Package 'pvclust'

DNA Microarray Data of Lung Tumors

Description

DNA Microarray data of 73 lung tissues including 67 lung tumors. There are 916 observations of genes for each lung tissue.

Usage

data(lung)

Format

data frame of size $916 \times 73$.

Details

This dataset has been modified from original data. Each one observation of duplicate genes has been removed. See source section in this help for original data source.

Source

http://genome-www.stanford.edu/lung_cancer/adeno/

References

Garber, M. E. et al. (2001) "Diversity of gene expression in adenocarcinoma of the lung", Proceedings of the National Academy of Sciences, 98, 13784-13789.

Examples

## Reading the data
data(lung)

## Multiscale Bootstrap Resampling
lung.pv <- pvclust(lung, nboot=100)

## CAUTION: nboot=100 may be too small for actual use.
##          We suggest nboot=1000 or larger.
##          plot/print functions will be useful for diagnostics.

## Plot the result
plot(lung.pv, cex=0.8, cex.pv=0.7)

ask.bak <- par()$ask
par(ask=TRUE)

pvrect(lung.pv, alpha=0.9)
msplot(lung.pv, edges=c(51,62,68,71))

par(ask=ask.bak)

## Print a cluster with high p-value
lung.pp <- pvpick(lung.pv, alpha=0.9)
lung.pp$clusters[[2]]

## Print its edge number
lung.pp$edges[2]


## We recommend parallel computing for large dataset as this one
## Not run: 
library(snow)
cl <- makeCluster(10, type="MPI")
lung.pv <- parPvclust(cl, lung, nboot=1000)

## End(Not run)

---

Curve Fitting for Multiscale Bootstrap Resampling

Description

msfit performs curve fitting for multiscale bootstrap resampling. It generates an object of class msfit. Several generic methods are available.

Usage

msfit(bp, r, nboot)

## S3 method for class 'msfit'
plot(x, curve=TRUE, main=NULL, sub=NULL, xlab=NULL, ylab=NULL, ...)

## S3 method for class 'msfit'
lines(x, col=2, lty=1, ...)

## S3 method for class 'msfit'
summary(object, digits=3, ...)

Arguments

bp	numeric vector of bootstrap probability values.
r	numeric vector of relative sample size of bootstrap samples defined as $r=n'/n$ for original sample size $n$ and bootstrap sample size $n'$.
nboot	numeric value (vector) of the number of bootstrap replications.
x	object of class msfit.
curve	logical. If TRUE, the fitted curve is drawn.
main, sub, xlab, ylab, col, lty	generic graphic parameters.
object	object of class msfit.
digits	integer indicating the precision to be used in rounding.
...	other parameters to be used in the functions.

Details

function msfit performs the curve fitting for multiscale bootstrap resampling. In package pvclust this function is only called from the function pvclust (or parPvclust), and may never be called from users. However one can access a list of msfit objects by x$msfit, where x is an object of class pvclust.

Value

msfit returns an object of class msfit. It contains the following objects:

p	numeric vector of $p$-values. au is AU (Approximately Unbiased) $p$-value computed by multiscale bootstrap resampling, which is more accurate than BP value (explained below) as unbiased $p$-value. bp is BP (Bootstrap Probability) value, which is simple but tends to be unbiased when the absolute value of c (a value in coef vector, explained below) is large.
se	numeric vector of estimated standard errors of $p$-values.
coef	numeric vector related to geometric aspects of hypotheses. v is signed distance and c is curvature of the boundary.
df	numeric value of the degree of freedom in curve fitting.
rss	residual sum of squares.
pchi	$p$-value of chi-square test based on asymptotic theory.

Author(s)

Ryota Suzuki [email protected]

References

Shimodaira, H. (2004) "Approximately unbiased tests of regions using multistep-multiscale bootstrap resampling", Annals of Statistics, 32, 2616-2641.

Shimodaira, H. (2002) "An approximately unbiased test of phylogenetic tree selection", Systematic Biology, 51, 492-508.

---

Drawing the Results of Curve Fitting for Pvclust Object

Description

draws the results of curve fitting for pvclust object.

Usage

msplot(x, edges=NULL, ...)

Arguments

x	object of class pvclust.
edges	numeric vector of edge numbers to be plotted.
...	other parameters to be used in the function.

Author(s)

Ryota Suzuki [email protected]

See Also

plot.msfit

---

Draws Dendrogram with P-values for Pvclust Object

Description

plot dendrogram for a pvclust object and add $p$-values for clusters.

Usage

## S3 method for class 'pvclust'
plot(x, print.pv=TRUE, print.num=TRUE, float=0.01,
  col.pv=c(si=4, au=2, bp=3, edge=8), cex.pv=0.8, font.pv=NULL,
  col=NULL, cex=NULL, font=NULL, lty=NULL, lwd=NULL, main=NULL,
  sub=NULL, xlab=NULL, ...)

