Dependency and conditional dependency detection between a level k (k > 1) categorical variable and a continuous variable via Bayes factor.

Description

Conditional dependency detection between a level k_x (k_x > 1) categorical variable x and a continuous variable y via Bayes factor given a level k_z categorical variable z. If k_z = 1, it is unconditional dependency detection method. It could be applied for non-parametric variable selecltion.

Usage

  bfslice_c(z, x, zdim, xdim, lambda, alpha)

Arguments

Value

Value of Bayes factor (nonnegative). Bayes factor could be treated as a statistic and one can take some threshold then calculates the corresponded Type I error rate. One can also take the value of Bayes factor for judgement.

References

Jiang, B., Ye, C. and Liu, J.S. Bayesian nonparametric tests via sliced inverse modeling. Bayesian Analysis, 12(1): 89-112, 2017.

See Also

bfslice_u, bfslice_eqp_c.

Examples

n <- 100
mu <- 0.5

## Unconditional test
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n), rep(1, n))
z <- rep(0, 2*n)

## Conditional test
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n/5), rep(1, n), rep(0, 4*n/5))
z <- c(rep(0, n), rep(1, n))
z <- z[order(y)]

x <- x[order(y)]
zdim <- max(z) + 1
xdim <- max(x) + 1
lambda <- 1.0
alpha <- 1.0
bfval <- bfslice_c(z, x, zdim, xdim, lambda, alpha)

Dependency and conditional dependency detection between a level k (k > 1) categorical variable and a continuous variable via Bayes factor.

Description

Conditional dependency detection between a level k_x (k_x > 1) categorical variable x and a continuous variable y via Bayes factor given a level k_z categorical variable z with O(n^{1/2})-resolution. The basic idea is almost the same as bfslice_c. The only different is that bfslice_eqp_c groups samples into approximate O(n^{1/2}) groups which contain approximate O(n^{1/2}) samples and treat the groups as a sample to calculate Bayes facor. If k_z = 1, it is unconditional dependency detection method. It could be applied for non-parametric variable selecltion.

Usage

  bfslice_eqp_c(z, x, zdim, xdim, lambda, alpha)

Arguments

Value

Value of Bayes factor (nonnegative). Bayes factor could be treated as a statistic and one can take some threshold then calculates the corresponded Type I error rate. One can also take the value of Bayes factor for judgement.

References

Jiang, B., Ye, C. and Liu, J.S. Bayesian nonparametric tests via sliced inverse modeling. Bayesian Analysis, 12(1): 89-112, 2017.

See Also

bfslice_c, bfslice_eqp_u.

Examples

n <- 1000
mu <- 0.2

## Unconditional test
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n), rep(1, n))
z <- rep(0, 2*n)

## Conditional test
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n/5), rep(1, n), rep(0, 4*n/5))
z <- c(rep(0, n), rep(1, n))
z <- z[order(y)]

x <- x[order(y)]
zdim <- max(z) + 1
xdim <- max(x) + 1
lambda <- 1.0
alpha <- 1.0
bfval <- bfslice_eqp_c(z, x, zdim, xdim, lambda, alpha)

Dependency detection between a level k (k > 1) categorical variable and a continuous variable via Bayes factor with given size of each group.

Description

Dependency detection between a level k (k > 1) categorical variable x and a continuous variable y via Bayes factor with O(n^{1/2})-resolution. The basic idea is almost the same as bfslice_u. The only different is that bfslice_eqp_u groups samples into approximate O(n^{1/2}) groups which contain approximate O(n^{1/2}) samples and treat the groups as a sample to calculate Bayes facor.

Usage

  bfslice_eqp_u(x, dim, lambda, alpha)

Arguments

Value

Value of Bayes factor (nonnegative). Bayes factor could be treated as a statistic and one can take some threshold then calculates the corresponded Type I error rate. One can also take the value of Bayes factor for judgement.

References

Jiang, B., Ye, C. and Liu, J.S. Bayesian nonparametric tests via sliced inverse modeling. Bayesian Analysis, 12(1): 89-112, 2017.

