coin (version 1.0-24)

mercuryfish: Chromosomal Effects of Mercury Contaminated Fish Consumption

Description

The mercury level in the blood, the proportion of cells with abnormalities and the proportion of cells with chromosome aberrations for a group of consuments of mercury contaminated fish and a control group.

Usage

data("mercuryfish")

source

S. Skerfving, K. Hansson, C. Mangs, J. Lindsten, N. Ryman (1974), Methylmercury-induced chromosome damage in men. Environmental Research 7, 83--98.

Details

Subjects who ate contaminated fish for more than three years in the exposed group and subjects of a control group are to be compared. Instead of a multivariate comparison, Rosenbaum (1994) applied a coherence criterion. The observations are partially ordered: an observation is smaller than another when all three variables (mercury, abnormal and ccells) are smaller and a score reflecting the `ranking' is attached to each observation. The distribution of the scores in both groups is to be compared and the corresponding test is called `POSET-test' (partially ordered sets).

References

P. R. Rosenbaum (1994). Coherence in observational studies. Biometrics 50, 368--374.

Torsten Hothorn, Kurt Hornik, Mark A. van de Wiel & Achim Zeileis (2006). A Lego system for conditional inference, The American Statistician, 60(3), 257--263.

Examples

### coherence criterion
  coherence <- function(data) {
      x <- as.matrix(data)
      matrix(apply(x, 1, function(y)
          sum(colSums(t(x) < y) == ncol(x)) - 
          sum(colSums(t(x) > y) == ncol(x))), ncol = 1)
  }

  ### POSET-test
  poset <- independence_test(mercury + abnormal + ccells ~ group, data =
                             mercuryfish, ytrafo = coherence)

  ### linear statistic (T in Rosenbaum's, 1994, notation)
  statistic(poset, "linear")

  ### expectation
  expectation(poset)

  ### variance (there is a typo in Rosenbaum, 1994, page 371, 
  ### last paragraph Section 2)
  covariance(poset)

  ### the standardized statistic
  statistic(poset)

  ### and asymptotic p-value
  pvalue(poset)

  ### exact p-value
  independence_test(mercury + abnormal + ccells ~ group, data =
                    mercuryfish, ytrafo = coherence, distribution = "exact")

  ### multivariate analysis
  mvtest <- independence_test(mercury + abnormal + ccells ~ group, 
                              data = mercuryfish)

  ### global p-value
  pvalue(mvtest)

  ### adjusted univariate p-value
  pvalue(mvtest, method = "single-step")