R: Parametric Estimate of Spatially-Varying Relative Risk

relrisk.ppm {spatstat} | R Documentation

## Parametric Estimate of Spatially-Varying Relative Risk

### Description

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, ...,
                         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 probability of a control.
`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 if there are more than 2 types of points.
`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. (Applies only when `at="pixels"`.)
`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 `at="pixels"`.)

### 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,...,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 `"solist"` 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.

The pixel values or matrix entries are the probabilities of each type of point if `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`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

### 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)
      rrX <- relrisk(fit, at="points", relative=TRUE, control="lung")

[Package spatstat version 1.54-0 Index]