relrisk.ppm {spatstat.model}

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,\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 "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 [e-mail], Rolf Turner [e-mail] and Ege Rubak [e-mail].

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")