Package 'Oncotree'

Constructing and evaluating oncogenetic trees

Description

Oncogenetic trees are directed tree structures that model the process of occurrence of genetic alterations during carcinogenesis.

Details

A pure oncogenetic tree is a directed rooted tree T with a probability $\pi (e)$ attached to each edge e such that for every vertex there is a unique directed path from the root to it along the edges of the tree. This tree generates observations on the presence/absence of genetic events the following way: each edge e is independently retained with probability $\pi (e)$; the set of vertices that are still reachable from the root gives the set of the observed genetic events.

To describe random deviations from the pure tree model an error model is added.

Error model

1. The tumor develops according to the pure oncogenetic tree model

2. The presence/absence of each alteration is independently measured

3. If the alteration is present it is not observed with probability $\epsilon_-$.

   If the alteration is absent it is observed with probability $\epsilon_+$.

Author(s)

Lisa Pappas, Aniko Szabo

Maintainer: Aniko Szabo <[email protected]>

References

[1] Desper R., Jiang F., Kallioniemi O.P., Moch H., Papadimitriou C.H., and Sch\"affer A.A. (1999) Inferring tree models for oncogenesis from comparative genome hybridization data. Journal of Computational Biology. 6m 37–51. [2] Szabo, A. and Boucher, K. (2002) Estimating an oncogenetic tree when false negative and positives are present. Mathematical Biosciences, 176/2, 219–236.

Examples

data(ov.cgh)
  ov.tree <- oncotree.fit(ov.cgh)
  plot(ov.tree, edge.weights="estimated")

---

Find ancestors within an oncogenetic tree.

Description

ancestors finds all the ancestors of the given vertex within the tree starting from itself up to the root. least.common.ancestor finds the common ancestor of two vertices that is closest to them (and farthest from the root).

Usage

ancestors(otree, vertex)
   least.common.ancestor(otree, v1, v2)

Arguments

otree	An object of class oncotree.
vertex, v1, v2	Character values giving the names of the nodes.

Value

For ancestors: a character vector giving the names of the ancestors of vertex. The first element is vertex, and the last one is “Root”.

For least.common.ancestor: a character value with the name of the least common ancestor of v1 and v2.

See Also

oncotree.fit

Examples

data(ov.cgh)
  ov.tree <- oncotree.fit(ov.cgh)
  ancestors(ov.tree, "4q-")
  ancestors(ov.tree, "Xp-")
  least.common.ancestor(ov.tree, "4q-","Xp-")  #"5q-"

---

Bootstrap an oncogenetic tree to assess stability

Description

bootstrap.oncotree provides a set of resampling based estimates of the oncogenetic tree. Both a parametric and non-parametric approach is available. The print and plot methods provide interfaces for printing a summary and plotting the resulting set of trees.

Usage

bootstrap.oncotree(otree, R, type = c("nonparametric", "parametric"))
   ## S3 method for class 'boottree'
print(x, ...)
   ## S3 method for class 'boottree'
plot(x, minfreq=NULL, minprop=NULL, nboots=NULL, draw.orig=TRUE,
                           draw.consensus=TRUE, fix.nodes=FALSE, 
                           ask=(prod(par("mfrow"))<ntrees)&&dev.interactive(), ...)

Arguments

otree	An object of class oncotree.
R	The number of bootstrap replicates.
type	The type of bootstrap - see Details for explanations.
x	An object of class boottree - the output of bootstrap.oncotree
minfreq	A lower limit on the occurrence frequency of the tree in “boottree” for plotting. By default, all unique trees are plotted, which can lead to a large number of plots.
minprop	A lower limit on the occurrence proportion of the tree in “boottree” for plotting.
nboots	A lower limit on the number of bootstrapped trees plotted.
draw.orig	logical; if TRUE the original tree is plotted.
draw.consensus	logical; if TRUE the consensus tree is plotted (see Details).
fix.nodes	logical; if TRUE, the nodes for all trees are kept in the same position. If node.coords is passed as an argument to plot.oncotree, then those coordinates are used for all trees, otherwise the coordinates computed for the original tree are used.
ask	logical; if TRUE, the user is asked before each plot, see par(ask=.).
...	Ignored for print. Passed to plot.oncotree for the plot method.

Details

Parametric bootstrap: This approach assumes that the model is correct. Based on otree, a random data set is generated R times using generate.data. An oncogenetic tree is fitted to each of these random data sets.

Non-parametric bootstrap: The samples (rows) from the data associated with the tree are resampled with replacement R times, each time obtaining a data set with the same sample size. An oncogenetic tree is fitted to each of these resampled data sets.