See Also

bfslice_u, bfslice_eqp_c.

Examples

n <- 1000
mu <- 0.2
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n), rep(1, n))
x <- x[order(y)]
dim <- max(x) + 1
lambda <- 1.0
alpha <- 1.0
bfval <- bfslice_eqp_u(x, dim, lambda, alpha)

Dependency detection between a level k (k > 1) categorical variable and a continuous variable via Bayes factor.

Description

Dependency detection between a level k (k > 1) categorical variable x and a continuous variable y via Bayes factor.

Usage

  bfslice_u(x, dim, lambda, alpha)

Arguments

Value

Value of Bayes factor (nonnegative). Bayes factor could be treated as a statistic and one can take some threshold then calculates the corresponded Type I error rate. One can also take the value of Bayes factor for judgement.

References

Jiang, B., Ye, C. and Liu, J.S. Bayesian nonparametric tests via sliced inverse modeling. Bayesian Analysis, 12(1): 89-112, 2017.

See Also

bfslice_c, bfslice_eqp_u.

Examples

n <- 100
mu <- 0.5
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n), rep(1, n))
x <- x[order(y)]
dim <- max(x) + 1
lambda <- 1.0
alpha <- 1.0
bfval <- bfslice_u(x, dim, lambda, alpha)

Non-parametric one-sample hypothesis testing via dynamic slicing

Description

Non-parametric one-sample hypothesis testing via dynamic slicing. By mapping sample values to the quantile of null distribution, ds_1 test whether they follow uniform distribution on [0, 1] via a regularized likelihood-ratio. Its calculated is based on a dynamic programming procedure.

Usage

  ds_1(y, lambda, alpha)

Arguments

Value

Value of dynamic slicing statistic for one-sample test. It is nonnegative. The null hypothesis that observations are from the null distribution is rejected if this statistic is greater than zero, otherwise accept the null hypothesis.

See Also

ds_eqp_1.

Examples

n <- 100
mu <- 0.5
x <- rnorm(n, mu, 1)
y <- pnorm(sort(x), 0, 1) 
lambda <- 1.0
alpha <- 1.0
dsres <- ds_1(y, lambda, alpha)

Non-parametric one-sample hypothesis testing via dynamic slicing

Description

Non-parametric one-sample hypothesis testing via dynamic slicing with O(n)-resolution. The basic idea of ds_eqp_1 is almost the same as ds_1. Difference between these two functions is that ds_eqp_1 considers an equal partition on [0, 1] but ds_1 does not. Candidate slicing boundaries in ds_eqp_1 only depend on the total number of samples and are unrelated to sample quantiles. In ds_1 they are immediately to the left or right of sample quantile.

Usage

  ds_eqp_1(y, lambda)

Arguments

Value

Value of dynamic slicing statistic for one-sample test. It is nonnegative. The null hypothesis that observations are from the null distribution is rejected if this statistic is greater than zero, otherwise accept the null hypothesis.

See Also

ds_1.

Examples

n <- 100
mu <- 0.5
x <- rnorm(n, mu, 1)
y <- pnorm(sort(x), 0, 1) 
lambda <- 1.0
dsres <- ds_eqp_1(y, lambda)

Dependency detection between level k (k > 1) categorical variable and continuous variable

Description

Dependency detection between level k (k > 1) categorical variable and continuous variable via dynamic slicing with O(n^{1/2})-resolution. The basic idea is almost the same as ds_k. The only different is that ds_eqp_k groups samples into approximate O(n^{1/2}) groups which contain approximate O(n^{1/2}) samples and performs dynamic slicing on their boundaries. This much faster version could reduce computation time substantially without too much power loss. Based on the strategy of ds_eqp_k, we recommend to apply it in large sample size problem and use ds_k for ordinary problem. For more details please refer to Jiang, Ye & Liu (2015). Results contains value of dynamic slicing statistic and slicing strategy. It could be applied for non-parametric K-sample hypothesis testing.

