mercuryfish {coin} | R Documentation |
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.
data("mercuryfish")
A data frame with 39 observations on the following 4 variables.
a factor with levels control
and exposed
.
the level of mercury in the blood.
the proportion of cells with structural abnormalities.
the proportion of cells with asymmetrical or incomplete-symmetrical chromosome aberrations called C_u cells.
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).
S. Skerfving, K. Hansson, C. Mangs, J. Lindsten, N. Ryman (1974), Methylmercury-induced chromosome damage in men. Environmental Research 7, 83–98.
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.
### 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")