Provided by: libgenome-model-tools-music-perl_0.04-3_all 
NAME
PathScan - the Path-Scan significance test for mutations in groups of putative cancer
genes
SYNOPSIS
use PathScan;
my $pmobj = PathScan->new ($list_of_gene_lengths);
my $pval = $pmobj->path_scan ($actual_hits, $background_mutation_rate);
DESCRIPTION
This package calculates the so-called path-scan statistic P-value for sets of putative
cancer genes under the null hypothesis that somatic mutations found in data are the result
of a random process characterized by the background mutation rate. This test is applied
to, for example, a biologically-relevant group of genes, say all the genes in a particular
pathway, for which somatic mutation data are available. A low p-value would imply that
the null hypothesis should be rejected. In other words, the result suggests that the
mutation configuration in this pathway is probably not the result of a strictly random
process.
Nature of the Path-Scan Test
This statistic considers individual genes in a "binary" fashion, i.e. a gene is either
mutated (has one or more mutations) or it is not mutated. The number of mutations in a
mutated gene is not considered. This is the "path-scan" aspect of the test.
Why is such information discarded? The somatic background mutation rate is typically very
small compared to the size of the average gene. Consequently, the expected number of
mutations in any given gene is very low, much less than one, in fact. Under the null
hypothesis, most genes will have no mutations. Genes with one (or just a few) may be
interesting, but when many genes in a biologically-relevant group (say a pathway) have one
(or just a few) mutations, that could be a sign of some underlying non-random process. In
other words, this test is useful in cases where many genes in a group might each
contribute a small component (i.e. a small fitness advantage) in the context of the
disease process. What this test is not concerned with (and will not detect) is the case
where a single, specific gene has a non-random association and it reflects this fact via a
large number of mutations. Other single-gene tests should presumably flag such cases.
The path-scan test should, therefore, be thought of as just one tool within a larger
statistical "toolbox".
Assumptions in the Test
The main assumption is that a single background mutation rate applies to the set of genes
of interest. That is, the rate does not vary among genes, among chromosomes (if more than
one hosts genes of interest), etc.
BUGS AND OPPORTUNITIES FOR EXTENSION
Coefficients are recalculated for every individual test, but it would be good for these to
persist between tests, adding more as necessary (i.e. if a subsequent test involves more
genes than the current one).
AUTHOR
Michael C. Wendl
mwendl@wustl.edu
Copyright (C) 2007, 2008 Washington University
This program is free software; you can redistribute it and/or modify it under the terms of
the GNU General Public License as published by the Free Software Foundation; either
version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program;
if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA.
METHODS
The available methods are as follows.
new
This is the usual object constructor, which optionally takes all the gene-length data as
input. If you want to use the exact probability solution or the asymptotic approximate
solution, pass all lengths in a single list reference
my $pmobj = PathScan->new ([3434, 54565, 6445, ...]);
but if you want to use the convolution approximation method, divide the list of gene sizes
into the desired number of bins and pass each of these as a reference
my $pmobj = PathScan->new ([3434, 54565], [6445, ...]);
In other words, the way you pass these arguments at partially determines the context in
which you will obtain your P-value for this set of genes. The latter choice is typically
betetr, as it gives good accuracy and good computational efficiency. Conversely, the
exact solution is identically correct, but can be difficult to compute. The asymptotic
approximation is always computationally efficient, but not necessarily accurate for small
test sets.
path_scan
This function calculates the path-scan statistic in one of the appropriate contexts (exact
or convolution approximation, as described above). It takes the actual number of "hits"
you've observed in the data, i.e. the number of genes that have a mutated status.
my $pval = $pmobj->path_scan (7);
If you have not yet done the pre-processing with respect to the background mutation rate
(see below), then pre-processing can be executed implicitly by passing the rate as the
second argument.
my $pval = $pmobj->path_scan (7, 0.000001);
cdf_truncated
This function returns the cummulative distribution in the context of the convolution
approximation truncated such that it contains only enough information to process the given
number of hits.