Usage

  ds_eqp_k(x, xdim, lambda, slice = FALSE)

Arguments

Value

References

Jiang, B., Ye, C. and Liu, J.S. Non-parametric K-sample tests via dynamic slicing. Journal of the American Statistical Association, 110(510): 642-653, 2015.

See Also

ds_k.

Examples

n <- 100
mu <- 0.5
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep("1", n), rep("2", n))
x <- relabel(x)
x <- x[order(y)]
xdim <- max(x) + 1
lambda <- 1.0
dsres <- ds_eqp_k(x, xdim, lambda, slice = TRUE)	

Gene set analysis via dynamic slicing

Description

Gene set analysis via dynamic slicing.

Usage

  ds_gsa(expdat, geneset, label, generank, ..., lambda = 1, bycol = FALSE,
         minsize = 15, maxsize = 500, randseed = 11235, rounds = 1000)

Arguments

Details

ds_gsa performs gene set analysis via dynamic slicing. It returns the DS statistics and slicing strategy of each gene set. ds_gsa does not attempt to integrate the ranking method into it. It requires ranking method or directly the gene rank as a parameter. Leaving ranking method as an optional input parameter is convenience for users who would like to use any ranking methods they want.

Value

A list with informations of gene sets whose size satisfy the minimum and maximum size thresholds. Its contains the following components:

References

Jiang, B., Ye, C. and Liu, J.S. Non-parametric K-sample tests via dynamic slicing. Journal of the American Statistical Association, 110(510): 642-653, 2015.

Subramanian, A., Tamayo, P., Mootha, V. K., et al. Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles. Proceedings of the National Academy of Sciences of the United States of America, 2005, 102(43): 15545-15550.

Benjamini, Y. and Hochberg, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodological), 1995, 57(1): 289-300.

See Also

ds_k.

Examples

##  Loading data from files
## Not run: 
gctpath <- "P53.gct"
clspath <- "P53.cls"
gmtpath <- "C2.gmt"
expdat <- load_gct(gctpath)
label <- load_cls(clspath)
geneset <- load_gmt(gmtpath)
fc <- function(x, label)
{
  d0 <- apply(x[,which(label == 0)], 1, mean)
  d1 <- apply(x[,which(label == 1)], 1, mean)
  d <- d1 / d0
  return(order(d))
}
ds_gsa_obj <- ds_gsa(expdat, geneset, label, "fc", lambda = 1.2, bycol = TRUE,
                     minsize = 15, maxsize = 500, randseed = 11235, rounds = 100)

## End(Not run)

Dependency detection between level k (k > 1) categorical variable and continuous variable

Description

Dependency detection between level k (k > 1) categorical variable and continuous variable. The basic idea is that the different values of categorical variable correspond to different distribution of continuous variable if there exist dependency between this two varibles, otherwise the distributions of continuous variable do not show difference conditioning on the values of categorical variable. Statistic for this dynamic slicing method is a regularized likelihood-ratio calculated via a dynamic programming procedure. For more details please refer to Jiang, Ye & Liu (2015). Results contains value of dynamic slicing statistic and slicing strategy. It could be applied for non-parametric K-sample hypothesis testing.

Usage

  ds_k(x, xdim, lambda, slice = FALSE)	

Arguments

Value

References

Jiang, B., Ye, C. and Liu, J.S. Non-parametric K-sample tests via dynamic slicing. Journal of the American Statistical Association, 110(510): 642-653, 2015.

See Also

ds_eqp_k.

Examples

n <- 100
mu <- 0.5
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep("1", n), rep("2", n))
x <- relabel(x)
x <- x[order(y)]
xdim <- max(x) + 1
lambda <- 1.0
dsres <- ds_k(x, xdim, lambda, slice = TRUE)

Hypothesis testing via dynamic slicing

Description

Perform a one- or K-sample (K > 1) hypothesis testing via dynamic slicing.

