nnspat (version 0.1.2)

funsZTkinv: Z-Test for Cuzick and Edwards \(T_k^{inv}\) statistic

Description

Two functions: ZTkinv and ZTkinv.sim, each of which is an object of class "htest" performing a \(z\)-test for Cuzick and Edwards \(T_k^{inv}\) test statistic. See ceTkinv for a description of \(T_k^{inv}\) test statistic.

The function ZTkinv performs a \(Z\)-test for \(T_k^{inv}\) using asymptotic normality with a simulation estimated variance under RL of cases and controls to the given points. And the function ZTkinv.sim performs test for\(T_k^{inv}\) based on MC simulations under the RL hypothesis.

Asymptotic normality for the \(T_k^{inv}\) is not established yet, but this seems likely according to cuzick:1990;textualnnspat. If asymptotic normality holds, it seems a larger sample size would be needed before this becomes an effective approximation. Hence the simulation-based test ZTkinv.sim is recommended for use to be safe. When ZTkinv is used, this is also highlighted with the warning "asymptotic normality of \(T_k^{inv}\) is not yet established, so, simulation-based test is recommended".

All arguments are common for both functions, except for ..., Nvar.sim which are used in ZTkinv only, and Nsim, which is used in ZTkinv.sim only.

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 Nvar.sim represents the number of resamplings (without replacement) in the RL scheme, with default being 1000 for estimating the variance of \(T_k^{inv}\) statistic in ZTkinv. The argument Nsim represents the number of resamplings (without replacement) in the RL scheme, with default being 1000 for estimating the \(T_k^{inv}\) values in ZTkinv.sim.

Both functions might take a very long time when data size is large or Nsim is large.

See also (cuzick:1990;textualnnspat) and the references therein.

Usage

ZTkinv(
  dat,
  k,
  cc.lab,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  case.lab = NULL,
  Nvar.sim = 1000,
  ...
)
ZTkinv.sim(
  dat,
  k,
  cc.lab,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  case.lab = NULL,
  Nsim = 1000
)

Value

A list with the elements

statistic

The \(Z\) test statistic for the Cuzick and Edwards \(T_k^{inv}\) test

p.value

The \(p\)-value for the hypothesis test for the corresponding alternative. In ZTkinv this is computed using the standard normal distribution, while in ZTkinv.sim, it is based on which percentile the observed \(T_k^{inv}\) value is among the generated \(T_k^{inv}\) values.

conf.int

Confidence interval for the Cuzick and Edwards \(T_k^{inv}\) value at the given confidence level conf.level and depends on the type of alternative.

\(z\)-critical values are used in the construction of the confidence interval in ZTkinv, while the percentile values are used in the generated sample of \(T_k^{inv}\) values in ZTkinv.sim

estimate

Estimate of the parameter, i.e., the Cuzick and Edwards \(T_k^{inv}\) value.

null.value

Hypothesized null value for the Cuzick and Edwards \(T_k^{inv}\) value which is \(k n_1 (n_1-1)/(n_0+1)\) under RL, where the number of cases are denoted as \(n_1\) and number of controls as \(n_0\).

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

Arguments

dat

The data set in one or higher dimensions, each row corresponds to a data point, used in both functions.

k

Integer specifying the number of the closest controls to subject \(i\), used in both functions.

cc.lab

Case-control labels, 1 for case, 0 for control, used in both functions.

alternative

Type of the alternative hypothesis in the test, one of "two.sided", "less" or "greater", used in both functions.

conf.level

Level of the upper and lower confidence limits, default is 0.95, for Cuzick and Edwards \(T_k^{inv}\) statistic. Used in both functions.

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, used in both functions.

Nvar.sim

The number of simulations, i.e., the number of resamplings under the RL scheme to estimate the variance of Tkinv, used in ZTkinv only.

...

are for further arguments, such as method and p, passed to the dist function. Used in ZTkinv only.

Nsim

The number of simulations, i.e., the number of resamplings under the RL scheme to estimate the \(T_k^{inv}\) values, used in ZTkinv.sim only.

Author

Elvan Ceyhan

References

See Also

ceTkinv and EV.Tkinv

Examples

n<-10 #try also 20, 50, 100
set.seed(123)
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(0:1,n,replace = TRUE)  #or try cls<-rep(0:1,c(10,10))
k<-2

ZTkinv(Y,k,cls)
ZTkinv(Y,k,cls+1,case.lab = 2,alt="l")
#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
ZTkinv(Y,k,fcls,case.lab="a")

n<-10 #try also 20, 50, 100
set.seed(123)
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(0:1,n,replace = TRUE)  #or try cls<-rep(0:1,c(10,10))
k<-2 # try also 3,5

ZTkinv.sim(Y,k,cls)
ZTkinv.sim(Y,k,cls,conf=.9,alt="g")

#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
ZTkinv.sim(Y,k,fcls,case.lab="a")

#with k=1
ZTkinv.sim(Y,k=1,cls)
ZTrun(Y,cls)