# relrisk.ppm

##### Parametric Estimate of Spatially-Varying Relative Risk

Given a point process model fitted to a multitype point pattern, this function computes the fitted spatially-varying probability of each type of point, or the ratios of such probabilities, according to the fitted model. Optionally the standard errors of the estimates are also computed.

##### Usage

```
## S3 method for class 'ppm':
relrisk(X, \dots,
at = c("pixels", "points"),
relative = FALSE, se = FALSE,
casecontrol = TRUE, control = 1, case,
ngrid = NULL, window = NULL)
```

##### Arguments

- X
- A fitted point process model (object of class
`"ppm"`

). - ...
- Ignored.
- at
- String specifying whether to compute the probability values
at a grid of pixel locations (
`at="pixels"`

) or only at the points of`X`

(`at="points"`

). - relative
- Logical.
If
`FALSE`

(the default) the algorithm computes the probabilities of each type of point. If`TRUE`

, it computes the*relative risk*, the ratio of probabilities of each type relative to the prob - se
- Logical value indicating whether to compute standard errors as well.
- casecontrol
- Logical. Whether to treat a bivariate point pattern as consisting of cases and controls, and return only the probability or relative risk of a case. Ignored if there are more than 2 types of points. See Details.
- control
- Integer, or character string, identifying which mark value corresponds to a control.
- case
- Integer, or character string, identifying which mark value
corresponds to a case (rather than a control)
in a bivariate point pattern.
This is an alternative to the argument
`control`

in a bivariate point pattern. Ignored i - ngrid
- Optional. Dimensions of a rectangular grid of locations
inside
`window`

where the predictions should be computed. An integer, or an integer vector of length 2, specifying the number of grid points in the $y$ and $x$ directions. - window
- Optional. A window (object of class
`"owin"`

)*delimiting*the locations where predictions should be computed. Defaults to the window of the original data used to fit the model`object`

. (Applies only when

##### Details

The command `relrisk`

is generic and can be used to
estimate relative risk in different ways.
This function `relrisk.ppm`

is the method for fitted point
process models (class `"ppm"`

). It computes *parametric*
estimates of relative risk, using the fitted model.

If `X`

is a bivariate point pattern
(a multitype point pattern consisting of two types of points)
then by default,
the points of the first type (the first level of `marks(X)`

)
are treated as controls or non-events, and points of the second type
are treated as cases or events. Then by default this command computes
the spatially-varying *probability* of a case,
i.e. the probability $p(u)$
that a point at spatial location $u$
will be a case. If `relative=TRUE`

, it computes the
spatially-varying *relative risk* of a case relative to a
control, $r(u) = p(u)/(1- p(u))$.

If `X`

is a multitype point pattern with $m > 2$ types,
or if `X`

is a bivariate point pattern
and `casecontrol=FALSE`

,
then by default this command computes, for each type $j$,
a nonparametric estimate of
the spatially-varying *probability* of an event of type $j$.
This is the probability $p_j(u)$
that a point at spatial location $u$
will belong to type $j$.
If `relative=TRUE`

, the command computes the
*relative risk* of an event of type $j$
relative to a control,
$r_j(u) = p_j(u)/p_k(u)$,
where events of type $k$ are treated as controls.
The argument `control`

determines which type $k$
is treated as a control.

If `at = "pixels"`

the calculation is performed for
every spatial location $u$ on a fine pixel grid, and the result
is a pixel image representing the function $p(u)$
or a list of pixel images representing the functions
$p_j(u)$ or $r_j(u)$
for $j = 1,\ldots,m$.
An infinite value of relative risk (arising because the
probability of a control is zero) will be returned as `NA`

.

If `at = "points"`

the calculation is performed
only at the data points $x_i$. By default
the result is a vector of values
$p(x_i)$ giving the estimated probability of a case
at each data point, or a matrix of values
$p_j(x_i)$ giving the estimated probability of
each possible type $j$ at each data point.
If `relative=TRUE`

then the relative risks
$r(x_i)$ or $r_j(x_i)$ are
returned.
An infinite value of relative risk (arising because the
probability of a control is zero) will be returned as `Inf`

.

Probabilities and risks are computed from the fitted intensity of the model,
using `predict.ppm`

.
If `se=TRUE`

then standard errors will also be computed,
based on asymptotic theory, using `vcov.ppm`

.

##### Value

- If
`se=FALSE`

(the default), the format is described below. If`se=TRUE`

, the result is a list of two entries,`estimate`

and`SE`

, each having the format described below. If`X`

consists of only two types of points, and if`casecontrol=TRUE`

, the result is a pixel image (if`at="pixels"`

) or a vector (if`at="points"`

). The pixel values or vector values are the probabilities of a case if`relative=FALSE`

, or the relative risk of a case (probability of a case divided by the probability of a control) if`relative=TRUE`

.If

`X`

consists of more than two types of points, or if`casecontrol=FALSE`

, the result is:- (if
`at="pixels"`

) a list of pixel images, with one image for each possible type of point. The result also belongs to the class`"listof"`

so that it can be printed and plotted. - (if
`at="points"`

) a matrix of probabilities, with rows corresponding to data points$x_i$, and columns corresponding to types$j$.

`relative=FALSE`

, or the relative risk of each type (probability of each type divided by the probability of a control) if`relative=TRUE`

.If

`relative=FALSE`

, the resulting values always lie between 0 and 1. If`relative=TRUE`

, the results are either non-negative numbers, or the values`Inf`

or`NA`

. - (if

##### See Also

There is another method `relrisk.ppp`

for point pattern datasets
which computes *nonparametric* estimates of relative risk
by kernel smoothing.

See also
`relrisk`

,
`relrisk.ppp`

,
`ppm`

##### Examples

```
fit <- ppm(chorley ~ marks * (x+y))
rr <- relrisk(fit, relative=TRUE, control="lung", se=TRUE)
plot(rr$estimate)
plot(rr$SE)
```

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*