Usage

  ds_test(y, x, ..., type = c("ds", "eqp"), lambda = 1, alpha = 1, rounds = 0)

Arguments

Details

If x is an integer vector, ds_test performs K-sample test (K > 1).

Under this scenario, suppose that there are observations y drawn from some continuous populations. Let x be a vector that stores values of indicator of samples from different populations, i.e., x has values 0, 1, \ldots, K-1. The null hypothesis is that these populations have the same distribution.

If x is a character string naming a continuous (cumulative) distribution function, ds_test performs one-sample test with the null hypothesis that the distribution function which generated y is distribution x with parameters specified by \ldots. The parameters specified in \ldots must be pre-specified and not estimated from the data.

Only empirical p-values are available by specifying the value of parameter rounds, the number of permutation. lambda and alpha (for one-sample test with type "ds") contributes to p-value.

The procedure of choosing parameter lambda was described in Jiang, Ye & Liu (2015). Refer to dataset ds_type_one_error in this package for the empirical relationship of lambda, sample size and type I error.

Value

A list with class "htest" containing the following components:

References

Jiang, B., Ye, C. and Liu, J.S. Non-parametric K-sample tests via dynamic slicing. Journal of the American Statistical Association, 110(510): 642-653, 2015.

Examples

##  One-sample test
n <- 100
mu <- 0.5
y <- rnorm(n, mu, 1)
lambda <- 1.0
alpha <- 1.0
dsres <- ds_test(y, "pnorm", 0, 1, lambda = 1, alpha = 1, rounds = 100)
dsres <- ds_test(y, "pnorm", 0, 1, type = "ds", lambda = 1, alpha = 1)
dsres <- ds_test(y, "pnorm", 0, 1, type = "eqp", lambda = 1, rounds = 100)
dsres <- ds_test(y, "pnorm", 0, 1, type = "eqp", lambda = 1)

##  K-sample test
n <- 100
mu <- 0.5
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))

##  generate x in this way:
x <- c(rep(0, n), rep(1, n))
x <- as.integer(x)

##  or in this way:
x <- c(rep("G1", n), rep("G2", n))
x <- relabel(x)

lambda <- 1.0
dsres <- ds_test(y, x, lambda = 1, rounds = 100)
dsres <- ds_test(y, x, type = "eqp", lambda = 1, rounds = 100)

Relationship between penalty and Type I error

Description

Because there are not close form relationship between the value of slicing penalty and Type-I error rate of dynamic slicing. Empirical relationship between them is provided in this dataset. Each row corresponds to the value of penalty. Each column corresponds to the total number of samples.

Usage

data(ds_type_one_error)

Format

A list on the following 2 variables.

two_sample

a matrix.

three_sample

a matrix.

Examples

data(ds_type_one_error)

Export gene set analysis result

Description

Export gene set analysis result.

Usage

  export_res(ds_gsa_obj, file = "", ..., cutoff = 1, decreasing = FALSE, 
             type = c("name", "size", "DS", "p-value", "FDR", "slice"))

Arguments

Details

The usage of export_res is similar to write.table.

See Also

The ‘R Data Import/Export’ manual.

Examples

## Not run: 
ds_gsa_obj <- ds_gsa(expdat, geneset, label, fc, lambda = 1.2, bycol = TRUE,
                 minsize = 15, maxsize = 500, randseed = 11235, rounds = 100)
export_res(ds_gsa_obj, "ds_gsa_res.txt", sep = "\t", type = "DS", cutoff = 0,
           row.names = F, col.names = T, quote = F, append = F)

## End(Not run)

Gene expression matrix in gene set analysis

Description

P53 NCI-60 data set provided by Subramanian et al., (2005). A gene expression matrix whose rows correspond to genes and column correspond to samples.

Usage

data(gsa_exp)

Format

A matrix.

Source

http://www.broadinstitute.org/gsea

References

Subramanian, A., Tamayo, P., Mootha, V. K., et al. Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles. Proceedings of the National Academy of Sciences of the United States of America, 2005, 102(43): 15545-15550.

