An example of GO term data

Description

A dataset containing the gene expressions for a Gene Ontology (GO) term on two phenotype groups: BCR/ABL and NEG. The id of the GO term is GO:0000003. The raw dataset is taken from ALL package. The data were preprocessed, for which the details are elaborated in Zhang and Wang (2020).

Usage

GO_example

Format

A list with two subsets of gene expression data.

X

A matrix containing gene expressions for the BCR/ABL group. The row id is for patient and the column id is for gene.

Y

A matrix containing gene expressions for the NEG group. The row id is for patient and the column id is for gene.

References

Zhang, H. and Wang, H. (2020). Result consistency of high dimensional two-sample tests applied to gene ontology terms with gene sets. Manuscript in review.

Apply the SKK test to multiple simulated two-sample datasets

Description

This function performs the SKK test of Srivastava, Katayama, and Kano(2013) on multiple high-dimensional two-sample datasets. It is useful for Monte Carlo experiments.

Usage

SKK_sim(DATA)

Arguments

Value

a dataframe, each row of which reports the values of the SKK test statistics and the p-values.

References

Srivastava, M. S., Katayama, S., and Kano, Y. (2013). A two sample test in high dimensional data. Journal of Multivariate Analysis, 114:349-358.

Examples

# Generate 3 simulated datasets and apply the SKK test
data <- buildData(n = 45, m =60, p = 300,
                 muX = rep(0,300), muY = rep(0,300),
                 dep = 'IND', S = 3, innov = rnorm)
SKK_sim(data)

High-dimensional two-sample test (SKK) proposed by Srivastava, Katayama, and Kano(2013)

Description

This function implements the two-sample high-dimensional test proposed by Srivastava, Katayama, and Kano(2013).

Usage

SKK_test(X, Y)

Arguments

Value

A list consisting of the values of the test statistic and p-value.

References

Srivastava, M. S., Katayama, S., and Kano, Y. (2013). A two sample test in high dimensional data. Journal of Multivariate Analysis, 114:349-358.

Examples

# Generate a simulated dataset and apply the SKK test
data <- buildData(n = 45, m =60, p = 300,
                 muX = rep(0,300), muY = rep(0,300),
                 dep = 'IND', S = 1, innov = rnorm)
SKK_test(data[[1]]$X, data[[1]]$Y)

# Apply the SKK test to the data for a GO term stored in GO_example
SKK_test(GO_example$X, GO_example$Y)

Two-sample datasets generator

Description

This function generates simulated high dimensional two-sample data from user specified populations with given mean vectors, covariance structure, sample sizes, and dimension of each observation. It could generate the long-range dependent process proposed by Hall et al. (1998) in additional to some processes provided in arima.sim().

Usage

buildData(
  n,
  m,
  p,
  muX,
  muY,
  dep,
  commoncov = TRUE,
  VarScaleY = 1,
  S = 1,
  innov = function(n, ...) stats::rnorm(n, 0, 1),
  heteroscedastic = FALSE,
  het.diag
)

Arguments

Value

A list of S lists, each consisting of an n by p matrix X, an m by p matrix Y, the sample sizes, n and m, for each population, and the dimensionality p.

References

Hall, P., Jing, B.-Y., and Lahiri, S. N. (1998). On the sampling window method for long-range dependent data. Statistica Sinica, 8(4):1189-1204.

Examples

# Generate 3 two-sample datasets of dimensionality 300
# with sample sizes 45 for one sample & 60 for the other.
buildData(n = 45, m =60, p = 300,
          muX = rep(0,300), muY = rep(0,300),
          dep = 'IND', S = 3, innov = rnorm)

highDmean: A package for testing of equal mean for two-sample high dimensional data

Description

This package is an implementation of the high-dimensional two-sample test proposed by Zhang and Wang (2020) "Result consistency of high dimensional two-sample tests applied to gene ontology terms with gene sets". It also implements the SKK test proposed by Srivastava, Katayama, and Kano (2013) "A two sample test in high dimensional data." These tests are particularly suitable for high dimensional data from two populations for which the classical multivariate Hotelling's T-square test fails due to sample sizes smaller than dimensionality. In this case, the ZWL and ZWLm tests proposed by Zhang and Wang (2020), referred to as zwl_test() in this package, provide a reliable and powerful test.

highDmean functions

The function zwl_test() conducts the ZWL and ZWLm test of equal mean for two-sample high dimensional data provided in matrices of dimension n by p and m by p, which are random samples from two populations. It returns the value of test statistic and p-value under the null hypothesis of equal means. The SKK_test() performs the SKK test and returns the value of test statistic and p-value. The buildData() function generates simulated high-dimensional data in the two-population setting with specified sample sizes, numbers of components, covariance structure, etc., and the functions zwl_sim() and SKK_sim() return test statistic values and p-values for lists of simulated data sets generated by buildData().

Random sample from shifted gamma distribution

Description

This function generates random samples from shifted gamma distribution. That is, random samples are first generated from gamma distribution with shape parameter shape and scale parameter scale and then the mean of the gamma distribution, shape*scale, is subtracted from the sample.

Usage

rgammashift(n, shape, scale)

Arguments

Value

A vector of n values. It is equivalent to rgamma(n, shape, scale)- shape * scale.

Examples

# Generate a sample of shifted gamma observations with shape parameter 4 and scale parameter 2.
set.seed(10)
rgammashift(n = 5, shape =4, scale = 2)
# It is equivalent to
set.seed(10)
rgamma(n = 5, shape=4, scale=2)- 4 * 2

Apply the test by Zhang and Wang (2020) to multiple simulated two-sample datasets

Description

Apply the two-sample high-dimensional test by Zhang and Wang (2020) to multiple simulated two-sample high dimensional datasets. This function is useful for Monte Carlo experiments.

Usage

zwl_sim(DATA, order = 0)

Arguments

Value

A dataframe with each row consisting the values of the test statistics, p-values, Tn, and the estimate of Var(Tn).

References

Zhang, H. and Wang, H. (2020). Result consistency of high dimensional two-sample tests applied to gene ontology terms with gene sets. Manuscript in review.

Examples

# Generate 3 simulated two-sample datasets and apply the ZWL test
data <- buildData(n = 45, m =60, p = 300,
          muX = rep(0,300), muY = rep(0,300),
          dep = 'IND', S = 3, innov = rnorm)
zwl_sim(data, order = 2)

High-dimensional two-sample test proposed by Zhang and Wang (2020)

Description

This function implements the test of equal mean for two-sample high-dimension data using the ZWL and ZWLm tests proposed by Zhang and Wang (2020).

Usage

zwl_test(X, Y, order = 0)

Arguments

Value

statistic

The value of the test statistic.

pvalue

The p-value of the test statistic based on the asymptotic normality established by Zhang and Wang (2020)

Tn

The average of the squared univariate t-statistics.

var

The estimated variance of Tn

References

Zhang, H. and Wang, H. (2020). Result consistency of high dimensional two-sample tests applied to gene ontology terms with gene sets. Manuscript in review.

Examples

# Generate a simulated two-sample dataset and apply the ZWL test
data <- buildData(n = 45, m =60, p = 300,
          muX = rep(0,300), muY = rep(0,300),
          dep = 'IND', S = 1, innov = rnorm)
zwl_test(data[[1]]$X, data[[1]]$Y, order = 2)

# Apply the ZWLm test to a GO term to see if the two groups are differentiately expressed.
# The data for the GO term were stored in GO_example.
zwl_test(GO_example$X, GO_example$Y, order = 0)
# Apply the ZWL test to the GO term
zwl_test(GO_example$X, GO_example$Y, order = 2)