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MCAR_INLA_ST_Model2.R
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MCAR_INLA_ST_Model2.R
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source("functions/INLA_Mmodel_icar.R")
source("functions/INLA_Mmodel_lcar.R")
source("functions/INLA_Mmodel_pcar.R")
options(dplyr.summarise.inform=FALSE)
######################################################################################
## Fit a spatial-temporal multivariate Poisson mixed model to areal count data, ##
## where dependence between spatial/temporal patterns of the diseases is addressed ##
## through the use of M-models (Botella-Rocamora et al, 2015) ##
######################################################################################
MCAR_INLA_ST <- function(carto=NULL, data=NULL, ID.area=NULL, ID.year=NULL, ID.disease=NULL,
O=NULL, E=NULL, W=NULL, spatial="intrinsic", temporal="rw1",
interaction="TypeIV", strategy="simplified.laplace"){
## Check for errors ##
if(is.null(carto))
stop("the 'carto' argument is missing")
if(!any(class(carto) %in% c("SpatialPolygonsDataFrame","sf")))
stop("the 'carto' argument must be of class 'SpatialPolygonsDataFrame' or 'sf'")
if(is.null(ID.area))
stop("the 'ID.area' argument is missing")
if(is.null(ID.year))
stop("the 'ID.year' argument is missing")
if(is.null(ID.disease))
stop("the 'ID.disease' argument is missing")
if(is.null(O))
stop("the 'O' argument is missing")
if(is.null(E))
stop("the 'E' argument is missing")
if(!(spatial %in% c("Leroux","intrinsic","proper")))
stop("invalid 'spatial' argument")
if(!(temporal %in% c("rw1","rw2")))
stop("invalid 'temporal' argument")
if(!(interaction %in% c("none","TypeI","TypeII","TypeIII","TypeIV")))
stop("invalid 'interaction' argument")
if(!(strategy %in% c("gaussian","simplified.laplace","laplace","adaptative")))
stop("invalid 'strategy' argument")
cat("STEP 1: Pre-processing data\n")
## Transform 'SpatialPolygonsDataFrame' object to 'sf' class
carto <- sf::st_as_sf(carto)
## Order the data ##
if(!ID.area %in% colnames(carto))
stop(sprintf("'%s' variable not found in carto object",ID.area))
if(!ID.area %in% colnames(data))
stop(sprintf("'%s' variable not found in data object",ID.area))
if(!ID.year %in% colnames(data))
stop(sprintf("'%s' variable not found in data object",ID.year))
if(!ID.disease %in% colnames(data))
stop(sprintf("'%s' variable not found in data object",ID.disease))
if(!O %in% colnames(data))
stop(sprintf("'%s' variable not found in carto object",O))
if(!E %in% colnames(data))
stop(sprintf("'%s' variable not found in carto object",E))
carto <- carto[order(sf::st_set_geometry(carto, NULL)[,ID.area]),]
data <- merge(data,carto[,c(ID.area)])
data$geometry <- NULL
data[,ID.year] <- paste(sprintf("%02d", as.numeric(as.character(data[,ID.year]))))
data[,ID.disease] <- paste(sprintf("%02d", as.numeric(as.character(data[,ID.disease]))))
data <- data[order(data[,ID.disease],data[,ID.year],data[,ID.area]),]
## Define spatial adjacency/structure matrix ##
if(is.null(W)){
carto.nb <- poly2nb(carto)
