mlf.test: Maxima Likelihood First Scan Test

In smerc: Statistical Methods for Regional Counts

Maxima Likelihood First Scan Test

Description

mlf.test implements the Maxima Likelihood First scan test of Yao et al. (2011), which is actually a special case of the Dynamic Minimum Spanning Tree of Assuncao et al. (2006). Find the single region that maximizes the likelihood ratio test statistic. Starting with this single region as a current zone, new candidate zones are constructed by combining the current zone with the connected region that maximizes the likelihood ratio test statisic. This procedure is repeated until the population and/or distance upper bound is reached.

Usage

mlf.test(
  coords,
  cases,
  pop,
  w,
  ex = sum(cases)/sum(pop) * pop,
  nsim = 499,
  alpha = 0.1,
  ubpop = 0.5,
  ubd = 0.5,
  longlat = FALSE,
  cl = NULL
)

Arguments

coords	An n \times 2 matrix of centroid coordinates for the regions in the form (x, y) or (longitude, latitude) is using great circle distance.
cases	The number of cases observed in each region.
pop	The population size associated with each region.
w	A binary spatial adjacency matrix for the regions.
ex	The expected number of cases for each region. The default is calculated under the constant risk hypothesis.
nsim	The number of simulations from which to compute the p-value.
alpha	The significance level to determine whether a cluster is signficant. Default is 0.10.
ubpop	The upperbound of the proportion of the total population to consider for a cluster.
ubd	A proportion in (0, 1]. The distance of potential clusters must be no more than ubd * m, where m is the maximum intercentroid distance between all coordinates.
longlat	The default is FALSE, which specifies that Euclidean distance should be used. If longlat is TRUE, then the great circle distance is used to calculate the intercentroid distance.
cl	A cluster object created by makeCluster, or an integer to indicate number of child-processes (integer values are ignored on Windows) for parallel evaluations (see Details on performance). It can also be "future" to use a future backend (see Details), NULL (default) refers to sequential evaluation.

Details

Only a single candidate zone is ever returned because the algorithm only constructs a single sequence of starting zones, and overlapping zones are not returned. Only the zone that maximizes the likelihood ratio test statistic is returned.

Value

Returns a list of length two of class scan. The first element (clusters) is a list containing the significant, non-ovlappering clusters, and has the the following components:

locids	The location ids of regions in a significant cluster.
pop	The total population in the cluser window.
cases	The observed number of cases in the cluster window.
expected	The expected number of cases in the cluster window.
smr	Standarized mortaility ratio (observed/expected) in the cluster window.
rr	Relative risk in the cluster window.
loglikrat	The loglikelihood ratio for the cluster window (i.e., the log of the test statistic).
pvalue	The pvalue of the test statistic associated with the cluster window.
w	The adjacency matrix of the cluster.
r	The maximum radius of the cluster (in terms of intercentroid distance from the starting region).

The second element of the list is the centroid coordinates. This is needed for plotting purposes.

Author(s)

Joshua French

References

Yao, Z., Tang, J., & Zhan, F. B. (2011). Detection of arbitrarily-shaped clusters using a neighbor-expanding approach: A case study on murine typhus in South Texas. International journal of health geographics, 10(1), 1.

Assuncao, R.M., Costa, M.A., Tavares, A. and Neto, S.J.F. (2006). Fast detection of arbitrarily shaped disease clusters, Statistics in Medicine, 25, 723-742.

See Also

print.smerc_cluster, summary.smerc_cluster, plot.smerc_cluster, scan.stat, scan.test

Examples

data(nydf)
data(nyw)
coords <- with(nydf, cbind(longitude, latitude))
out <- mlf.test(
  coords = coords, cases = floor(nydf$cases),
  pop = nydf$pop, w = nyw,
  alpha = 0.12, longlat = TRUE,
  nsim = 10, ubpop = 0.1, ubd = 0.5
)
plot(out)

smerc documentation built on Oct. 10, 2023, 5:07 p.m.