point to the first point. In the matrix poly, NA values separate complete subpolygons.
In the case with an area consists of more than one separate closed polygon, nrepeats specifies the number of closed polygons associated with each area.
An object of class SpatialPolygons (See SpatialPolygons-class from the sp package).
Albert Y. Kim
Bivand, R. S., Pebesma E. J., and Gomez-Rubio V. (2008) Applied Spatial Data Analysis with R. Springer Series in Statistics. E. J. Pebesma and R. S. Bivand. (2005) Classes and methods for spatial data in R. R News, 5, 9–13.
data(scotland) polygon <- scotland$polygon$polygon coord.system <- "+proj=eqc +lat_ts=0 +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 " coord.system <- paste(coord.system, "+ellps=WGS84 +datum=WGS84 +units=m +no_defs", sep = "") names <- scotland$data$county.names nrepeats <- scotland$polygon$nrepeats spatial.polygon <- polygon2spatial_polygon(polygon,coord.system,names,nrepeats) par(mfrow=c(1,2)) # plot using polygon function plot(polygon,type='n',xlab="Eastings (km)",ylab="Northings (km)",main="Polygon File") polygon(polygon) # plot as spatial polygon object plot(spatial.polygon,axes=TRUE) title(xlab="Eastings (km)",ylab="Northings (km)",main="Spatial Polygon") # Note that area 23 (argyll-bute) consists of 8 separate polygons nrepeats[23] plot(spatial.polygon[23],add=TRUE,col="red")data(scotland) polygon <- scotland$polygon$polygon coord.system <- "+proj=eqc +lat_ts=0 +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 " coord.system <- paste(coord.system, "+ellps=WGS84 +datum=WGS84 +units=m +no_defs", sep = "") names <- scotland$data$county.names nrepeats <- scotland$polygon$nrepeats spatial.polygon <- polygon2spatial_polygon(polygon,coord.system,names,nrepeats) par(mfrow=c(1,2)) # plot using polygon function plot(polygon,type='n',xlab="Eastings (km)",ylab="Northings (km)",main="Polygon File") polygon(polygon) # plot as spatial polygon object plot(spatial.polygon,axes=TRUE) title(xlab="Eastings (km)",ylab="Northings (km)",main="Spatial Polygon") # Note that area 23 (argyll-bute) consists of 8 separate polygons nrepeats[23] plot(spatial.polygon[23],add=TRUE,col="red")
Take the output of sampled configurations from MCMC_simulation and produce area-by-area summaries
process_MCMC_sample(sample, param, RR.area, cluster.list, cutoffs)process_MCMC_sample(sample, param, RR.area, cluster.list, cutoffs)
sample |
list objects of sampled configurations |
param |
mean relative risk associted with each of the |
RR.area |
mean relative risk associated with each of the |
cluster.list |
list of length |
cutoffs |
cutoffs used to declare highs (clusters) and lows (anti-clusters) |
high.area |
Probability of cluster membership for each area |
low.area |
Probability of anti-cluster membership for each area |
RR.est.area |
Smoothed relative risk estimates for each area |
Wakefield J. and Kim A.Y. (2013) A Bayesian model for cluster detection. Biostatistics, 14, 752–765.
County-level (n=56) data for lip cancer among males in Scotland between 1975-1980
scotlandscotland
List containing:
a table of county IDs, x-coordinates (eastings) and y-coordinates (northings) of the geographic centroid of each county.
a table of county IDs, number of cases, population and strata information
a Spatial Polygons class (See SpatialPolygons-class) map of Scotland
a polygon map of Scotland (See polygon2spatial_polygon()
Kemp I., Boyle P., Smans M. and Muir C. (1985) Atlas of cancer in Scotland, 1975-1980, incidence and epidemiologic perspective International Agency for Research on Cancer 72.
Clayton D. and Kaldor J. (1987) Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43, 671–681.
data(scotland) data <- scotland$data scotland.map <- scotland$spatial.polygon SMR <- data$cases/data$expected mapvariable(SMR,scotland.map)data(scotland) data <- scotland$data scotland.map <- scotland$spatial.polygon SMR <- data$cases/data$expected mapvariable(SMR,scotland.map)
County-level (n=56) data for lip cancer among males in Scotland between 1975-1980
scotland_sfscotland_sf
A data frame with 56 rows representing counties and 5 variables:
Geometric representation of counties in Scotland
Number of Lip Cancer cases per county
Scotland County name
Proportion of the population who work in agricultural fishing and farming
Expected number of lip cancer cases
Kemp I., Boyle P., Smans M. and Muir C. (1985) Atlas of cancer in Scotland, 1975-1980, incidence and epidemiologic perspective International Agency for Research on Cancer 72.
Clayton D. and Kaldor J. (1987) Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43, 671–681.
library(ggplot2) ## Not run: ggplot() + geom_sf(data = scotland_sf, aes(fill= cases)) ## End(Not run)library(ggplot2) ## Not run: ggplot() + geom_sf(data = scotland_sf, aes(fill= cases)) ## End(Not run)
Based on the population counts and centroid coordinates of each of n areas, output the set of n.zones single zones as defined by Kulldorff and other geographical information.
zones(geo, population, pop.upper.bound)zones(geo, population, pop.upper.bound)
geo |
|
population |
a vector of population counts of each area |
pop.upper.bound |
maximum proportion of study region each zone can contain |
A list containing
nearest.neighbors |
list of |
cluster.coords |
|
dist |
|
Albert Y. Kim
Kulldorff, M. (1997) A spatial scan statistic. Communications in Statistics: Theory and Methods, 26, 1481–1496. Kulldorff M. and Nagarwalla N. (1995) Spatial disease clusters: Detection and Inference. Statistics in Medicine, 14, 799–810.
data(pennLC) geo <- pennLC$geo[,2:3] geo <- latlong2grid(geo) population <- tapply(pennLC$data$population, pennLC$data$county, sum) pop.upper.bound <- 0.5 geo.info <- zones(geo, population, pop.upper.bound)data(pennLC) geo <- pennLC$geo[,2:3] geo <- latlong2grid(geo) population <- tapply(pennLC$data$population, pennLC$data$county, sum) pop.upper.bound <- 0.5 geo.info <- zones(geo, population, pop.upper.bound)