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|
#
# relrisk.R
#
# Estimation of relative risk
#
# $Revision: 1.53 $ $Date: 2022/03/28 07:05:55 $
#
relrisk <- function(X, ...) UseMethod("relrisk")
relrisk.ppp <- local({
relrisk.ppp <- function(X, sigma=NULL, ...,
at=c("pixels", "points"),
weights = NULL, varcov=NULL,
relative=FALSE,
adjust=1, edge=TRUE, diggle=FALSE, se=FALSE,
casecontrol=TRUE, control=1, case) {
stopifnot(is.ppp(X))
stopifnot(is.multitype(X))
control.given <- !missing(control)
case.given <- !missing(case)
at <- match.arg(at)
## evaluate numerical weights (multiple columns not allowed)
weights <- pointweights(X, weights=weights, parent=parent.frame())
weighted <- !is.null(weights)
##
npts <- npoints(X)
marx <- marks(X)
imarks <- as.integer(marx)
types <- levels(marx)
ntypes <- length(types)
if(ntypes == 1)
stop("Data contains only one type of points")
##
casecontrol <- casecontrol && (ntypes == 2)
if((control.given || case.given) && !(casecontrol || relative)) {
aa <- c("control", "case")[c(control.given, case.given)]
nn <- length(aa)
warning(paste(ngettext(nn, "Argument", "Arguments"),
paste(sQuote(aa), collapse=" and "),
ngettext(nn, "was", "were"),
"ignored, because relative=FALSE and",
if(ntypes==2) "casecontrol=FALSE" else
"there are more than 2 types of points"))
}
## prepare for analysis
Y <- split(X)
splitweights <- if(weighted) split(weights, marx) else rep(list(NULL), ntypes)
uX <- unmark(X)
## compute bandwidth (default bandwidth selector is bw.relrisk)
ker <- resolve.2D.kernel(...,
sigma=sigma, varcov=varcov, adjust=adjust,
bwfun=bw.relrisk, x=X)
sigma <- ker$sigma
varcov <- ker$varcov
## determine smoothing parameters
if(bandwidth.is.infinite(sigma))
edge <- FALSE
SmoothPars <- resolve.defaults(list(sigma=sigma, varcov=varcov, at=at,
edge=edge, diggle=diggle),
list(...))
## threshold for 0/0
tinythresh <- 8 * .Machine$double.eps
##
if(se) {
## determine other bandwidth for variance estimation
VarPars <- SmoothPars
if(bandwidth.is.infinite(sigma)) {
varconst <- 1
} else if(is.null(varcov)) {
varconst <- 1/(4 * pi * prod(sigma))
VarPars$sigma <- sigma/sqrt(2)
} else {
varconst <- 1/(4 * pi * sqrt(det(varcov)))
VarPars$varcov <- varcov/2
}
if(edge) {
## evaluate edge correction weights
edgeim <- do.call(second.moment.calc,
append(list(x=uX, what="edge"), SmoothPars))
if(diggle || at == "points") {
edgeX <- safelookup(edgeim, uX, warn=FALSE)
diggleX <- 1/edgeX
diggleX[!is.finite(diggleX)] <- 0
}
edgeim <- edgeim[Window(X), drop=FALSE]
