# Tcomb: Cuzick & Edwards Tcomb Test Statistic In nnspat: Nearest Neighbor Methods for Spatial Patterns

## Description

This function computes the value of Cuzick & Edwards T_{comb} test statistic in disease clustering, where T_{comb} is a linear combination of some T_k tests.

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 page 87 of (\insertCitecuzick:1990;textualnnspat) for more details.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```Tcomb( dat, cc.lab, klist, case.lab = NULL, nonzero.mat = TRUE, asy.cov = FALSE, ... ) ```

## 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}. `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 N_s and N_t. 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. If `TRUE` the asymptotic covariance values are used, otherwise exact covariance values are used. `...` are for further arguments, such as `method` and `p`, passed to the `dist` function.

## Value

Returns the value of the T_{comb} test statistic

Elvan Ceyhan

## References

\insertAllCited

`ceTk`, `EV.Tcomb`, and `ZTcomb`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```n<-20 #or try sample(1:20,1) #try also n<-50, 100 Y<-matrix(runif(3*n),ncol=3) cls<-sample(0:1,n,replace = TRUE) #or try cls<-rep(0:1,c(10,10)) n1<-sum(cls==1) kl<-sample(1:5,3) #try also sample(1:5,2) kl Tcomb(Y,cls,kl) Tcomb(Y,cls,kl,method="max") Tcomb(Y,cls+1,kl,case.lab=2) Tcomb(Y,cls,kl,nonzero.mat = FALSE) Tcomb(Y,cls,kl,asy.cov = TRUE) #cls as a factor na<-floor(n/2); nb<-n-na fcls<-rep(c("a","b"),c(na,nb)) Tcomb(Y,fcls,kl,case.lab="a") ```