closed testing with globaltest {ctgt}

Approximated Closed Testing with Global Test

Description

To detect the significance of the set of features after correcting for multiple global tests, with family-wise error rate controlled.

Usage

  actgt (y, X, xs, hyps, maxit = 0, alpha = 0.05)

Arguments

y

The response vector (numeric vector).

X

The full design matrix, whose columns are named by the covariates.

xs

The name vector of all covariates (character vector).

hyps

The name vector of the covariates in the pathway of interest (character vector).

maxit

An optional integer to denote the maximal interations for branch and bound method. The default value 0 means the single-step shortcut without branch and bound method. Note that larger value is more time-consuming.

alpha

The type I error rate allowed. The default is 0.05.

Value

Returns a list of rejection indicator and the number of iterations.

Author(s)

Ningning Xu

Maintainer: Ningning Xu <[e-mail]; [e-mail]>

References

Ningning Xu, Aldo solari, Jelle Goeman, Clsoed testing with global test, with applications on metabolomics data, arXiv:2001.01541, https://arxiv.org/abs/2001.01541

Examples

  #Generate the design matrix and response vector for logistic regression models
  n= 100
  m = 5
  X = matrix(data = 0, nrow = n, ncol = m,byrow = TRUE )
  for ( i in 1:n){
    set.seed(1234+i)
    X[i,] =  as.vector(arima.sim(model = list(order = c(1, 0, 0), ar = 0.2), n = m) )
  }

  y = rbinom(n,1,0.6)
  X[which(y==1),1:3] = X[which(y==1),1:3] + 0.8


  xs = paste("x",seq(1,m,1),sep="") 
  colnames(X) = xs

  hyps=xs[1]

  #The sinle-step ctgt procedure
  actgt(y = y, X = X, xs = xs, hyps = hyps, maxit = 0, alpha = 0.05)
  #Result Iterations 
  #"unsure"        "0" 

  # The iterative ctgt procedure with more iterations
  actgt(y = y, X = X, xs = xs, hyps = hyps, maxit = 0, alpha = 0.05)
  #Result Iterations 
  #"reject"       "2" 
  #which means that x1 is rejected by closed testing within two more iterations of the shortcut


  # For a group of feature sets
  mysets = list(xs[1:5], xs[c(1,4)], xs[c(1,4,5)])
  sapply(mysets, function(i) actgt(y = y, X = X, xs = xs, hyps = i, maxit = 0, alpha = 0.05))
  #Result     "reject" "unsure" "reject"
  #Iterations "0"      "0"      "0"         

  mysets = list(xs[1:5], xs[c(1,4)], xs[c(1,4,5)])
  sapply(mysets, function(i) actgt(y = y, X = X, xs = xs, hyps = i, maxit = 0, alpha = 0.05))
  #Result     "reject" "reject" "reject"
  #Iterations "0"      "2"          "0"