surveillance (version 1.12.1)

knox: Knox Test for Space-Time Interaction

Description

Given temporal and spatial distances as well as corresponding critical thresholds defining what close means, the function knox performs Knox (1963, 1964) test for space-time interaction. The corresponding p-value can be calculated either by the Poisson approximation or by a Monte Carlo permutation approach (Mantel, 1967) with support for parallel computation via plapply. There is a simple plot-method showing a truehist of the simulated null distribution together with the expected and observed values. This implementation of the Knox test is due to Meyer et al. (2016).

Usage

knox(dt, ds, eps.t, eps.s, simulate.p.value = TRUE, B = 999, ...)
## S3 method for class 'knox':
plot(x, ...)

Arguments

dt,ds

numeric vectors containing temporal and spatial distances, respectively. Logical vectors indicating temporal/spatial closeness may also be supplied, in which case eps.t/eps.s is ignored. To test for space-time interac

eps.t,eps.s

Critical distances defining closeness in time and space, respectively. Distances lower than or equal to the critical distance are considered "close".

simulate.p.value

logical indicating if a Monte Carlo permutation test should be performed (as per default). Do not forget to set the .Random.seed via an extra .seed argument if reproducibility

B

number of permutations for the Monte Carlo approach.

...

arguments configuring plapply: .parallel, .seed, and .verbose. By default, no parallelization is performed (.parallel = 1), and a progress bar

x

an object of class "knox" as returned by the knox test.

Value

• an object of class "knox" (inheriting from "htest"), which is a list with the following components:
• method
  a character string indicating the type of test performed, and whether the Poisson approximation or Monte Carlo simulation was used.
• data.name
  a character string giving the supplied dt and ds arguments.
• statistic
  the number of close pairs.
• parameter
  if simulate.p.value = TRUE, the number B of permutations, otherwise the lambda parameter of the Poisson distribution, i.e., the same as null.value.
• p.value
  the p-value for the test. In case simulate.p.value = TRUE, the p-value from the Poisson approximation is still attached as an attribute "Poisson".
• alternative
  the character string "greater" (this is a one-sided test).
• null.value
  the expected number of close pairs in the absence of space-time interaction.
• table
  the contingency table of dt <= eps.t<="" code=""> and ds <= eps.s<="" code="">.
• The plot-method invisibly returns NULL.

References

Knox, G. (1963): Detection of low intensity epidemicity: application to cleft lip and palate. British Journal of Preventive & Social Medicine, 17, 121-127. Knox, E. G. (1964): The detection of space-time interactions. Journal of the Royal Statistical Society. Series C (Applied Statistics), 13, 25-30.

Kulldorff, M. and Hjalmars, U. (1999): The Knox method and other tests for space-time interaction. Biometrics, 55, 544-552. Mantel, N. (1967): The detection of disease clustering and a generalized regression approach. Cancer Research, 27, 209-220.

Meyer, S., Warnke, I., R�{oe}ssler, W. and Held, L. (2016): Model-based testing for space-time interaction using point processes: An application to psychiatric hospital admissions in an urban area. Spatial and Spatio-temporal Epidemiology, 17, 15-25. 10.1016/j.sste.2016.03.002. Eprint: http://arxiv.org/abs/1512.09052.

See Also

the space-time K-function test stKtest to combine information from different scales eps.t and eps.s while also handling edge effects, as well as function epitest for testing "twinstim" models.

Examples

data("imdepi")
imdepiB <- subset(imdepi, type == "B")

## Obtain the p-value via a Monte Carlo permutation test,
## where the permutations can be computed in parallel
## (using forking on Unix-alikes and a cluster on Windows, see ?plapply)
knoxtest <- knox(
    dt = dist(imdepiB$events$time), eps.t = 30,
    ds = dist(coordinates(imdepiB$events)), eps.s = 50,
    simulate.p.value = TRUE, B = 199,
    .parallel = 2, .seed = 1, .verbose = FALSE
)
knoxtest
plot(knoxtest)