ceTk {nnspat}

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 and Edwards (1990) 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 (2014); Cuzick and Edwards (1990)) and the references therein.

Usage

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

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.

Value

Cuzick and Edwards T_k test statistic for disease clustering

Author(s)

Elvan Ceyhan

References

Ceyhan E (2014). “Segregation indices for disease clustering.” Statistics in Medicine, 33(10), 1662-1684.

Cuzick J, Edwards R (1990). “Spatial clustering for inhomogeneous populations (with discussion).” Journal of the Royal Statistical Society, Series B, 52, 73-104.

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