Description Usage Arguments Details Value References See Also Examples
This function gives P-value for the permuted modified maximum contrast method.
1 2 3 4 5 6 7 8 9 10 | mmcm.resamp(
x,
g,
contrast,
alternative = c("two.sided", "less", "greater"),
nsample = 20000,
abseps = 0.001,
seed = NULL,
nthread = 2
)
|
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 permuted 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. |
nsample |
specifies the number of resamples (default: 20000) |
abseps |
specifies the absolute error tolerance (default: 0.001) |
seed |
a single value, interpreted as an integer;
see |
nthread |
sthe number of threads used in parallel computing, or FALSE that means single threading (default: 2) |
mmcm.resamp
performs the permuted 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 permuted 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 k-th pattern.
c_k = (c_k1, c_k2, ..., c_ki)^T (sum from i of c_ki = 0)
M_max is a permuted 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), M_k = c_k^t Ybar / (c_k^t c_k)^(1/2),
M_max = max(M_1, M_2, ..., M_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 M_max under the overall null hypothesis is
P-value = Pr(M_max > m_max | H0)
m_max is observed value of statistics. This function gives distribution of M_max by using the permutation method, follow algorithm:
1. Initialize counting variable: COUNT = 0. Input parameters: NRESAMPMIN (minimum resampling count, we set 1000), NRESAMPMAX (maximum resampling count), and epsilon (absolute error tolerance).
2. Calculate m_max that is the observed value of the test statistic.
3. Let y_ij(r) donate data, which are sampled without replacement, and independently, form observed value y_ij. Where, (r) is suffix of the resampling number (r = 1, 2, ...).
4. Calculate m(r)_max from y_ij(r). If m(r)_max > m_max, then increment the counting variable: COUNT = COUNT + 1. Calculate approximate P-value hat-p(r) = COUNT / r, and the simulation standard error [hat-p(r) (1 - hat-p(r)) / r]^(1/2).
5. Repeat 3–4, while r > 1000 and 3.5 SE(hat-p(r)) < epsilon (corresponding to 99% confidence level), or NRESAMPMAX times. Output the approximate P-value hat-p(r).
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 permuted 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
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 <- mmcm.resamp(x, g, contrast, nsample = 20000,
abseps = 0.01, seed = 5784324)
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$pos, function(x) mmcm.resamp(x$x, x$g,
contrast, abseps = 0.02, nsample = 10000))
y <- do.call(rbind, y)[,c(3,7,9)]
y
|
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