For both approaches, a consensus tree that assigns to each vertex the parent that occurs most frequently in the bootstrapped trees, is also computed.

Value

For bootstrap.oncotree: an object of class boottree with the following components:

original	The parent component of the original tree (otree).
consensus	A numeric vector with the parent$parent.num component of the consensus tree - this defines the tree structure uniquely.
parent.freq	A matrix giving the number of trees with each possible child-parent edge. The rows correspond to children while the column to parents.
tree.list	A data frame with each row representing a unique tree obtained during the bootstrap. The ‘Tree’ variable contains the parent$parent.num component of the tree (each pasted into one dot-separated string), while the ‘Freq’ variable gives the frequency of the tree among the R bootstrap replicates.
type	A character value with the type of the bootstrap performed.

For print.boottree: the original object is returned invisibly. It prints a summary showing the number of replicates, the number of unique trees found, and the number of times that the original tree was obtained.

For plot.oncotree: nothing is returned. It is used for its side effect of producing a sequence of plots of the bootstrapped trees. Specifically, it plots the original tree (if draw.orig=TRUE), the consensus tree (if draw.consensus=TRUE), and then the other trees by frequency of occurrence. To limit the number of bootstrapped trees plotted, specify exactly one of minfreq, minprop or nboots. By default, if the session is interactive, the user is asked for confirmation before each new tree is drawn. To avoid this, either use ask=FALSE in the function call, or set up a layout that fits all the trees.

Author(s)

Lisa Pappas, Aniko Szabo

See Also

oncotree.fit

Examples

data(ov.cgh)
   ov.tree <- oncotree.fit(ov.cgh[1:5])
   set.seed(43636)
   ov.b1 <- bootstrap.oncotree(ov.tree, R=100, type="parametric")
   ov.b1
   opar <- par(mfrow=c(3,2), mar=c(2,0,0,0))
   plot(ov.b1, nboots=4)
   plot(ov.b1, nboots=4, fix.nodes=TRUE)
   par(opar)

---

Find the event distribution defined by an oncogenetic tree

Description

distribution.oncotree calculates the joint distribution of the events defined by the tree, while marginal.distr calculates the marginal probability of occurrence of each event.

Usage

distribution.oncotree(otree, with.probs = TRUE, with.errors=FALSE,
          edge.weights=if (with.errors) "estimated" else "observed")
   marginal.distr(otree, with.errors = TRUE,
          edge.weights=if (with.errors) "estimated" else "observed")

Arguments

otree	An object of class oncotree.
with.probs	A logical value specifying if only the set of possible outcomes should be returned (if TRUE), or the associated probabilities of occurrence as well.
with.errors	A logical value specifying whether false positive and negative error rates should be incorporated into the distribution.
edge.weights	A choice of whether the observed or estimated edge transition probabilities should be used in the calculation of probabilities. See oncotree.fit for explanation of the difference. By default, estimated edge transition probabilities if with.errors=TRUE and the observed ones if with.errors=FALSE.

Value

For distribution.oncotree: a data frame each row of which gives a possible outcome.

For marginal.distr: a named numeric vector - the names are the event names (+ ‘Root’) and the values are the corresponding marginal probability of occurrence.

Author(s)

Aniko Szabo

See Also

oncotree.fit

Examples

data(ov.cgh)
   ov.tree <- oncotree.fit(ov.cgh[1:5])
   
   #joint distribution
   jj <- distribution.oncotree(ov.tree, edge.weights="obs")
   head(jj)
   # including errors - time/size exponential in number of events
   jj.eps <- distribution.oncotree(ov.tree, with.errors=TRUE)
   head(jj.eps)
  
   #marginal distribution
   marginal.distr(ov.tree, with.error=FALSE)
   #marginal distribution calculated from the joint
   apply(jj[1:ov.tree$nmut], 2, function(x){sum(x*jj$Prob)})
   
   ##Same with errors incorporated
   #marginal distribution
   marginal.distr(ov.tree, with.error=TRUE)
   #marginal distribution calculated from the joint
   apply(jj.eps[1:ov.tree$nmut], 2, function(x){sum(x*jj.eps$Prob)})

---

Set the error rates of an oncotree manually

Description

Allows to set the false positive and false negative error rate associated with an object of class oncotree to values other than those found by the optimization in oncotree.fit. The estimated edge transition probabilities are updated appropriately.

