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

In nnspat: Nearest Neighbor Methods for Spatial Patterns

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, \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.

See also (\insertCiteceyhan: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,
  ...
)

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

Author(s)

Elvan Ceyhan

References

\insertAllCited

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")

nnspat documentation built on Aug. 30, 2022, 9:06 a.m.