Ws <- as(nb2mat(carto.nb, style="B"),"Matrix")
}else{
carto.nb <- mat2listw(W, style="B")$neighbours
Ws <- W
}
carto.nc <- n.comp.nb(carto.nb)$nc
if(carto.nc!=1) stop(sprintf("'carto' object has %d disjoint connected subgraphs",carto.nc))
S <- length(carto.nb)
Rs <- as(Diagonal(S,colSums(Ws))-Ws,"Matrix")
Rs.Leroux <- as(Diagonal(S)-Rs,"Matrix")
## Define temporal adjacency/structure matrix ##
T <- length(unique(data[,ID.year]))
if(temporal=="rw1") dif <- 1
if(temporal=="rw2") dif <- 2
D <- diff(diag(T), differences=dif)
Rt <- as(t(D)%*%D,"Matrix")
Wt <- -Rt
diag(Wt) <- 0
Wt <- drop0(Wt)
## Define hyperprior distributions ##
sdunif="expression:
logdens=-log_precision/2;
return(logdens)"
lunif = "expression:
a = 1;
b = 1;
beta = exp(theta)/(1+exp(theta));
logdens = lgamma(a+b)-lgamma(a)-lgamma(b)+(a-1)*log(beta)+(b-1)*log(1-beta);
log_jacobian = log(beta*(1-beta));
return(logdens+log_jacobian)"
## Identifiability constraints for the interaction term ##
constraints <- function(Rs, Rt) {
S <- nrow(Rs)
T <- nrow(Rt)
if(interaction=="none"){
R <- NULL
r.def <- NULL
A.constr.st <- NULL
}
if(interaction=="TypeI"){
R <- Diagonal(S*T)
r.def <- 0
if(temporal=="rw1") A.constr.st <- matrix(1,1,S*T)
if(temporal=="rw2") A.constr.st <- matrix(rep(1:S,each=T),1,S*T)
}
if(interaction=="TypeII"){
R <- kronecker(Rt,Diagonal(S))
if(temporal=="rw1") r.def <- S
if(temporal=="rw2") r.def <- 2*S
A.constr.st <- kronecker(matrix(1,1,T),Diagonal(S))
A.constr.st <- as(A.constr.st[-1,],"matrix")
}
if(interaction=="TypeIII"){
R <- kronecker(Diagonal(T),Rs)
r.def <- T
A.constr.st <- kronecker(Diagonal(T),matrix(1,1,S))
A.constr.st <- as(A.constr.st[-1,],"matrix")
}
if(interaction=="TypeIV"){
R <- kronecker(Rt,Rs)
if(temporal=="rw1") r.def <- S+T-1
if(temporal=="rw2") r.def <- 2*S+T-2
A1 <- kronecker(matrix(1,1,T),Diagonal(S))
A2 <- kronecker(Diagonal(T),matrix(1,1,S))
A.constr.st <- as(rbind(A1[-1,],A2[-1,]),"matrix")
}
return(list(R=R,r.def=r.def,A.constr.st=A.constr.st))
}
# Formula for INLA model ##
J <- length(unique(data[,ID.disease]))
form <- "O ~ -1+"
form <- paste(form, paste(paste0("I",1:J),collapse="+"),sep="")
form <- paste(form, "+ f(idx, model=Mmodel.s, constr=FALSE, extraconstr=list(A=A.constr.s, e=rep(0,J)))")
form <- paste(form, "+", paste(paste0("f(idy.",1:J,", model='generic0', Cmatrix=Rt, rankdef=dif, constr=FALSE, extraconstr=list(A=A.constr.t, e=rep(0,nrow(A.constr.t))), hyper=list(prec=list(prior=sdunif)))"), collapse=" + "), sep=" ")
if(interaction!="none"){
form <- paste(form, "+", paste(paste0("f(idz.",1:J,", model='generic0', Cmatrix=R, rankdef=r.def, constr=FALSE, extraconstr=list(A=A.constr.st, e=rep(0,nrow(A.constr.st))), hyper=list(prec=list(prior=sdunif)))"), collapse=" + "), sep=" ")
}
formula <- stats::as.formula(form)
cat("STEP 2: Fitting the model with INLA (this may take a while...)\n")
## Identifiability constraints for each disease ##
A.constr.s <- kronecker(diag(J), matrix(1,1,S))
if(temporal=="rw2" & interaction=="TypeII"){
A.constr.t <- rbind(matrix(1,1,T),matrix(1:T,1,T))
}else{
A.constr.t <- matrix(1,1,T)
