surveillance (version 1.12.1)

twinstim_epitest: Permutation Test for Space-Time Interaction in "twinstim"

Description

The function epitest takes an epidemic "twinstim" model (with homogeneous infectivity of events, i.e., epidemic = ~1), and tests if the spatio-temporal interaction invoked by the epidemic model component is statistically significant. A permutation test is performed by default, which is only valid if the endemic intensity is space-time separable. The approach is described in detail in Meyer et al. (2016), where it is also compared to alternative global tests for clustering such as the knox test.

Usage

epitest(model, data, tiles, method = "time", B = 199,
        eps.s = NULL, eps.t = NULL, fixed = NULL,
        verbose = TRUE, compress = FALSE, ...)
## S3 method for class 'epitest':
coef(object, which = c("m1", "m0"), ...)
## S3 method for class 'epitest':
plot(x, teststat = c("simpleR0", "D"), ...)

Arguments

model

a simple epidemic "twinstim" without covariates, i.e., epidemic = ~1. This is because covariate effects in the epidemic component are not well identified when there is no space-tim

data

an object of class "epidataCS", the data to which the model was fitted.

tiles

(only used by method = "simulate") a "SpatialPolygons" representation of the tiles in data$stgrid.

method

one of the following character strings specifying the test method: [object Object],[object Object],[object Object]

B

the number of permutations for the Monte Carlo approach. The default number is rather low; if computationally feasible, B = 999 is more appropriate. Note that this determines the resolution of the p-value: the sma

eps.s,eps.t

arguments for simpleR0.

fixed

optional character vector naming parameters to fix at their original value when re-fitting the model on permuted data. The special value fixed = TRUE means to fix all epidemic parameters but the intercept.

verbose

the amount of tracing in the range 0:3. Set to 0 (or FALSE) for no output, 1 (or TRUE, the default) for a progress bar, 2 for the test statistics resulting from each permutation, and to 3 for addition

compress

logical indicating if the nobs-dependent elements "fitted", "fittedComponents", and "R0" should be dropped from the permutation-based model fits. Not keeping these elements saves a lot of mem

...

further arguments for plapply to configure parallel operation, i.e., .parallel as well as .seed to make the results reproducible. For the plot-method, further

object,x

an object of class "epitest" as returned by epitest.

which

a character string indicating either the full ("m1", default) or the endemic-only ("m0") model.

teststat

a character string determining the test statistic to plot, either "simpleR0" or "D" (twice the log-likelihood difference of the models).

Value

• a list (inheriting from "htest") with the following components:
• method
  a character string indicating the type of test performed.
• data.name
  a character string giving the supplied data and model arguments.
• statistic
  the observed test statistic.
• parameter
  the (effective) number of permutations used to calculate the p-value (only those with convergent fits are used).
• p.value
  the p-value for the test. For the methods involving resampling under the null (method != "LRT"), it is based on the subset of convergent fits only and the p-value from the simple LRT is attached as an attribute "LRT".
• In addition, if method != "LRT", the result will have the following elements:
• permfits
  the list of model fits (endemic-only and epidemic) from the B permutations.
• permstats
  a data frame with B rows and the columns "l0" (log-likelihood of the endemic-only model m0), "l1" (log-likelihood of the epidemic model m1), "D" (twice their difference), "simpleR0" (the results of simpleR0(m1, eps.s, eps.t)), and "converged" (a boolean indicator if both models converged).
• The plot-method invisibly returns NULL. The coef-method returns the B x length(coef(model)) matrix of parameter estimates.

Details

The test statistic is the reproduction number simpleR0. A likelihood ratio test of the supplied epidemic model against the corresponding endemic-only model is also available. By default, the null distribution of the test statistic under no space-time interaction is obtained by a Monte Carlo permutation approach (via permute.epidataCS) and therefore relies on a space-time separable endemic model component. The plot-method shows a truehist of the simulated null distribution together with the observed value. The coef-method extracts the parameter estimates from the B permfits (by default for the full model which = "m1").

References

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

permute.epidataCS, knox

Examples

data("imdepi")
data("imdepifit")

## test for space-time interaction of the B-cases
## assuming spatial interaction to be constant within 50 km
imdepiB50 <- update(subset(imdepi, type == "B"), eps.s = 50)
imdfitB50 <- update(imdepifit, data = imdepiB50,
                    epidemic = ~1, epilink = "identity",
                    siaf = NULL, control.siaf = NULL,
                    start = c("e.(Intercept)" = 1e-6))

## simple likelihood ratio test
epitest(imdfitB50, imdepiB50, method = "LRT")

## permutation test (only a few permutations for speed)
et <- epitest(imdfitB50, imdepiB50, B = 3 + 26*surveillance.options("allExamples"),
              verbose = 2 * (.Platform$OS.type == "unix"),
              .seed = 1, .parallel = 1 + surveillance.options("allExamples"))
et
plot(et)
summary(coef(et))