}
}
## .........................................
## compute intensity estimates for each type
## .........................................
switch(at,
pixels = {
## intensity estimates of each type
Deach <- do.call(density.splitppp,
append(list(x=Y, weights=splitweights),
SmoothPars))
## compute intensity estimate for unmarked pattern
Dall <- im.apply(Deach, sum, check=FALSE)
## WAS: Dall <- Reduce("+", Deach)
## variance terms
if(se) {
if(!edge) {
## no edge correction
Veach <- do.call(density.splitppp,
append(list(x=Y, weights=splitweights),
VarPars))
} else if(!diggle) {
## edge correction e(u)
Veach <- do.call(density.splitppp,
append(list(x=Y, weights=splitweights),
VarPars))
#' Ops.imlist not yet working
Veach <- imagelistOp(Veach, edgeim, "/")
} else {
## Diggle edge correction e(x_i)
diggweights <- if(weighted) { diggleX * weights } else diggleX
Veach <- as.solist(mapply(density.ppp,
x=Y,
weights=split(diggweights, marx),
MoreArgs=VarPars,
SIMPLIFY=FALSE))
}
#' Ops.imlist not yet working
Veach <- imagelistOp(Veach, varconst, "*")
Vall <- im.apply(Veach, sum, check=FALSE)
## WAS: Vall <- Reduce("+", Veach)
}
},
points = {
## intensity estimates of each type **at each data point**
## dummy variable matrix
dumm <- matrix(0, npts, ntypes)
dumm[cbind(seq_len(npts), imarks)] <- 1
colnames(dumm) <- types
if(weighted) dumm <- dumm * weights
Deach <- do.call(density.ppp,
append(list(x=uX, weights=dumm),
SmoothPars))
## compute intensity estimate for unmarked pattern
Dall <- rowSums(Deach)
## variance terms
if(se) {
if(!edge) {
## no edge correction
Veach <- do.call(density.ppp,
append(list(x=uX, weights=dumm),
VarPars))
} else if(!diggle) {
## edge correction e(u)
Veach <- do.call(density.ppp,
append(list(x=uX, weights=dumm),
VarPars))
Veach <- Veach * diggleX
} else {
## Diggle edge correction e(x_i)
Veach <- do.call(density.ppp,
append(list(x=uX, weights=dumm * diggleX),
VarPars))
}
Veach <- Veach * varconst
Vall <- rowSums(Veach)
}
})
## .........................................
## compute probabilities/risks
## .........................................
if(ntypes == 2 && casecontrol) {
if(control.given || !case.given) {
stopifnot(length(control) == 1)
if(is.numeric(control)) {
icontrol <- control <- as.integer(control)
stopifnot(control %in% 1:2)
} else if(is.character(control)) {
icontrol <- match(control, types)
if(is.na(icontrol)) stop(paste("No points have mark =", control))
} else
stop(paste("Unrecognised format for argument", sQuote("control")))
if(!case.given)
icase <- 3 - icontrol
}
if(case.given) {
stopifnot(length(case) == 1)
if(is.numeric(case)) {
icase <- case <- as.integer(case)
stopifnot(case %in% 1:2)
} else if(is.character(case)) {
icase <- match(case, types)
if(is.na(icase)) stop(paste("No points have mark =", case))
} else stop(paste("Unrecognised format for argument", sQuote("case")))
if(!control.given)
icontrol <- 3 - icase
}
## compute ......
switch(at,
pixels = {
## compute probability of case
Dcase <- Deach[[icase]]
pcase <- Dcase/Dall
dodgy <- (Dall < tinythresh)
## correct small numerical errors
pcase <- clamp01(pcase)
## trap NaN values, and similar
nbg <- badvalues(pcase) | really(dodgy)
if(any(nbg)) {
## apply l'Hopital's rule:
## p(case) = 1{nearest neighbour is case}
distcase <- distmap(Y[[icase]], xy=pcase)
distcontrol <- distmap(Y[[icontrol]], xy=pcase)
closecase <- eval.im(as.integer(distcase < distcontrol))
pcase[nbg] <- closecase[nbg]
}
if(!relative) {
if(!se) {
result <- pcase
} else {
Vcase <- Veach[[icase]]
NUM <- eval.im(Vcase * (1-2*pcase) + Vall * pcase^2)
SE <- eval.im(sqrt(pmax(NUM, 0))/Dall)
