mercuryfish               package:coin               R Documentation

_C_h_r_o_m_o_s_o_m_a_l _e_f_f_e_c_t_s _o_f _m_e_r_c_u_r_y _c_o_n_t_a_m_i_n_a_t_e_d _f_i_s_h _c_o_n_s_u_m_p_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

     data(mercuryfish)

_F_o_r_m_a_t:

     A data frame with 39 observations on the following 4 variables.

     _g_r_o_u_p a factor with levels 'control' and 'exposed'.

     _m_e_r_c_u_r_y the level of mercury in the blood.

     _a_b_n_o_r_m_a_l the proportion of cells with structural abnormalities.

     _c_c_e_l_l_s the proportion of cells with asymmetrical or
          incomplete-symmetrical chomosome aberrations called  C_u
          cells.

_D_e_t_a_i_l_s:

     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 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_o_u_r_c_e:

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

_R_e_f_e_r_e_n_c_e_s:

     P. R. Rosenbaum (1994), Coherence in Observational Studies.
     _Biometrics_, *50*, 368-374.

_E_x_a_m_p_l_e_s:

     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 (Rosenbaum, 1994, uses the unconditional approach)
     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, adjusted = TRUE)