## S3 method for class 'pvclust'
text(x, col=c(au=2, bp=3, edge=8), print.num=TRUE,
  float=0.01, cex=NULL, font=NULL, ...)

Arguments

x	object of class pvclust, which is generated by function pvclust. See pvclust for details.
print.pv	logical flag to specify whether print $p$-values around the edges (clusters), or character vector of length 0 to 3 which specifies the names of $p$-values to print (c("si", "au", "bp") for example).
print.num	logical flag to specify whether print edge numbers below clusters.
float	numeric value to adjust the height of $p$-values from edges.
col.pv	named numeric vector to specify the colors for $p$-values and edge numbers. For back compatibility it can also be unnamed numeric vector of length 3, which corresponds to the color of AU, BP values and edge numbers.
cex.pv	numeric value which specifies the size of characters for $p$-values and edge numbers. See cex argument for par.
font.pv	numeric value which specifies the font of characters for $p$-values and edge numbers. See font argument for par.
col, cex, font	in text function, they correspond to col.pv, cex.pv and font.pv in plot function, respectively. In plot function they are used as generic graphic parameters.
lty, lwd, main, sub, xlab, ...	generic graphic parameters. See par for details.

Details

This function plots a dendrogram with $p$-values for given object of class pvclust. SI $p$-value (printed in blue color in default) is the approximately unbiased $p$-value for selective inference, and AU $p$-value (printed in red color in default) is also the approximately unbiased $p$-value but for non-selective inference. They ared calculated by multiscale bootstrap resampling. BP value (printed in green color in default) is "bootstrap probability" value, which is less accurate than AU value as $p$-value. One can consider that clusters (edges) with high SI or AU values (e.g. 95%) are strongly supported by data. SI value is newly introduced in Terada and Shimodaira (2017) for selective inference, which is more appropriate for testing clusters identified by looking at the tree. AU value has been used since Shimodaira (2002), which is not designed for selective inference. AU is valid when you know the clusters before looking at the data. See also documatation (Multiscale Bootstrap using Scaleboot Package, verison 0.4-0 or higher) in scaleboot package.

Author(s)

Ryota Suzuki [email protected]

References

Terada, Y. and Shimodaira, H. (2007) "Selective inference for the problem of regions via multiscale bootstrap", arXiv:1711.00949.

Shimodaira, H. (2004) "Approximately unbiased tests of regions using multistep-multiscale bootstrap resampling", Annals of Statistics, 32, 2616-2641.

Shimodaira, H. (2002) "An approximately unbiased test of phylogenetic tree selection", Systematic Biology, 51, 492-508.

See Also

text.pvclust

---

Print Function for Pvclust Object

Description

print clustering method and distance measure used in hierarchical clustering, $p$-values and related statistics for a pvclust object.

Usage

## S3 method for class 'pvclust'
print(x, which=NULL, digits=3, ...)

Arguments

x	object of class pvclust.
which	numeric vector which specifies the numbers of edges (clusters) of which the values are printed. If NULL is given, it prints the values of all edges. The default is NULL.
digits	integer indicating the precision to be used in rounding.
...	other parameters used in the function.

Value

this function prints $p$-values and some related statistics.

au	AU (Approximately Unbiased) $p$-value, which is more accurate than BP value as unbiased $p$-value. It is computed by multiscale bootstrap resampling.
bp	BP (Bootstrap Probability) value, which is a simple statistic computed by bootstrap resampling. This value tends to be biased as $p$-value when the absolute value of c (explained below) is large.
se.au, se.bp	estimated standard errors for au and bp, respectively.
v, c	values related to geometric aspects of hypotheses. v is signed distance and c is curvature of the boundary.
pchi	$p$-values of chi-square test based on asymptotic theory.

Author(s)

Ryota Suzuki [email protected]

---

Calculating P-values for Hierchical Clustering

Description

calculates $p$-values for hierarchical clustering via multiscale bootstrap resampling. Hierarchical clustering is done for given data and $p$-values are computed for each of the clusters.

