Description Usage Arguments Details Value References See Also Examples
This function gives P-value for the maximum contrast statistics by using
randomized quasi-Monte Carlo method from pmvt
function of package mvtnorm
.
1 2 3 4 5 6 7 |
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 |
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | ## 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
|
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