nnspat (version 0.1.2)

ceTk: Cuzick and Edwards \(T_k\) Test statistic

Description

This function computes Cuzick and Edwards \(T_k\) test statistic based on the number of cases within kNNs of the cases in the data.

For disease clustering, cuzick:1990;textualnnspat suggested a k-NN test based on number of cases among k NNs of the case points. Let \(z_i\) be the \(i^{th}\) point and \(d_i^k\) be the number cases among k NNs of \(z_i\). Then Cuzick-Edwards' k-NN test is \(T_k=\sum_{i=1}^n \delta_i d_i^k\), where \(\delta_i=1\) if \(z_i\) is a case, and 0 if \(z_i\) is a control.

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. Also, \(T_1\) is identical to the count for cell \((1,1)\) in the nearest neighbor contingency table (NNCT) (See the function nnct for more detail on NNCTs).

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

Usage

ceTk(dat, cc.lab, k = 1, case.lab = NULL, ...)

Value

Cuzick and Edwards \(T_k\) test statistic for disease clustering

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

k

Integer specifying the number of NNs (of subject \(i\)), default is 1.

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.

...

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

Author

Elvan Ceyhan

References

See Also

Tcomb, seg.ind, Pseg.coeff and ceTkinv

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))

ceTk(Y,cls)
ceTk(Y,cls,method="max")
ceTk(Y,cls,k=3)
ceTk(Y,cls+1,case.lab = 2)

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

#############
n<-40
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(1:4,n,replace = TRUE)  # here ceTk(Y,cls) gives an error message