coin (version 0.4-2)

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.

Examples

data("mercuryfish")

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")