}
constr <- constraints(Rs,Rt)
R <- constr$R
r.def <- constr$r.def
A.constr.st <- constr$A.constr.st
## Define data frame for INLA model ##
data.INLA <- data.frame(O=data[,O], E=data[,E], Area=data[,ID.area], Year=data[,ID.year], Disease=data[,ID.disease],
ID.area=rep(1:S,T*J), ID.year=rep(rep(1:T,each=S),J), ID.disease=rep(1:J,each=S*T), ID.area.year=rep(1:J,each=S*T))
intercepts <- dummy_cols(data.INLA$ID.disease)[,-1]
intercepts[intercepts==0] <- NA
colnames(intercepts) <- paste0("I",1:J)
data.INLA <- cbind(data.INLA, intercepts)
data.INLA$idx <- (data.INLA$ID.disease-1)*S + data.INLA$ID.area
idy.<- paste0("idy.", 1:J)
for(j in 1:J){
data.INLA[data.INLA$ID.disease==j, idy.[j]] <- data.INLA[data.INLA$ID.disease==j, "ID.year"]
}
idz.<- paste0("idz.", 1:J)
for(j in 1:J){
data.INLA[data.INLA$ID.disease==j, idz.[j]] <- (data.INLA[data.INLA$ID.disease==j, "ID.year"]-1)*S + data.INLA[data.INLA$ID.disease==j, "ID.area"]
}
## Initial values for spatial M-model ##
aux <- as.data.frame(data.INLA %>% group_by(ID.disease, ID.area) %>% summarise(SMR=sum(O)/sum(E)))
Sigma <- cov(matrix(aux$SMR,S,J,byrow=F))
N <- t(chol(Sigma))
initial.values.s <- as.vector(c(log(diag(N)), N[lower.tri(N,diag=FALSE)]))
## Define selected M-model ##
if(spatial=="intrinsic"){
Mmodel.s <- inla.rgeneric.define(Mmodel_icar, debug=FALSE, J=J, W=Ws, initial.values=initial.values.s)
}
if(spatial=="Leroux"){
Mmodel.s <- inla.rgeneric.define(Mmodel_lcar, debug=FALSE, J=J, W=Ws, initial.values=initial.values.s, alpha.min=0, alpha.max=1)
}
if(spatial=="proper"){
Mmodel.s <- inla.rgeneric.define(Mmodel_pcar, debug=FALSE, J=J, W=Ws, initial.values=initial.values.s, alpha.min=0, alpha.max=1)
}
## Fit the INLA model ##
Model <- inla(formula, family="poisson", data=data.INLA, E=E,
control.predictor=list(compute=TRUE, link=1, cdf=c(log(1))),
control.compute=list(dic=TRUE, cpo=TRUE, waic=TRUE, config=TRUE, return.marginals.predictor=TRUE),
control.inla=list(strategy=strategy))
Model$Mmodel <- list(spatial=spatial, temporal=temporal, interaction=interaction)
## Compute spatial/temporal between-disease correlations and marginal variances ##
Mmodel.compute <- Mmodel_compute_cor(Model, n.sample=10000)
Model$summary.cor <- Mmodel.compute$summary.cor
Model$marginals.cor <- Mmodel.compute$marginals.cor
Model$summary.var <- Mmodel.compute$summary.var
Model$marginals.var <- Mmodel.compute$marginals.var
return(Model)
}
#########################
## Auxiliary functions ##
#########################
tryCatch.W.E <- function(expr){
W <- NULL
w.handler <- function(w){ # warning handler
W <<- w
invokeRestart("muffleWarning")
}
list(value = withCallingHandlers(tryCatch(expr, error = function(e) e),
warning = w.handler),
warning = W)
}
compute.summary <- function(marginal){
o <- tryCatch.W.E({
aux <- data.frame(INLA::inla.emarginal(function(x) x, marginal),
sqrt(INLA::inla.emarginal(function(x) x^2, marginal)-INLA::inla.emarginal(function(x) x, marginal)^2),
INLA::inla.qmarginal(0.025,marginal),
INLA::inla.qmarginal(0.5,marginal),
INLA::inla.qmarginal(0.975,marginal),
