mercuryfish {coin} | R Documentation |
The mercury level in blood, the proportion of cells with abnormalities, and the proportion of cells with chromosome aberrations in consumers of mercury-contaminated fish and a control group.
mercuryfish
A data frame with 39 observations on 4 variables.
group
a factor with levels "control"
and "exposed"
.
mercury
mercury level in blood.
abnormal
the proportion of cells with structural abnormalities.
ccells
the proportion of C_u
cells, i.e., cells with asymmetrical or
incomplete-symmetrical chromosome aberrations.
Control subjects ("control"
) and subjects who ate contaminated fish for
more than three years ("exposed"
) are under study.
Rosenbaum (1994) proposed a coherence criterion defining a partial ordering, i.e., an observation is smaller than another when all responses are smaller, and a score reflecting the “ranking” is attached to each observation. The corresponding partially ordered set (POSET) test can be used to test if the distribution of the scores differ between the groups. Alternatively, a multivariate test can be applied.
Skerfving, S., Hansson, K., Mangs, C., Lindsten, J. and Ryman, N. (1974). Methylmercury-induced chromosome damage in men. Environmental Research 7(1), 83–98. doi: 10.1016/0013-9351(74)90078-4
Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. The American Statistician 60(3), 257–263. doi: 10.1198/000313006X118430
Rosenbaum, P. R. (1994). Coherence in observational studies. Biometrics 50(2), 368–374. doi: 10.2307/2533380
## 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)
}
## Asymptotic POSET test
poset <- independence_test(mercury + abnormal + ccells ~ group,
data = mercuryfish, ytrafo = coherence)
## Linear statistic (T in the notation of Rosenbaum, 1994)
statistic(poset, type = "linear")
## Expectation
expectation(poset)
## Variance
## Note: typo in Rosenbaum (1994, p. 371, Sec. 2, last paragraph)
variance(poset)
## Standardized statistic
statistic(poset)
## P-value
pvalue(poset)
## Exact POSET test
independence_test(mercury + abnormal + ccells ~ group,
data = mercuryfish, ytrafo = coherence,
distribution = "exact")
## Asymptotic multivariate test
mvtest <- independence_test(mercury + abnormal + ccells ~ group,
data = mercuryfish)
## Global p-value
pvalue(mvtest)
## Single-step adjusted p-values
pvalue(mvtest, method = "single-step")
## Step-down adjusted p-values
pvalue(mvtest, method = "step-down")