my $pvals_list = $pmobj->cdf_truncated ($hits);
The list is ordered from most extreme to least extreme probability tail values, i.e. the
last value in the list is always unity. However, tailed p-values more extreme than that
associated with the argument are not, in fact, calculated, but rather are replaced with
the flag -1. This saves processing time and also reduces the chances of numerical
overflow for large pathways, as the full CDF must ultimately raise an "mval" (>1) to a
power equal to the number of genes in the pathway. The method assumes you have already
done the pre-processing with respect to the background mutation rate.
cdf
This function returns the cummulative distribution in one of the appropriate contexts
(exact or convolution approximation, as described above). There are no arguments,
my $pvals_list = $pmobj->cdf;
unless you have not yet done the pre-processing with respect to the background mutation
rate (see below), in which case the pre-processing can be executed implicitly by passing
the rate as the sole argument.
my $pvals_list = $pmobj->cdf (0.000001);
The list is ordered from most extreme to least extreme probability tail values, i.e. the
last value in the list is always unity.
cdf_asymptot
This function returns the cummulative distribution based on asymptotic analysis. There
are no arguments, i.e.
my $pvals_list = $pmobj->cdf_asymptot;
unless you have not yet done the pre-processing with respect to the background mutation
rate (see below), in which case the pre-processing can be executed implicitly by passing
the rate as the sole argument.
my $pvals_list = $pmobj->cdf_asymptot (0.000001);
The list is ordered from most extreme to least extreme probability tail values, i.e. the
last value in the list is always unity.
Note that asymptotic analysis gives a function (the Poisson) having infinite support. The
infinite tail probability for all values past the most extreme physical case are all
bundled into that most extreme p-value.
path_scan_asymptot
This function calculates the path-scan statistic in the asymptotic (Poisson) context. It
takes the actual number of "hits" you've observed in the data, i.e. the number of genes
that have a mutated status.
my $pval = $pmobj->path_scan_asymptot (7);
If you have not yet done the pre-processing with respect to the background mutation rate
(see below), then pre-processing can be executed implicitly by passing the rate as the
second argument.
my $pval = $pmobj->path_scan_asymptot (7, 0.000001);
You must set up the object, somewhat paradoxically, as if you will be doing the
calculation in the exact context. (This is a consequence of how data are stored
internally within the object.)
additional methods
The basic functionality of this package is encompassed in the methods described above.
However, some lower-level functions can also sometimes be useful.
p_value_exact
This function returns the exact value of the probability mass for a specific number of
hits.
$pval_exact = $pmobj->p_value_exact (7);
You must make sure to call this only if you've configured the object in the exact context
(see above).
p_value_binomial_approx
This function returns the convolution approximated value (i.e. using the binomial binning
approximation) of the probability mass for a specific number of hits.
$pval_exact = $pmobj->p_value_binomial_approx (7);
You must make sure to call this only if you've configured the object in the approximate
binomial context (see above). Also, you must explicitly calculate the necessary binomial
coefficients beforehand (see "binom_coeffs").
p_value_asymptot_approx
This function returns the asymptotic approximated value (i.e. using the Poisson limit
approximation) of the probability mass for a specific number of hits.
$pval_exact = $pmobj->p_value_asymptot_approx (7);
Somewhat paradoxically, you must make sure to call this only if you've configured the
object in the exact context (see above).
store_genes
Stores the raw gene length data. Use this if you did not pass these data to "new" before
you call any calculation methods. Works in the same way as "new", described above.
Specifically, the context is partially determined by whether you pass a single list (exact
context or asymptotic approximation)
$pmobj->store_genes ([3434, 54565, 6445, ...]);
or more than one list (convolution approximate context)
$pmobj->store_genes ([3434, 54565], [6445, ...]);
binom_coeffs
Calculates the binomial coefficients needed in the binomial (convolution) approximate
solution.
