inla.rgeneric.Mmodel.model: M-model: Proper multivariate CAR latent effect with a different spatial autorcorrelation parameter for each disease.

Description

Multivariate generalization of the proper conditional autorregresive model with one common correlation parameter. This model is performed using the M-model aproximation of Rocamora et. al. (2015).

Usage

inla.rgeneric.Mmodel.model(cmd, theta)
inla.Mmodel.model(...)

Arguments

...

Arguments to be passed to 'inla.rgeneric.define'.

cmd

Arguments used by latent effects defined using the 'rgeneric' latent effect.

theta

Vector of hyperparameters.

Value

This is used internally by the 'INLA::inla()'.

Prior distributions of the hyperparameters

The hyperparamenters of this lattent effect are the common spatial autocorrelation parameters (one for each disease) and the entries of the M matrix (considered all as a random effects).

Details

This function is used to define a latent effect that is a multivariate spatial effect based on the M-model aproximation of Rocamora et. al. (2015) in which \(\theta\) is modelled as a product of a \(\Phi \cdot M\) where the colums of \(\Phi\) are modeled independently with a proper conditional autorregresive distribution with a different spatial autocorrelation parameter for each disease and M is a square matrix which introduce de dependence between the diseases. Due to this effect is a multivariate spatial latent effect this function requires the following arguments when defining the latent effect:

W Adjacency SPARSE matrix for spatial effect in the basic binary code.
k Number of diseases of the multivariate study.
alpha.min Minimum value of the spatial autocorrelation parameter.
alpha.max Maximum value of the spatial autocorrelation parameter.

This model is defined using the 'f()' function and an index in order to identify the spatial areas. See the example.

Examples

Run this code

# NOT RUN {
# }
# NOT RUN {
if (require("INLA", quietly = TRUE)) {
require(spdep)
require(spData)
require(rgdal)

#Load SIDS data
nc.sids <- readOGR(system.file("shapes/sids.shp", package="spData")[1])
proj4string(nc.sids) <- CRS("+proj=longlat +ellps=clrk66")

#Compute adjacency matrix, as nb object 'adj' and sparse matrix 'W'
adj <- poly2nb(nc.sids)
W <- as(nb2mat(adj, style = "B"), "Matrix")

#Compute expected cases
r74 <- sum(nc.sids$SID74) / sum(nc.sids$BIR74)
nc.sids$EXP74 <- r74 * nc.sids$BIR74
nc.sids$SMR74 <- nc.sids$SID74 / nc.sids$EXP74
nc.sids$NWPROP74 <- nc.sids$NWBIR74 / nc.sids$BIR74

r79 <- sum(nc.sids$SID79) / sum(nc.sids$BIR79)
nc.sids$EXP79 <- r79 * nc.sids$BIR79
nc.sids$SMR79 <- nc.sids$SID79 / nc.sids$EXP79
nc.sids$NWPROP79 <- nc.sids$NWBIR79 / nc.sids$BIR79

# Data (replicated to assess scalability)

#Real data
n.rep <- 1
d <- list(OBS = c(nc.sids$SID74, nc.sids$SID79),
          NWPROP = c(nc.sids$NWPROP74, nc.sids$NWPROP79),
          EXP = c(nc.sids$EXP74, nc.sids$EXP79))
d <- lapply(d, function(X) { rep(X, n.rep)})
d$idx <- 1:length(d$OBS)

#Parameters of the Mmodel
k <- 2
alpha.min <- 0
alpha.max <- 1



model <- inla.rgeneric.define(inla.rgeneric.Mmodel.model, debug = FALSE,
                              k = k, W = W, alpha.min = alpha.min,
                              alpha.max = alpha.max)

r.Mmodel <- inla(OBS ~ -1 + f(idx, model = model), data = d, E = EXP,
  family = "poisson", control.predictor = list(compute = TRUE))

nc.sids$Model1 <- r.Mmodel$summary.random$idx[1:100, "mean"]
nc.sids$Model2 <- r.Mmodel$summary.random$idx[100 + 1:100, "mean"]

spplot(nc.sids, c("Model1", "Model2"))

nc.sids$Fit1 <- r.Mmodel$summary.fitted[1:100, "mean"]
nc.sids$Fit2 <- r.Mmodel$summary.fitted[100 + 1:100, "mean"]

spplot(nc.sids, c("Fit1", "SMR74", "Fit2", "SMR79"))


## Running UNIVARIATE MODEL

#Real data
n.rep <- 1
d <- list(OBS = nc.sids$SID74,
          NWPROP = nc.sids$NWPROP74,
          EXP = nc.sids$EXP74)
d <- lapply(d, function(X) { rep(X, n.rep)})
d$idx <- 1:length(d$OBS)

#Fit model
r.uni <- inla(OBS ~ 1 + f(idx, model = "besag", graph = W), # + NWPROP,
              data = d, E = EXP, family = "poisson",
              control.predictor = list(compute = TRUE))

summary(r.uni)

nc.sids$FITTED74.uni <- r.uni$summary.fitted.values[ , "mean"]

#Display univariate VS multivariate  fitted relative risks.
dev.new()
spplot(nc.sids, c("SMR74", "Fit1", "FITTED74.uni"))
spplot(nc.sids, c("Fit1", "FITTED74.uni"),
       main=list(label="Relative risk estimation",cex=2))
dev.new()
plot(nc.sids$FITTED74.uni, nc.sids$Fit1, main="Relative Risk estimations",
     xlab="Univariate RR estimations"
     , ylab="Multivariate RR estimations")#, xlim=c(0.5, 2.5), ylim=c(0, 2))
abline(h=0, col="grey")
abline(v=0, col="grey")
abline(a=0, b=1, col="red")

}
# }
# NOT RUN {
# }

Run the code above in your browser using DataCamp Workspace