Usage

error.rates(x) <- value

Arguments

x	An object of class oncotree.
value	A numeric vector of length 2. The false positive error rate will be set to value[1], while the false negative error rate to value[2].

See Also

oncotree.fit

Examples

data(ov.cgh)
  ov.tree <- oncotree.fit(ov.cgh)
  ov.tree
  error.rates(ov.tree) <- c(0,0)
  ov.tree

---

Generate random data from an oncogenetic tree

Description

Generates random event occurrence data based on an oncogenetic tree model.

Usage

generate.data(N, otree, with.errors=TRUE,
          edge.weights=if (with.errors) "estimated" else "observed",
          method=c("S","D1","D2"))

Arguments

N	The required sample size.
otree	An object of the class oncotree.
with.errors	A logical value specifying whether false positive and negative errors should be applied.
edge.weights	A choice of whether the observed or estimated edge transition probabilities should be used in the calculation of probabilities. See oncotree.fit for explanation of the difference. By default, estimated edge transition probabilities if with.errors=TRUE and the observed ones if with.errors=FALSE.
method	Simulation method, see Details for explanation of the options.

Details

There are three choices for the method of simulation; the best choice depends on the size of the tree, required sample size, and whether errors are needed.

Method “S” generates the data based on the conditional probability definition of the oncogenetic tree, and then ‘corrupts’ the resulting sample by introducing random errors. This method is applicable in all circumstances, but can be slower than other methods if N is large and with.errors=FALSE is used.

Method “D1” calculates the joint distribution generated by the tree exactly (using distribution.oncotree), and the observations are generated by sampling this distribution. Thus if with.errors=TRUE and the tree is large, this method might fail due to the exponential growth in the number of potential outcomes. On the other hand, for a moderately sized tree and a large desired sample size N this is the most efficient method.

Method “D2” calculates the joint distribution generated by the tree without false positives/negatives, samples from it, and then ‘corrupts’ the resulting sample. If with.errors=FALSE is used then this method is equivalent to method “D1”.

Value

A data set where each row is an independent observation.

Author(s)

Aniko Szabo

See Also

oncotree.fit

Examples

data(ov.cgh)
   ov.tree <- oncotree.fit(ov.cgh[1:5])
   
   set.seed(7365)
   rd <- generate.data(200, ov.tree, with.errors=TRUE)
   
   #compare timing of methods
   system.time(generate.data(20, ov.tree, with.errors=TRUE, method="S"))
   system.time(generate.data(20, ov.tree, with.errors=TRUE, method="D1"))
   system.time(generate.data(20, ov.tree, with.errors=TRUE, method="D2"))

---

Build and display an oncogenetic tree

Description

Build a directed tree structure to model the process of occurrence of genetic alterations (events) in carcinogenesis. The model is described in more detail in Oncotree-package. Methods for printing a short summary, displaying the tree on an R plot, and producing latex code for drawing the tree (using the ‘pstricks’ and ‘pst-tree’ LaTeX packages) are provided.

Usage

oncotree.fit(dataset, error.fun = function(x, y){sum((x - y)^2)})
  ## S3 method for class 'oncotree'
print(x, ...)
  ## S3 method for class 'oncotree'
plot(x, edge.weights = c("none", "observed", "estimated"),
    edge.digits=2, node.coords=NULL, plot=TRUE, cex = par("cex"), 
		col.edge=par("col"), col.text=par("col"), col.weight=par("col"),...)
            
  pstree.oncotree(x, edge.weights=c("none","observed","estimated"), edge.digits=2,
                  shape=c("none","oval", "circle", "triangle", "diamond"),
                  pstree.options=list(arrows="->", treefit="loose", 
                                      arrowscale="1.5 0.8", nodesep="3pt"))

Arguments

dataset	A data frame or a matrix with variable names as a listing of genetic events taking on binary values indicating missing (0) or present (1). Each row is an independent sample.
error.fun	A function of two variables that measures the deviation of the observed marginal frequencies of the events (which will be the first argument in the call) from the estimated ones. The false positive and negative error rates are obtained by minimizing error.fun. If error.fun=NULL is used, the error rates are not estimated.
x	An object of class oncotree.
edge.weights	Choice of edge weights to show on the plot.
edge.digits	The number of significant digits to use when displaying edge weights.
node.coords	A matrix with node-coordinates or NULL if the coordinates should be computed automatically (default).
plot	Logical; indicates whether the tree should be plotted.
cex	Scaling factor for the text in the nodes.
col.edge	color of the tree edges.
col.text	color of the node label.
col.weight	color of the edge weights.
...	Ignored for print. For plot these can be graphical parameters passed to lines when the edges are drawn
shape	The shape of the node in the pst-tree representation.
pstree.options	Additional options for pst-tree. See the pstricks documentation for possible values.