INLA::inla.mmarginal(marginal),
1-INLA::inla.pmarginal(0,marginal))
colnames(aux) <- c("mean","sd","0.025quant","0.5quant","0.975quant","mode","1 cdf")
})
if(any(class(o[[1]])=="error")){
aux <- data.frame(NA,NA,NA,NA,NA,NA,NA)
colnames(aux) <- c("mean","sd","0.025quant","0.5quant","0.975quant","mode","1 cdf")
}
return(aux)
}
Mmodel_compute_cor <- function(model, n.sample=10000){
o <- tryCatch.W.E({
J <- length(unique(model$.args$data$ID.disease))
hyperpar.sample <- INLA::inla.hyperpar.sample(n.sample, model, improve.marginals=TRUE)
hyperpar.sample.s <- hyperpar.sample[,grep("idx",colnames(hyperpar.sample))]
## Covariance/correlation matrix for spatial M-model ##
if(model$Mmodel$spatial=="intrinsic"){
hyperpar.sample.s[,1:J] <- exp(hyperpar.sample.s[,1:J])
hyperpar.sample.s <- split(hyperpar.sample.s[,seq(J*(J+1)/2)], seq(nrow(hyperpar.sample.s)))
}else{
hyperpar.sample.s[,seq(J+1,2*J)]<- exp(hyperpar.sample.s[,seq(J+1,2*J)])
hyperpar.sample.s <- split(hyperpar.sample.s[,seq(1+J,J+J*(J+1)/2)], seq(nrow(hyperpar.sample.s)))
}
param.sample.s <- lapply(hyperpar.sample.s, function(x){
N <- diag(x[seq(J)])
N[lower.tri(N, diag=FALSE)] <- x[-seq(J)]
Sigma <- N %*% t(N)
Rho <- cov2cor(Sigma)
Rho.values <- Rho[lower.tri(Rho)]
return(list(sigma=diag(Sigma),rho=Rho.values))
})
cor.sample.s <- do.call(rbind,lapply(param.sample.s, function(x) x$rho))
cor.density.s <- apply(cor.sample.s, 2, function(x) density(x, n=75, bw="SJ", from=-1, to=1))
marginals.cor.s <- lapply(cor.density.s, function(xx) cbind(x=xx$x, y=xx$y))
names(marginals.cor.s) <- paste("rho.s",apply(combn(J,2), 2, function(x) paste0(x, collapse="")),sep="")
summary.cor.s <- do.call(rbind,lapply(marginals.cor.s, compute.summary))[,1:6]
var.sample.s <- do.call(rbind,lapply(param.sample.s, function(x) x$sigma))
var.density.s <- apply(var.sample.s, 2, function(x) density(x, n=75, bw="SJ", from=0))
marginals.var.s <- lapply(var.density.s, function(xx) cbind(x=xx$x, y=xx$y))
names(marginals.var.s) <- paste("var.s",1:J,sep="")
summary.var.s <- do.call(rbind,lapply(marginals.var.s, compute.summary))[,1:6]
})
if(any(class(o[[1]])=="error")){
summary.cor <- data.frame(rep(NA,ncol(combn(J,2))),rep(NA,ncol(combn(J,2))),rep(NA,ncol(combn(J,2))),rep(NA,ncol(combn(J,2))),rep(NA,ncol(combn(J,2))),rep(NA,ncol(combn(J,2))))
colnames(summary.cor) <- c("mean","sd","0.025quant","0.5quant","0.975quant","mode")
rownames(summary.cor) <- paste("rho.s",apply(combn(J,2), 2, function(x) paste0(x, collapse="")),sep="")
marginals.cor <- as.list(rep(NA,ncol(combn(J,2))))
names(marginals.cor) <- rownames(summary.cor)
summary.var <- data.frame(rep(NA,J),rep(NA,J),rep(NA,J),rep(NA,J),rep(NA,J),rep(NA,J))
colnames(summary.var) <- c("mean","sd","0.025quant","0.5quant","0.975quant","mode")
rownames(summary.var) <- paste("var.s",1:J,sep="")
marginals.var <- as.list(rep(NA,J))
names(marginals.var) <- rownames(summary.var)
}
Mmodel.compute <- list(summary.cor=summary.cor.s, marginals.cor=marginals.cor.s,
summary.var=summary.var.s, marginals.var=marginals.var.s)
return(Mmodel.compute)
}