Chromosomal Effects of Mercury-Contaminated Fish Consumption

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

Format

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.

Details

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.

Source

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

References

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

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)
}

## 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")
#>             
#> control -237

## Expectation
expectation(poset)
#>          
#> control 0

## Variance
## Note: typo in Rosenbaum (1994, p. 371, Sec. 2, last paragraph)
variance(poset)
#>                 
#> control 3097.954

## Standardized statistic
statistic(poset)
#> [1] -4.258051

## P-value
pvalue(poset)
#> [1] 2.062169e-05

## Exact POSET test
independence_test(mercury + abnormal + ccells ~ group,
                  data = mercuryfish, ytrafo = coherence,
                  distribution = "exact")
#> 
#> 	Exact General Independence Test
#> 
#> data:  mercury, abnormal, ccells by group (control, exposed)
#> Z = -4.2581, p-value = 4.486e-06
#> alternative hypothesis: two.sided
#> 

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

## Global p-value
pvalue(mvtest)
#> [1] 0.007172738
#> 99 percent confidence interval:
#>  0.006411937 0.007933540 
#> 

## Single-step adjusted p-values
pvalue(mvtest, method = "single-step")
#>             mercury   abnormal     ccells
#> control 0.006578934 0.01745591 0.03816166

## Step-down adjusted p-values
pvalue(mvtest, method = "step-down")
#>             mercury  abnormal    ccells
#> control 0.007012714 0.0111254 0.0152947