# ZTcomb: Z-test for Cuzick and Edwards T_{comb} statistic In nnspat: Nearest Neighbor Methods for Spatial Patterns

## 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, \insertCitecuzick: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 (\insertCitecuzick: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.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```ZTcomb( dat, cc.lab, klist, alternative = c("two.sided", "less", "greater"), conf.level = 0.95, 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}. `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.

## 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`

Elvan Ceyhan

## References

\insertAllCited

`Tcomb`, `EV.Tcomb`, and `covTcomb`
 ``` 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) 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") ```