Examples

data(gsa_exp)

Sample labels in gene set analysis

Description

P53 NCI-60 data set provided by Subramanian et al., (2005). A list with phenotypes vector and a vector of sample label values.

Usage

data(gsa_label)

Format

A list on the following 2 variables.

pheotype

a character vector contains two genotypes.

value

a numeric vector contains sample label 0 and 1, where 0 and 1 stands for “MUT” and “WT”, respectively.

Source

http://www.broadinstitute.org/gsea

References

Subramanian, A., Tamayo, P., Mootha, V. K., et al. Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles. Proceedings of the National Academy of Sciences of the United States of America, 2005, 102(43): 15545-15550.

Examples

data(gsa_label)

Gene set list in gene set analysis

Description

Gene set provided by Subramanian et al., (2005). A list with gene set vector, gene set description vector and a list whose elements are vector of genes in each gene set.

Usage

data(gsa_set)

Format

A list with three elements: gene set name, gene set description and genes in gene set.

set_name

a character vector of gene set name.

set_description

a character vector of gene set description.

set_description

a list whose elements are vector. Each of them contains genes in each gene set.

Source

http://www.broadinstitute.org/gsea

References

Subramanian, A., Tamayo, P., Mootha, V. K., et al. Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles. Proceedings of the National Academy of Sciences of the United States of America, 2005, 102(43): 15545-15550.

Examples

data(gsa_set)

Load phenotype file

Description

Load phenotype file from .cls file

Usage

  load_cls(file)

Arguments

Value

A list with components:

Examples

# Pheotype files are available after registration at Broad institute GSEA website
# http://www.broadinstitute.org/gsea

## Not run: 
filename <- "P53.cls"
label <- load_cls(filename)

## End(Not run)

Load gene expression file

Description

Load gene expression data from .gct file

Usage

  load_gct(file)

Arguments

Value

A matrix with row names and column names.

Examples

# Gene expression files are available after registration at Broad institute GSEA website
# http://www.broadinstitute.org/gsea

## Not run: 
filename <- "P53.gct"
expdat <- load_gct(filename)

## End(Not run)

Load gene set file

Description

Load gene set from .gmt file

Usage

  load_gmt(file)

Arguments

Value

A list with components:

Examples

# Gene set files are available after registration at Broad institute GSEA website
# http://www.broadinstitute.org/gsea

## Not run: 
filename <- "C2.gmt"
geneset <- load_gmt(filename)

## End(Not run)

Ranking genes by signal to noise ratio

Description

Ranking genes by signal to noise ratio according to their expression data.

Usage

  rank_by_s2n(expmat, label)

Arguments

Value

A vector of rank of each gene according to signal to noise ratio.

Examples

expdat <- matrix(rnorm(500), nrow = 25, ncol = 20)
label <- rep(c(0, 1), 10)
ranklist <- rank_by_s2n(expdat, label)

Reassigning values of categorical variable

Description

Reassigning values of categorical variable. It is used for generating legal value of categorical variable before applying dynamic slicing.

Usage

  relabel(x)

Arguments

Value

An integer vector with values range from 0 to k (k > 0).

See Also

ds_test.

Examples

n <- 10
x <- c(rep("G1", n), rep("G2", n))
x <- relabel(x)

x <- c(rep(4, n), rep(5, n), rep(NA, n))
x <- relabel(x)

Show the slicing result

Description

Showing slicing result and plotting counts of observations in each slice.

Usage

  slice_show(slices_obj, main="Counts in each slice", xlab="Slices", ylab="Percentage")

Arguments

Value

A “ggplot” object which illustrates details of slicing.

See Also

ds_k, ds_eqp_k.

Examples

n <- 100
mu <- 0.5
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n), rep(1, n))
x <- x[order(y)]
xdim <- max(x) + 1
lambda <- 1.0
dsres <- ds_k(x, xdim, lambda, slice = TRUE)

ds_show <- slice_show(dsres$slices)