nnspat (version 0.1.2)

ZTcomb: \(Z\)-test for Cuzick and Edwards \(T_{comb}\) statistic

Description

An object of class "htest" performing a \(z\)-test for Cuzick and Edwards \(T_{comb}\) test statisticin disease clustering, where \(T_{comb}\) is a linear combination of some \(T_k\) tests.

For disease clustering, cuzick:1990;textualnnspat developed a \(k\)-NN test \(T_k\) based on number of cases among \(k\) NNs of the case points, and also proposed a test combining various \(T_k\) tests, denoted as \(T_{comb}\).

See page 87 of (cuzick:1990;textualnnspat) for more details.

Under RL of \(n_1\) cases and \(n_0\) controls to the given locations in the study region, \(T_{comb}\) approximately has \(N(E[T_{comb}],Var[T_{comb}])\) distribution for large \(n_1\).

The argument cc.lab is case-control label, 1 for case, 0 for control, if the argument case.lab is NULL, then cc.lab should be provided in this fashion, if case.lab is provided, the labels are converted to 0's and 1's accordingly.

The argument klist is the vector of integers specifying the indices of the \(T_k\) values used in obtaining the \(T_{comb}\).

The logical argument nonzero.mat (default=TRUE) is for using the \(A\) matrix if FALSE or just the matrix of nonzero locations in the \(A\) matrix (if TRUE) in the computations.

The logical argument asy.cov (default=FALSE) is for using the asymptotic covariance or the exact (i.e., finite sample) covariance for the vector of \(T_k\) values used in Tcomb in the standardization of \(T_{comb}\). If asy.cov=TRUE, the asymptotic covariance is used, otherwise the exact covariance is used.

See also (ceyhan:SiM-seg-ind2014,cuzick:1990;textualnnspat) and the references therein.

Usage

ZTcomb(
  dat,
  cc.lab,
  klist,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  case.lab = NULL,
  nonzero.mat = TRUE,
  asy.cov = FALSE,
  ...
)

Value

A list with the elements

statistic

The \(Z\) test statistic for the Cuzick and Edwards \(T_{comb}\) test

p.value

The \(p\)-value for the hypothesis test for the corresponding alternative

conf.int

Confidence interval for the Cuzick and Edwards \(T_{comb}\) value at the given confidence level conf.level and depends on the type of alternative.

estimate

Estimate of the parameter, i.e., the Cuzick and Edwards \(T_{comb}\) value.

null.value

Hypothesized null value for the Cuzick and Edwards \(T_{comb}\) value which is \(E[T_{comb}]\) for this function, which is the output of EV.Tcomb function.

alternative

Type of the alternative hypothesis in the test, one of "two.sided", "less", "greater"

method

Description of the hypothesis test

data.name

Name of the data set, dat

Arguments

dat

The data set in one or higher dimensions, each row corresponds to a data point.

cc.lab

Case-control labels, 1 for case, 0 for control

klist

list of integers specifying the indices of the \(T_k\) values used in obtaining the \(T_{comb}\).

alternative

Type of the alternative hypothesis in the test, one of "two.sided", "less" or "greater".

conf.level

Level of the upper and lower confidence limits, default is 0.95, for Cuzick and Edwards \(T_{comb}\) statistic

case.lab

The label used for cases in the cc.lab (if cc.lab is not provided then the labels are converted such that cases are 1 and controls are 0), default is NULL.

nonzero.mat

A logical argument (default is TRUE) to determine whether the \(A\) matrix or the matrix of nonzero locations of the \(A\) matrix will be used in the computation of covariance of \(T_k\) values forming the T_{comb} statistic (argument is passed on to covTcomb). If TRUE the nonzero location matrix is used, otherwise the \(A\) matrix itself is used.

asy.cov

A logical argument (default is FALSE) to determine whether asymptotic or exact (i.e., finite sample) covariances between \(T_k\) and \(T_l\) values are to be used to obtain the entries of the covariance matrix.

...

are for further arguments, such as method and p, passed to the dist function.

Author

Elvan Ceyhan

References

See Also

Tcomb, EV.Tcomb, and covTcomb

Examples

n<-20  #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(0:1,n,replace = TRUE)  #or try cls<-rep(0:1,c(10,10))

kl<-sample(1:5,3) #try also sample(1:5,2)
ZTcomb(Y,cls,kl)
ZTcomb(Y,cls,kl,method="max")

ZTcomb(Y,cls,kl,nonzero.mat=FALSE)
ZTcomb(Y,cls+1,kl,case.lab = 2,alt="l")
ZTcomb(Y,cls,kl,conf=.9,alt="g")
ZTcomb(Y,cls,kl,asy=TRUE,alt="g")

#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
ZTcomb(Y,fcls,kl,case.lab="a")