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

Description Usage Arguments Details Value References See Also Examples

View source: R/mmcm.mvt.R

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

mmcm.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 modified 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.

mmcm.mvt performs the modified maximum contrast method that is detecting a true response pattern under the unequal sample size situation.

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 modified 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)^T (sum from i of c_ki = 0)

S_max is the modified 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),

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),

S_k = c_k^t Ybar / (V c_k^t c_k)^(1/2),

S_max = max(S_1, S_2, ..., S_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 S_max under the overall null hypothesis is

P-value = Pr(S_max > s_max | H0)

s_max is observed value of statistics. This function gives distribution of S_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 modified maximum contrast statistics (row number of the coefficient matrix).
`error`	estimated absolute error and,
`msg`	status messages.

Nagashima, K., Sato, Y., Hamada, C. (2011). A modified maximum contrast method for unequal sample sizes in pharmacogenomic studies Stat Appl Genet Mol Biol. 10(1): Article 41. http://dx.doi.org/10.2202/1544-6115.1560

Sato, Y., Laird, N.M., Nagashima, K., et al. (2009). A new statistical screening approach for finding pharmacokinetics-related genes in genome-wide studies. Pharmacogenomics J. 9(2): 137–146. http://www.ncbi.nlm.nih.gov/pubmed/19104505

pmvt, GenzBretz, mmcm.resamp

## 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 <- mmcm.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)]
y