$pmobj->binom_coeffs;
The internal data structure is essentially the symmetric half of the appropriately-sized
Pascal triangle. Considerable memory is saved by not storing the full triangle.
preprocess
Calculates the Bernoulli kernel probabilities for the individual genes or gene bins
$pmobj_binom->preprocess ($background_mutation_rate);
The data structure can be re-configured to run the test with different background mutation
rates by just re-calling this routine with a different value
$pmobj_binom->preprocess ($new_background_mutation_rate);
EXAMPLES
The following examples may be helpful in using this package. In each case, assume we have
first executed some required preliminary code.
#__USE THE PACKAGE
use PathScan;
#__SOME DATA FOR AN "EXACT CONTEXT" CALCULATION
my $genes_exact = [
4000, 4000, 4000, 4000, 4000,
15000, 15000, 15000, 15000, 15000,
35000, 35000, 35000, 35000, 35000
];
#__SOME DATA FOR AN "APPROXIMATE CONTEXT" CALCULATION
my @genes_binned = (
[4000, 4000, 4000, 4000, 4000],
[15000, 15000, 15000, 15000, 15000],
[35000, 35000, 35000, 35000, 35000]
);
simple path-scan test
Here, we compare the values returned by both the exact and approximate algorithms over the
whole domain of possible hits for a case where the answers should be identical.
#__SET BACKGROUND MUTATION RATE
my $rho = 0.00002;
#__CONFIGURE OBJECTS IN "EXACT" AND "APPROXIMATE" CONTEXTS
my $pmobj_exact = PathScan->new ($genes_exact);
$pmobj_exact->preprocess ($rho);
my $pmobj_binom = PathScan->new (@genes_binned);
$pmobj_binom->preprocess ($rho);
#__CALCULATE AND TALLY THE MAXIMUM DIFFERENCE
my $maxdiff = 0;
for (my $i = 0; $i <= scalar @{$genes_exact}; $i++) {
my $pm_pval_exact = $pmobj_exact->path_scan($i);
my $pm_pval_binom = $pmobj_binom->path_scan($i);
my $diff = abs ($pm_pval_exact - $pm_pval_binom);
$maxdiff = $diff if $diff > $maxdiff;
print "$i hits: $pm_pval_exact $pm_pval_binom $diff\n";
}
print "MAXIMUM DIFFERENCE IS $maxdiff\n";
testing at different background rates
This example shows how to run the test for a fixed number of hits, say 7 in this case, for
various different background mutation rates.
#__CONFIGURE OBJECT
my $pmobj_binom = PathScan->new (@genes_binned);
#__CALCULATE
for (my $rho = 0.00001; $rho <= 0.0001; $rho += 0.00001) {
my $pm_pval_binom = $pmobj_binom->path_scan(7, $rho);
print "7 hits at background $rho : P = $pm_pval_binom\n";
}
Note that we did not run "preprocess" explicitly, but rather let the "path_scan" method
call it implicitly for each new value of the background mutation rate.
computing asymptotic approximate solution
The asymptotic (Poisson) approximate probabiltiy value is straightforward to compute.
#__SET BACKGROUND MUTATION RATE
my $rho = 0.00002;
#__CONFIGURE OBJECT
my $pmobj_poisson = PathScan->new ($genes_exact);
$pmobj_poisson->preprocess ($rho);
#__P-VALUE FOR 7 OBSERVED MUTATED GENES
my $pm_pval_poisson = $pmobj_exact->path_scan_asymptot (7);
accessing individual probability masses
The probability masses for specific numbers of hits can also be calculated.
#__SET BACKGROUND MUTATION RATE
my $rho = 0.00002;
#__CONFIGURE OBJECT
my $pmobj_exact = PathScan->new ($genes_exact);
$pmobj_exact->preprocess ($rho);
#__CALCULATE MASSES
my $total_prob = 0;
for (my $i = 0; $i <= scalar @{$genes_exact}; $i++) {
my $pval_exact = $pmobj_exact->p_value_exact ($i);
$total_prob += $pval_exact;
print "$i hits : probability mass = $pval_exact\n";
}
print "total probability = $total_prob\n";
perl v5.22.1 2Genome::Model::Tools::Music::PathScan::PathScan(3pm)