mcm.mvt: The maximum contrast method by using the randomized...
In mmcm: Modified Maximum Contrast Method

Description Usage Arguments Details Value References See Also Examples

View source: R/mcm.mvt.R

This function gives P-value for the maximum contrast statistics by using randomized quasi-Monte Carlo method from pmvt function of package mvtnorm.

mcm.mvt(
  x,
  g,
  contrast,
  alternative = c("two.sided", "less", "greater"),
  algorithm = GenzBretz()
)

`x`	a numeric vector of data values
`g`	a integer vector giving the group for the corresponding elements of x
`contrast`	a numeric contrast coefficient matrix for the maximum contrast statistics
`alternative`	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
`algorithm`	an object of class `GenzBretz` defining the hyper parameters of this algorithm

mcm.mvt performs the maximum contrast method that is detecting a true response pattern.

Y_ij (i = 1, 2, ...; j = 1, 2, ..., n_i) is an observed response for j-th individual in i-th group.

C is coefficient matrix for the maximum contrast statistics (i x k matrix, i: No. of groups, k: No. of pattern).

C = (c_1, c_2, ..., c_k)^T

c_k is coefficient vector of kth pattern.

c_k = (c_k1, c_k2, ..., c_ki)^{\rm{T}} (sum from i of c_ki = 0)

T_max is the maximum contrast statistic.

Ybar_i = (sum from j of Y_ij) / n_i, Ybar = (Ybar_1 Ybar_2 ... Ybar_i ... Ybar_a)^T (a x 1 vector),

D = diag(n_1, n_2, ..., n_i, ..., n_a) (a x a matrix), V = 1/gamma * sum_{j=1}^{n_i} sum_{i=1}^{a} (Y_ij-Ybar_i)^2,

gamma = sum_{i=1}^{a} (n_i-1), T_k = c_k^t Ybar / (V c_k^t D c_k)^(1/2),

T_max = max(T_1, T_2, ..., T_k).

Consider testing the overall null hypothesis H_0: μ_1=μ_2=…=μ_i, versus alternative hypotheses H_1 for response petterns (H_1: μ_1<μ_2<…<μ_i,~ μ_1=μ_2<…<μ_i,~ μ_1<μ_2<…=μ_i). The P-value for the probability distribution of T_max under the overall null hypothesis is

P-value = Pr(T_max > t_max | H0)

t_max is observed value of statistics. This function gives distribution of T_max by using randomized quasi-Monte Carlo method from package mvtnorm.

`statistic`	the value of the test statistic with a name describing it.
`p.value`	the p-value for the test.
`alternative`	a character string describing the alternative hypothesis.
`method`	the type of test applied.
`contrast`	a character string giving the names of the data.
`contrast.index`	a suffix of coefficient vector of the kth pattern that gives maximum contrast statistics (row number of the coefficient matrix).
`error`	estimated absolute error and,
`msg`	status messages.

Yoshimura, I., Wakana, A., Hamada, C. (1997). A performance comparison of maximum contrast methods to detect dose dependency. Drug Information J. 31: 423–432.

pmvt, GenzBretz, mmcm.mvt

## Example 1 ##
#  true response pattern: dominant model c=(1, 1, -2)
set.seed(136885)
x <- c(
  rnorm(130, mean =  1 / 6, sd = 1),
  rnorm( 90, mean =  1 / 6, sd = 1),
  rnorm( 10, mean = -2 / 6, sd = 1)
)
g <- rep(1:3, c(130, 90, 10))
boxplot(
  x ~ g,
  width = c(length(g[g==1]), length(g[g==2]), length(g[g==3])),
  main = "Dominant model (sample data)",
  xlab = "Genotype",
  ylab = "PK parameter"
)

# coefficient matrix
# c_1: additive, c_2: recessive, c_3: dominant
contrast <- rbind(
  c(-1, 0, 1), c(-2, 1, 1), c(-1, -1, 2)
)
y <- mcm.mvt(x, g, contrast)
y

## Example 2 ##
#  for dataframe
#  true response pattern:
#    pos = 1 dominant  model c=( 1,  1, -2)
#          2 additive  model c=(-1,  0,  1)
#          3 recessive model c=( 2, -1, -1)
set.seed(3872435)
x <- c(
  rnorm(130, mean =  1 / 6, sd = 1),
  rnorm( 90, mean =  1 / 6, sd = 1),
  rnorm( 10, mean = -2 / 6, sd = 1),
  rnorm(130, mean = -1 / 4, sd = 1),
  rnorm( 90, mean =  0 / 4, sd = 1),
  rnorm( 10, mean =  1 / 4, sd = 1),
  rnorm(130, mean =  2 / 6, sd = 1),
  rnorm( 90, mean = -1 / 6, sd = 1),
  rnorm( 10, mean = -1 / 6, sd = 1)
)
g   <- rep(rep(1:3, c(130, 90, 10)), 3)
pos <- rep(c("rsXXXX", "rsYYYY", "rsZZZZ"), each=230)
xx  <- data.frame(pos = pos, x = x, g = g)

# coefficient matrix
# c_1: additive, c_2: recessive, c_3: dominant
contrast <- rbind(
  c(-1, 0, 1), c(-2, 1, 1), c(-1, -1, 2)
)
y <- by(xx, xx$pos, function(x) mmcm.mvt(x$x, x$g,
  contrast))
y <- do.call(rbind, y)[,c(3,7,9)]
# miss-detection!
y