Details

‘pst-tree’ is a very flexible package, and very detailed formatting of the tree is possible. pstree.oncotree provides some default settings for drawing trees, but they can be easily overridden: most options can be set in pstree.options, while the appearance of the tree nodes can be controlled by defining a one-parameter \lab command that gives the desired appearance. For example, if red, non-mathematical test is desired in an oval, you could use \newcommand{\lab}[1]{\Toval[name=#1]{{\red #1}}}.

Value

For oncotree.fit: an object of class oncotree which has components

data	data frame used, after dropping events with zero observed frequency, and adding a column for the artificial ‘Root’ node
nmut	number of tree nodes: the number genetic events present in data +1 for the ‘Root’ node
parent	a list containing information about the tree structure with the following components childa character vector of the event names starting with ‘Root’ parenta character vector of the names of the parents of child parent.numa numeric vector with column indices corresponding to parent obs.weightsraw edge transition probabilities P(child|parent) est.weightsedge transition probabilities adjusted for the error rates eps
level	a numeric vector of the depth of each node in the tree (1 for the root, 2 for its children, etc.)
numchild	a numeric vector giving the number of children for each node
levelnodes	a numeric vector of the number of nodes found at each level of the tree
levelgrp	a character matrix with its rows giving the ordered nodes at each level
eps	a numeric vector of length two showing the estimated false positive and negative error rates (if error.fun is not NULL). Do not modify directly, but rather through error.rates<-.

For print.oncotree:

the original object is returned invisibly. It prints a summary showing the number of nodes, the parent-child relationships, and the false positive and negative error rates.

For plot.oncotree:

a matrix with node-coordinates is returned invisibly. The column names of the matrix are the names of the nodes/events (including 'Root'), the rows gives the x- and y-coordinates, respectively. This matrix provides a valid input for node.coords. If plot=TRUE, a plot of the tree is produced.

For pstree.oncotree:

a character string with the LaTeX code needed to draw a tree. \usepackage{pstricks,pst-tree} is required in the preamble of the LaTeX file, and it should be processed through a PostScript intermediary (DVIPS or similar) and not through PDFLaTeX.

Author(s)

Lisa Pappas

References

Szabo, A. and Boucher, K. (2002) Estimating an oncogenetic tree when false negative and positives are present. Mathematical Biosciences, 176/2, 219-236.

See Also

bootstrap.oncotree,error.rates<-, generate.data,ancestors,distribution.oncotree

Examples

data(ov.cgh)
  ov.tree <- oncotree.fit(ov.cgh, error.fun=function(x,y){max(abs(x-y))})
  ov.tree
  nodes <- plot(ov.tree, edge.weights="est")
  #move the Root node to the left
  nodes["x","Root"] <- nodes["x","8q+"]
  plot(ov.tree, node.coords=nodes)
  #output for pstricks+pst-tree
  pstree.oncotree(ov.tree, edge.weights="obs", shape="oval")

---

Ovarian cancer CGH data

Description

This is a data set obtained using the comparative genomic hybridization technique (CGH) on samples from papillary serous cystadenocarcinoma of the ovary. Only the seven most commonly occurring events are given.

Usage

data(ov.cgh)

Format

A data frame with 87 observations on the following 7 variables.

8q+

a 0/1 indicator of the presence of the ‘8q+’ event

3q+

a 0/1 indicator of the presence of the ‘3q+’ event

5q-

a 0/1 indicator of the presence of the ‘5q-’ event

4q-

a 0/1 indicator of the presence of the ‘4q-’ event

8p-

a 0/1 indicator of the presence of the ‘8p-’ event

1q+

a 0/1 indicator of the presence of the ‘1q+’ event

Xp-

a 0/1 indicator of the presence of the ‘Xp-’ event

Details

The CGH technique uses fluorescent staining to detect abnormal (increased or decreased) number of DNA copies. Often the results are reported as a gain or loss on a certain arm, without further distinction for specific regions. It is common to denote a change in DNA copy number on a specific chromosome arm by prefixing a “-” sign for decrease and a “+” for increase. Thus, say, -3q denotes abnormally low DNA copy number on the q arm of the 3rd chromosome.

Source

NCBI's SKY-CGH database

Examples

data(ov.cgh)
  heatmap(data.matrix(ov.cgh), Colv=NA, scale="none", col=c("gray90","red"))

---