Usage

pvclust(data, method.hclust="average",
        method.dist="correlation", use.cor="pairwise.complete.obs",
        nboot=1000, parallel=FALSE, r=seq(.5,1.4,by=.1),
        store=FALSE, weight=FALSE, iseed=NULL, quiet=FALSE)

parPvclust(cl=NULL, data, method.hclust="average",
           method.dist="correlation", use.cor="pairwise.complete.obs",
           nboot=1000, r=seq(.5,1.4,by=.1), store=FALSE, weight=FALSE,
           init.rand=NULL, iseed=NULL, quiet=FALSE)

Arguments

data	numeric data matrix or data frame.
method.hclust	the agglomerative method used in hierarchical clustering. This should be (an abbreviation of) one of "average", "ward.D", "ward.D2", "single", "complete", "mcquitty", "median" or "centroid". The default is "average". See method argument in hclust.
method.dist	the distance measure to be used. This should be a character string, or a function which returns a dist object. A character string should be (an abbreviation of) one of "correlation", "uncentered", "abscor" or those which are allowed for method argument in dist function. The default is "correlation". See details section in this help and method argument in dist.
use.cor	character string which specifies the method for computing correlation with data including missing values. This should be (an abbreviation of) one of "all.obs", "complete.obs" or "pairwise.complete.obs". See the use argument in cor function.
nboot	the number of bootstrap replications. The default is 1000.
parallel	switch for parallel computation. If FALSE the computation is done in non-parallel mode. If TRUE or a positive integer is supplied, parallel computation is done with automatically generated PSOCK cluster. Use TRUE for default cluster size (parallel::detectCores() - 1), or specify the size by an integer. If a cluster object is supplied the cluster is used for parallel computation. Note that NULL is currently not allowed for using the default cluster.
r	numeric vector which specifies the relative sample sizes of bootstrap replications. For original sample size $n$ and bootstrap sample size $n'$, this is defined as $r=n'/n$.
store	locical. If store=TRUE, all bootstrap replications are stored in the output object. The default is FALSE.
cl	a cluster object created by package parallel or snow. If NULL, use the registered default cluster.
weight	logical. If weight=TRUE, resampling is made by weight vector instead of index vector. Useful for large r value (r>10). Currently, available only for distance "correlation" and "abscor".
init.rand	logical. If init.rand=TRUE, random number generators are initialized. Use iseed argument to achieve reproducible results. This argument is duplicated and will be unavailable in the future.
iseed	An integer. If non-NULL value is supplied random number generators are initialized. It is passed to set.seed or clusterSetRNGStream.
quiet	logical. If TRUE it does not report the progress.

Details

Function pvclust conducts multiscale bootstrap resampling to calculate $p$-values for each cluster in the result of hierarchical clustering. parPvclust is the parallel version of this procedure which depends on package parallel for parallel computation.

For data expressed as $(n \times p)$ matrix or data frame, we assume that the data is $n$ observations of $p$ objects, which are to be clustered. The $i$'th row vector corresponds to the $i$'th observation of these objects and the $j$'th column vector corresponds to a sample of $j$'th object with size $n$.

There are several methods to measure the dissimilarities between objects. For data matrix $X=\{x_{ij}\}$, "correlation" method takes

$1 - \frac{ \sum_{i=1}^n (x_{ij} - \bar{x}_j) (x_{ik} - \bar{x}_k) } { \sqrt{\sum_{i=1}^n (x_{ij} - \bar{x}_j)^2} \sqrt{\sum_{i=1}^n (x_{ik} - \bar{x}_k)^2} }$

for dissimilarity between $j$'th and $k$'th object, where $\bar{x}_j = \frac{1}{n} \sum_{i=1}^n x_{ij} \mbox{and} \bar{x}_k = \frac{1}{n} \sum_{i=1}^n x_{ik}$.

"uncentered" takes uncentered sample correlation

$1 - \frac{ \sum_{i=1}^n x_{ij} x_{ik} } { \sqrt{\sum_{i=1}^n x_{ij}^2} \sqrt{\sum_{i=1}^n x_{ik}^2} }$

and "abscor" takes the absolute value of sample correlation

$1 - \ \Biggl| \frac{ \sum_{i=1}^n (x_{ij} - \bar{x}_j) (x_{ik} - \bar{x}_k) } { \sqrt{\sum_{i=1}^n (x_{ij} - \bar{x}_j)^2} \sqrt{\sum_{i=1}^n (x_{ik} - \bar{x}_k)^2} } \Biggl|.$

Value

hclust	hierarchical clustering for original data generated by function hclust. See hclust for details.
edges	data frame object which contains $p$-values and supporting informations such as standard errors.
count	data frame object which contains primitive information about the result of multiscale bootstrap resampling.
msfit	list whose elements are results of curve fitting for multiscale bootstrap resampling, of class msfit. See msfit for details.
nboot	numeric vector of number of bootstrap replications.
r	numeric vector of the relative sample size for bootstrap replications.
store	list contains bootstrap replications if store=TRUE was given for function pvclust or parPvclust.
version	package_version of pvclust used to generate this object.

Author(s)

Ryota Suzuki [email protected]

References

Suzuki, R. and Shimodaira, H. (2006) "Pvclust: an R package for assessing the uncertainty in hierarchical clustering", Bioinformatics, 22 (12): 1540-1542.

