closed: Closed Testing for Exploratory Research
In cherry: Multiple Testing Methods for Exploratory Research

Description Usage Arguments Details Value Note Author(s) References Examples

Performs the closed testing procedure for user-specified local test.

1	closed (test, hypotheses, alpha = 0.05, adjust=FALSE)

`test`	A function that performs the local test. The function should accept a subvector of the `hypotheses` argument as input, and return a p-value.
`hypotheses`	Identifiers of the collection of elementary hypotheses.
`alpha`	The significance level of the test procedure. If set to `NA`, the function calculates adjusted p-values for each hypothesis in the closure.
`adjust`	Whether adjusted p-values should be calculated.

The function closed performs the closed testing procedure on the collection hypotheses, testing all their intersection hypotheses and controlling the familywise error rate.

The function closed returns an object of class closure.

The number of intersection hypotheses is exponential in the number of elementary hypotheses. The number of elementary hypotheses is therefore limited to log2(.Machine$integer.max+1) (typically 31) for computational reasons.

It is possible to set both adjust to TRUE and specify alpha. In that case, adjusted p-values are calculated up to a value alpha; all higher p-values are set to 1.

Jelle Goeman: j.j.goeman@lumc.nl

Goeman and Solari (2011) Statistical Science 26 (4) 584-597.

  # Example: the birthwt data set from the MASS library
  # We want to find variables associated with low birth weight
  library(MASS)
  fullfit <- glm(low~age+lwt+race+smoke+ptl+ht+ui+ftv, family=binomial, data=birthwt)
  hypotheses <- c("age", "lwt", "race", "smoke", "ptl", "ht", "ui", "ftv")

  # Define the local test to be used in the closed testing procedure
  mytest <- function(hyps) {
    others <- setdiff(hypotheses, hyps)
    form <- formula(paste(c("low~",  paste(c("1", others), collapse="+"))))
    anov <- anova(glm(form, data=birthwt, family=binomial), fullfit, test="Chisq")
    res <- anov$"Pr("[2]                    # for R >= 2.14.0
    if (is.null(res)) res <- anov$"P("[2]   # earlier versions
    res
  }

  # perform the closed testing
  cl <- closed(mytest, hypotheses)
  cl

  # how many variables among a chosen set are associated with the response?
  pick(cl, c("ht", "lwt", "smoke", "ui"))
  
  # adjusted p-values and a confidence distribution
  cl <- closed(mytest, hypotheses, alpha=NA)
  pick(cl, c("ht", "lwt", "smoke", "ui"))