result <- solist(estimate=pcase, SE=SE)
}
} else {
rcase <- eval.im(ifelse(pcase < 1, pcase/(1-pcase), NA))
if(!se) {
result <- rcase
} else {
Vcase <- Veach[[icase]]
Vctrl <- Veach[[icontrol]]
Dctrl <- Deach[[icontrol]]
NUM <- eval.im(Vcase + Vctrl * rcase^2)
SE <- eval.im(sqrt(pmax(NUM, 0))/Dctrl)
result <- solist(estimate=rcase, SE=SE)
}
}
},
points={
## compute probability of case
pcase <- Deach[,icase]/Dall
dodgy <- (Dall < tinythresh)
## correct small numerical errors
pcase <- clamp01(pcase)
## trap NaN values
if(any(nbg <- badvalues(pcase) | really(dodgy))) {
## apply l'Hopital's rule
nntype <- imarks[nnwhich(X)]
pcase[nbg] <- as.integer(nntype[nbg] == icase)
}
if(!relative) {
if(!se) {
result <- pcase
} else {
NUM <- Veach[,icase] * (1-2*pcase) + Vall * pcase^2
SE <- sqrt(pmax(NUM, 0))/Dall
result <- list(estimate=pcase, SE=SE)
}
} else {
rcase <- ifelse(pcase < 1, pcase/(1-pcase), NA)
if(!se) {
result <- rcase
} else {
NUM <- Veach[,icase] + Veach[,icontrol] * rcase^2
SE <- sqrt(pmax(NUM, 0))/Deach[,icontrol]
result <- list(estimate=rcase, SE=SE)
}
}
})
} else {
## several types
if(relative) {
## need 'control' type
stopifnot(length(control) == 1)
if(is.numeric(control)) {
icontrol <- control <- as.integer(control)
stopifnot(control %in% 1:ntypes)
} else if(is.character(control)) {
icontrol <- match(control, types)
if(is.na(icontrol)) stop(paste("No points have mark =", control))
} else
stop(paste("Unrecognised format for argument", sQuote("control")))
}
switch(at,
pixels={
#' Ops.imagelist not yet working
probs <- imagelistOp(Deach, Dall, "/")
dodgy <- (Dall < tinythresh)
## correct small numerical errors
probs <- as.solist(lapply(probs, clamp01))
## trap NaN values
nbg <- lapply(probs, badvalues)
nbg <- Reduce("|", nbg)
nbg <- nbg | really(dodgy)
if(any(nbg)) {
## apply l'Hopital's rule
distX <- distmap(X, xy=Dall)
whichnn <- attr(distX, "index")
typenn <- eval.im(imarks[whichnn])
typennsub <- as.matrix(typenn)[nbg]
for(k in seq_along(probs))
probs[[k]][nbg] <- (typennsub == k)
}
if(!relative) {
if(!se) {
result <- probs
} else {
SE <- list()
for(i in 1:ntypes) {
NUM <- (Veach[[i]] * (1 - 2 * probs[[i]])
+ Vall * probs[[i]]^2)
SE[[i]] <- eval.im(sqrt(pmax(NUM, 0))/Dall)
}
SE <- as.solist(SE)
names(SE) <- types
result <- list(estimate=probs, SE=SE)
}
} else {
risks <- as.solist(lapply(probs,
divideifpositive,
d = probs[[icontrol]]))
if(!se) {
result <- risks
} else {
Vctrl <- Veach[[icontrol]]
Dctrl <- Deach[[icontrol]]
SE <- list()
for(i in 1:ntypes) {
NUM <- Veach[[i]] + Vctrl * risks[[i]]^2
SE[[i]] <- eval.im(sqrt(pmax(NUM, 0))/Dctrl)
}
SE <- as.solist(SE)
names(SE) <- types
result <- list(estimate=risks, SE=SE)
}
}
},
points = {
probs <- Deach/Dall
dodgy <- (Dall < tinythresh)
## correct small numerical errors
probs <- clamp01(probs)
## trap NaN values
bad <- badvalues(probs)
badrow <- matrowany(bad) | really(dodgy)
if(any(badrow)) {
## apply l'Hopital's rule
typenn <- imarks[nnwhich(X)]
probs[badrow, ] <- (typenn == col(result))[badrow, ]
}
if(!relative) {
if(!se) {
result <- probs
} else {
NUM <- Veach * (1-2*probs) + Vall * probs^2
SE <- sqrt(pmax(NUM, 0))/Dall
result <- list(estimate=probs, SE=SE)
}
} else {
risks <- probs/probs[,icontrol]
if(!se) {
result <- risks
} else {
NUM <- Veach + Veach[,icontrol] * risks^2
NUM[,icontrol] <- 0
SE <- sqrt(pmax(NUM, 0))/Deach[,icontrol]
result <- list(estimate=risks, SE=SE)
}
}
})
}
attr(result, "sigma") <- sigma
attr(result, "varcov") <- varcov
return(result)
}
clamp01 <- function(x) {
if(is.im(x)) return(eval.im(pmin(pmax(x, 0), 1)))
return(pmin(pmax(x, 0), 1))
