logrr computes the estimated log relative risk of
cases relative to controls. The log relative risk at
location s is defined as r(s) = ln(f(s)/g(s)). The
numerator, f(s), is the spatial density of the
case group. The denominator, g(s), is the spatial
density of the control group. If nsim > 0, then
pointwise (at each pixel) tolerance envelopes are
estimated under the random labeling hypothesis. The
tolerance envelopes can be used to assess pixels where
the log relative risk differs significantly from zero.
See Details.
logrr(
x,
sigma = NULL,
sigmacon = NULL,
case = 2,
nsim = 0,
level = 0.9,
alternative = "two.sided",
envelope = "pixelwise",
...,
bwargs = list(),
weights = NULL,
edge = TRUE,
varcov = NULL,
at = "pixels",
leaveoneout = TRUE,
adjust = 1,
diggle = FALSE,
kernel = "gaussian",
scalekernel = is.character(kernel),
positive = FALSE,
verbose = TRUE,
return_sims = FALSE
)The function produces an object of type
logrrenv. Its components are similar to those
returned by the
density.ppp, with the
intensity values replaced by the log ratio of spatial
densities of f and g. Includes an array simr of
dimension c(nx, ny, nsim + 1), where nx and ny are the
number of x and y grid points used to estimate the
spatial density. simr[,,1] is the log ratio of
spatial densities for the observed data, and the
remaining nsim elements in the third dimension
of the array are the log ratios of spatial densities
from a new ppp simulated under the random labeling
hypothesis.
A ppp object
package with marks for the case and control groups.
x$marks is assumed to be a factor. Automatic
conversion is attempted if it is not.
Standard deviation of isotropic smoothing
kernel for cases. Either a numerical value, or a
function that computes an appropriate value of
sigma. If not specified, then
bw.relrisk is used.
Standard deviation of isotropic smoothing
kernel for controls. Default is the same as
sigma.
The name of the desired "case" group in
levels(x$marks). Alternatively, the position of
the name of the "case" group in levels(x$marks).
Since we don't know the group names, the default is 2,
the second position of levels(x$marks).
x$marks is assumed to be a factor. Automatic
conversion is attempted if it is not.
The number of simulated data sets from which to construct tolerance envelopes under the random labeling hypothesis. The default is 0 (i.e., no envelopes).
The level of the tolerance envelopes.
The type of envelopes to construct.
The default is "two.sided" (upper and lower
envelopes). The values "less" (lower envelope)
and "greater" (upper envelope) are also valid.
The type of envelope to construct. The
default is "pixelwise". The other option is
"simulataneous", which controls the tolerance
level across the entire study area.
Additional arguments passed to pixellate.ppp
and as.mask to determine
the pixel resolution, or passed to sigma if it is a function.
A list of arguments for the bandwidth
function supplied to sigma and sigmacon,
if applicable.
Optional weights to be attached to the points.
A numeric vector, numeric matrix, an expression,
or a pixel image.
Logical value indicating whether to apply edge correction.
Variance-covariance matrix of anisotropic smoothing kernel.
Incompatible with sigma.
String specifying whether to compute the intensity values
at a grid of pixel locations (at="pixels") or
only at the points of x (at="points").
Logical value indicating whether to compute a leave-one-out
estimator. Applicable only when at="points".
Optional. Adjustment factor for the smoothing parameter.
Logical. If TRUE, use the Jones-Diggle improved edge correction,
which is more accurate but slower to compute than the default
correction.
The smoothing kernel.
A character string specifying the smoothing kernel
(current options are "gaussian", "epanechnikov",
"quartic" or "disc"),
or a pixel image (object of class "im")
containing values of the kernel, or a function(x,y) which
yields values of the kernel.
Logical value.
If scalekernel=TRUE, then the kernel will be rescaled
to the bandwidth determined by sigma and varcov:
this is the default behaviour when kernel is a character string.
If scalekernel=FALSE, then sigma and varcov
will be ignored: this is the default behaviour when kernel is a
function or a pixel image.
Logical value indicating whether to force all density values to
be positive numbers. Default is FALSE.
Logical value indicating whether to issue warnings about numerical problems and conditions.
A logical value indicating whether
parts of the simulated data shoudl be returned. The
default is FALSE. This is mostly used for
debugging purposes.
Joshua French (and a small chunk by the authors
of the density.ppp)
function for consistency with the default behavior of
that function).
If nsim=0, the plot function creates a heat
map of the log relative risk. If nsim > 0, the
plot function colors the pixels where the
estimated log relative risk is outside the tolerance
envelopes created under the random labeling hypothesis
(i.e., pixels with potential clustering of cases or
controls). Colored regions with values above 0 indicate a
cluster of cases relative to controls (without
controlling for multiple comparisons), i.e., a region
where the the density of the cases is greater than the
the density of the controls. Colored regions with values
below 0 indicate a cluster of controls relative to cases
(without controlling for multiple comparisons), i.e., a
region where the density of the controls is greater than
the density of the cases.
The two.sided alternative test constructs
two-sided tolerance envelopes to assess whether the
estimated r(s) deviates more than what is expected
under the random labeling hypothesis. The greater
alternative constructs an upper tolerance envelope to
assess whether the estimated r(s) is greater than
what is expected under the random labeling hypothesis,
i.e., where there is clustering of cases relative to
controls. The lower alternative constructs a lower
tolerance envelope to assess whether the estimated
r(s) is lower than what is expected under the
random labeling hypothesis, i.e., where there is
clustering of controls relative to cases.
If the estimated density of the case or control group
becomes too small, this function may produce warnings due
to numerical underflow. Increasing the bandwidth
(sigma) may help.
Waller, L.A. and Gotway, C.A. (2005). Applied Spatial Statistics for Public Health Data. Hoboken, NJ: Wiley.
Kelsall, Julia E., and Peter J. Diggle. "Kernel estimation of relative risk." Bernoulli (1995): 3-16.
Kelsall, Julia E., and Peter J. Diggle. "Non-parametric estimation of spatial variation in relative risk." Statistics in Medicine 14.21-22 (1995): 2335-2342.
Hegg, Alex and French, Joshua P. (2022) "Simultaneous tolerance bands of log relative risk for case-control point data. Technical report.
data(grave)
# estimate and plot log relative risk
r = logrr(grave, case = "affected")
plot(r)
# use scott's bandwidth
r2 = logrr(grave, case = 2, sigma = spatstat.explore::bw.scott)
plot(r2)
# construct pointwise tolerance envelopes for log relative risk
if (FALSE) {
renv = logrr(grave, nsim = 9)
print(renv) # print information about envelopes
plot(renv) # plot results
# plot using a better gradient
grad = gradient.color.scale(min(renv$v, na.rm = TRUE), max(renv$v, na.rm = TRUE))
plot(renv, col = grad$col, breaks = grad$breaks, conlist = list(col = "lightgrey"))}
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