Xsq.ceTk: Chi-square Approximation to Cuzick and Edwards \(T_k\) Test statistic

Description

An object of class "Chisqtest" performing a chi-square approximation for Cuzick and Edwards \(T_k\) test statistic based on the number of cases within kNNs of the cases in the data.

This approximation is suggested by tango:2007;textualnnspat since \(T_k\) statistic had high skewness rendering the normal approximation less efficient. The chi-square approximation is as follows: \(\frac{T_k- ET_k}{\sqrt{Var T_k}} \approx \frac{\chi^2_\nu-\nu}{\sqrt{2 \nu}}\) where \(\chi^2_\nu\) is a chi-square random variable with \(\nu\) df, and \(\nu=8/skewnees(T_k)\) (see SkewTk for the skewness).

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 logical argument nonzero.mat (default=FALSE) is for using the \(A\) matrix if FALSE or just the matrix of nonzero locations in the \(A\) matrix (if TRUE).

The logical argument asy.var (default=FALSE) is for using the asymptotic variance or the exact (i.e., finite sample) variance for the variance of \(T_k\) in its standardization. If asy.var=TRUE, the asymptotic variance is used for \(Var[T_k]\) (see asyvarTk), otherwise the exact variance (see varTk) is used.

See also (tango:2007;textualnnspat) and the references therein.

Usage

Xsq.ceTk(
  dat,
  cc.lab,
  k,
  case.lab = NULL,
  nonzero.mat = TRUE,
  asy.var = FALSE,
  ...
)

Value

A list with the elements

statistic: The chi-squared test statistic for Tango's chi-square approximation to Cuzick & Edwards' \(T_k\) test for disease clustering.
p.value: The \(p\)-value for the hypothesis test
df: Degrees of freedom for the chi-squared test, which is \(8/\)skewness where skewness is the output of SkewTk function.
estimate: Estimates, i.e., the observed \(T_k\) value.
est.name,est.name2: Names of the estimates, they are almost identical for this function.
null.value: Hypothesized null value for Cuzick & Edwards' \(T_k\), which is \(ET_k\).
method: Description of the hypothesis test
data.name: Name of the data set, dat

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 \(i\)).
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 computations. If TRUE the nonzero location matrix is used, otherwise the \(A\) matrix itself is used.
asy.var: A logical argument (default is FALSE) to determine whether the asymptotic variance or the exact (i.e., finite sample) variance for the variance of \(T_k\) in its standardization. If TRUE, the asymptotic variance is used for \(Var[T_k]\), otherwise the exact variance is used.
...: are for further arguments, such as method and p, passed to the dist function.

Author

Elvan Ceyhan

References

Examples

Run this code

set.seed(123)
n<-20
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(0:1,n,replace = TRUE)

k<-sample(1:5,1) # try also 1, 3, 5,
k

Xsq.ceTk(Y,cls,k)
Xsq.ceTk(Y,cls,k,nonzero.mat=FALSE)
Xsq.ceTk(Y,cls+1,k,case.lab = 2)
Xsq.ceTk(Y,cls,k,method="max")

Xsq.ceTk(Y,cls,k,asy.var=TRUE)

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