}
badvalues <- function(x) {
if(is.im(x)) x <- as.matrix(x)
return(!(is.finite(x) | is.na(x)))
}
really <- function(x) {
if(is.im(x)) x <- as.matrix(x)
x[is.na(x)] <- FALSE
return(x)
}
reciprocal <- function(x) 1/x
divideifpositive <- function(z, d) { eval.im(ifelse(d > 0, z/d, NA)) }
relrisk.ppp
})
bw.stoyan <- function(X, co=0.15) {
## Stoyan's rule of thumb
stopifnot(is.ppp(X))
n <- npoints(X)
W <- Window(X)
a <- area(W)
stoyan <- co/sqrt(5 * max(1,n)/a)
return(stoyan)
}
bw.relrisk <- function(X, method="likelihood",
nh=spatstat.options("n.bandwidth"),
hmin=NULL, hmax=NULL, warn=TRUE) {
stopifnot(is.ppp(X))
stopifnot(is.multitype(X))
## rearrange in ascending order of x-coordinate (for C code)
X <- X[fave.order(X$x)]
##
Y <- split(X)
ntypes <- length(Y)
if(ntypes == 1)
stop("Data contains only one type of points")
n <- npoints(X)
marx <- marks(X)
method <- pickoption("method", method,
c(likelihood="likelihood",
leastsquares="leastsquares",
ls="leastsquares",
LS="leastsquares",
weightedleastsquares="weightedleastsquares",
wls="weightedleastsquares",
WLS="weightedleastsquares"))
##
if(method != "likelihood") {
## dummy variables for each type
imarks <- as.integer(marx)
if(ntypes == 2) {
## 1 = control, 2 = case
indic <- (imarks == 2)
y01 <- as.integer(indic)
} else {
indic <- matrix(FALSE, n, ntypes)
indic[cbind(seq_len(n), imarks)] <- TRUE
y01 <- indic * 1
}
X01 <- X %mark% y01
}
## cross-validated bandwidth selection
## determine a range of bandwidth values
if(is.null(hmin) || is.null(hmax)) {
W <- Window(X)
a <- area(W)
d <- diameter(as.rectangle(W))
## Stoyan's rule of thumb applied to the least and most common types
mcount <- table(marx)
nmin <- max(1, min(mcount))
nmax <- max(1, max(mcount))
stoyan.low <- 0.15/sqrt(nmax/a)
stoyan.high <- 0.15/sqrt(nmin/a)
if(is.null(hmin))
hmin <- max(minnndist(unique(X)), stoyan.low/5)
if(is.null(hmax)) {
hmax <- min(d/4, stoyan.high * 20)
hmax <- max(hmax, hmin * 2)
}
} else stopifnot(hmin < hmax)
##
h <- geomseq(from=hmin, to=hmax, length.out=nh)
cv <- numeric(nh)
##
## compute cross-validation criterion
switch(method,
likelihood={
methodname <- "Likelihood"
## for efficiency, only compute the estimate of p_j(x_i)
## when j = m_i = mark of x_i.
Dthis <- numeric(n)
for(i in seq_len(nh)) {
Dall <- density.ppp(X, sigma=h[i], at="points", edge=FALSE,
sorted=TRUE)
Deach <- density.splitppp(Y, sigma=h[i], at="points", edge=FALSE,
sorted=TRUE)
split(Dthis, marx) <- Deach
pthis <- Dthis/Dall
cv[i] <- -mean(log(pthis))
}
},
leastsquares={
methodname <- "Least Squares"
for(i in seq_len(nh)) {
phat <- Smooth(X01, sigma=h[i], at="points", leaveoneout=TRUE,
sorted=TRUE)
phat <- as.matrix(phat)
cv[i] <- mean((y01 - phat)^2)
}
},
weightedleastsquares={
methodname <- "Weighted Least Squares"
## need initial value of h from least squares
h0 <- bw.relrisk(X, "leastsquares", nh=ceiling(nh/4))
phat0 <- Smooth(X01, sigma=h0, at="points", leaveoneout=TRUE,
sorted=TRUE)
phat0 <- as.matrix(phat0)
var0 <- phat0 * (1-phat0)
var0 <- pmax.int(var0, 1e-6)
for(i in seq_len(nh)) {
phat <- Smooth(X01, sigma=h[i], at="points", leaveoneout=TRUE,
sorted=TRUE)
phat <- as.matrix(phat)
cv[i] <- mean((y01 - phat)^2/var0)
}
})
## optimize
result <- bw.optim(cv, h,
hname="sigma",
creator="bw.relrisk",
criterion=paste(methodname, "Cross-Validation"),
warnextreme=warn,
hargnames=c("hmin", "hmax"),
unitname=unitname(X))
return(result)
}
which.max.im <- function(x) {
.Deprecated("im.apply", "spatstat.geom",
"which.max.im(x) is deprecated: use im.apply(x, which.max)")
ans <- im.apply(x, which.max)
return(ans)
}
|