Shimodaira, H. (2004) "Approximately unbiased tests of regions using multistep-multiscale bootstrap resampling", Annals of Statistics, 32, 2616-2641.

Shimodaira, H. (2002) "An approximately unbiased test of phylogenetic tree selection", Systematic Biology, 51, 492-508.

Suzuki, R. and Shimodaira, H. (2004) "An application of multiscale bootstrap resampling to hierarchical clustering of microarray data: How accurate are these clusters?", The Fifteenth International Conference on Genome Informatics 2004, P034.

http://www.sigmath.es.osaka-u.ac.jp/shimo-lab/prog/pvclust/

See Also

lines.pvclust, print.pvclust, msfit, plot.pvclust, text.pvclust, pvrect and pvpick.

Examples

### example using Boston data in package MASS
data(Boston, package = "MASS")

## multiscale bootstrap resampling (non-parallel)
boston.pv <- pvclust(Boston, nboot=100, parallel=FALSE)

## CAUTION: nboot=100 may be too small for actual use.
##          We suggest nboot=1000 or larger.
##          plot/print functions will be useful for diagnostics.

## plot dendrogram with p-values
plot(boston.pv)

ask.bak <- par()$ask
par(ask=TRUE)

## highlight clusters with high au p-values
pvrect(boston.pv)

## print the result of multiscale bootstrap resampling
print(boston.pv, digits=3)

## plot diagnostic for curve fitting
msplot(boston.pv, edges=c(2,4,6,7))

par(ask=ask.bak)

## print clusters with high p-values
boston.pp <- pvpick(boston.pv)
boston.pp

### Using a custom distance measure

## Define a distance function which returns an object of class "dist".
## The function must have only one argument "x" (data matrix or data.frame).
cosine <- function(x) {
    x <- as.matrix(x)
    y <- t(x) %*% x
    res <- 1 - y / (sqrt(diag(y)) %*% t(sqrt(diag(y))))
    res <- as.dist(res)
    attr(res, "method") <- "cosine"
    return(res)
}

result <- pvclust(Boston, method.dist=cosine, nboot=100)
plot(result)

## Not run: 
### parallel computation
result.par <- pvclust(Boston, nboot=1000, parallel=TRUE)
plot(result.par)

## End(Not run)

---

Find Clusters with High/Low P-values

Description

find clusters with relatively high/low $p$-values. pvrect and lines (S3 method for class pvclust) highlight such clusters in existing plot, and pvpick returns a list of such clusters.

Usage

pvpick(x, alpha=0.95, pv="au", type="geq", max.only=TRUE)

pvrect(x, alpha=0.95, pv="au", type="geq", max.only=TRUE, border=NULL, ...)

## S3 method for class 'pvclust'
lines(x, alpha=0.95, pv="au", type="geq", col=2, lwd=2, ...)

Arguments

x	object of class pvclust.
alpha	threshold value for $p$-values.
pv	character string which specifies the $p$-value to be used. It should be one of "si", "au" and "bp", corresponding to SI, AU $p$-value and BP value, respectively. See plot.pvclust for details.
type	one of "geq", "leq", "gt" or "lt". If "geq" is specified, clusters with $p$-value greater than or equals the threshold given by "alpha" are returned or displayed. Likewise "leq" stands for lower than or equals, "gt" for greater than and "lt" for lower than the threshold value. The default is "geq".
max.only	logical. If some of clusters with high/low $p$-values have inclusion relation, only the largest cluster is returned (or displayed) when max.only=TRUE.
border	numeric value which specifies the color of borders of rectangles.
col	numeric value which specifies the color of lines.
lwd	numeric value which specifies the width of lines.
...	other graphic parameters to be used.

Value

pvpick returns a list which contains the following values.

clusters	a list of character string vectors. Each vector corresponds to the names of objects in each cluster.
edges	numeric vector of edge numbers. The $i$'th element (number) corresponds to the $i$'th name vector in clusters.

Author(s)

Ryota Suzuki [email protected]

---

Diagnostic Plot for Standard Error of p-value

Description

draws diagnostic plot for standard error of $p$-value for pvclust object.

Usage

seplot(object, type=c("au", "si", "bp"), identify=FALSE,
  main=NULL, xlab=NULL, ylab=NULL, ...)

Arguments

object	object of class pvclust.
type	the type of $p$-value to be plotted, one of "si", "au" or "bp".
identify	logical. If TRUE, edge numbers can be identified interactively. See identify for basic usage.
main, xlab, ylab	generic graphic parameters. See par for details.
...	other graphical parameters to be passed to generic plot or identify function.

Author(s)

Ryota Suzuki [email protected]

---