Bum-class {ClassComparison} | R Documentation |
Class "Bum"
Description
The Bum
class is used to fit a beta-uniform mixture model to a
set of p-values.
Usage
Bum(pvals, ...)
## S4 method for signature 'Bum'
summary(object, tau=0.01, ...)
## S4 method for signature 'Bum'
hist(x, res=100, xlab='P Values', main='', ...)
## S4 method for signature 'Bum'
image(x, ...)
## S4 method for signature 'Bum'
cutoffSignificant(object, alpha, by='FDR', ...)
## S4 method for signature 'Bum'
selectSignificant(object, alpha, by='FDR', ...)
## S4 method for signature 'Bum'
countSignificant(object, alpha, by='FDR', ...)
likelihoodBum(object)
Arguments
pvals |
numeric vector containing values between |
object |
object of class |
tau |
numeric scalar between |
x |
object of class |
res |
positive integer scalar specifying the resolution at which to plot the fitted distribution curve |
xlab |
character string specifying the label for the x axis |
main |
character string specifying the graph title |
alpha |
Either the false discovery rate (if |
by |
character string denoting the method to use for determining cutoffs. Valid values are:
|
... |
extra arguments for generic or plotting routines |
Details
The BUM method was introduced by Stan Pounds and Steve Morris, although it was simultaneously discovered by several other researchers. It is generally applicable to any analysis of microarray or proteomics data that performs a separate statistical hypothesis test for each gene or protein, where each test produces a p-value that would be valid if the analyst were only performing one statistical test. When performing thousands of statistical tests, however, those p-values no longer have the same interpretation as Type I error rates. The idea behind BUM is that, under the null hypothesis that none of the genes or proteins is interesting, the expected distribution of the set of p-values is uniform. By contrast, if some of the genes are interesting, then we should see an overabundance of small p-values (or a spike in the histogram near zero). We can model the alternative hypothesis with a beta distribution, and view the set of all p-values as a mixture distribution.
Fitting the BUM model is straightforward, using a nonlinear optimizer to compute the maximum likelihood parameters. After the model has been fit, one can easily determine cutoffs on the p-values that correspond to desired false discovery rates. Alternatively, the original Pounds and Morris paper shows that their results can be reinterpreted to recover the empirical Bayes method introduced by Efron and Tibshirani. Thus, one can also determine cutoffs by specifying a desired posterior probability of significance.
Value
Graphical functions (hist
and image
) invisibly return the
object on which they were invoked.
The cutoffSignificant
method returns a real number between zero
and one. P-values below this cutoff are considered statistically
significant at either the specified false discovery rate or at the
specified posterior probability.
The selectSignificant
method returns a vector of logical values
whose length is equal to the length of the vector of p-values that was
used to construct the Bum
object. True values in the return
vector mark the statistically significant p-values.
The countSignificant
method returns an integer, the number of
statistically significant p-values.
The summary
method returns an object of class
BumSummary
.
Creating Objects
Although objects can be created directly using new
, the most
common usage will be to pass a vector of p-values to the
Bum
function.
Slots
pvals
:numeric vector of p-values used to construct the object.
ahat
:Model parameter
lhat
:Model parameter
pihat
:Model parameter
Methods
- summary(object, tau=0.01, ...)
For each value of the p-value cutoff
tau
, computes estimates of the fraction of true positives (TP), false negatives (FN), false positives (FP), and true negatives (TN).- hist(x, res=100, xlab='P Values', main=”, ...)
Plots a histogram of the object, and overlays (1) a straight line to indicate the contribution of the uniform component and (2) the fitted beta-uniform distribution from the observed values. Colors in the plot are controlled by
oompaColor$EXPECTED
andoompaColor$OBSERVED
.- image(x, ...)
Produces four plots in a 2x2 layout: (1) the histogram produced by
hist
; (2) a plot of cutoffs against the desired false discovery rate; (3) a plot of cutoffs against the posterior probability of coming from the beta component; and (4) an ROC curve.- cutoffSignificant(object, alpha, by='FDR', ...)
Computes the cutoff needed for significance, which in this case means arising from the beta component rather than the uniform component of the mixture. Significance is specified either by the false discovery rate (when
by = 'FDR'
orby = 'FalseDiscovery'
) or by the posterior probability (whenby = 'EmpiricalBayes'
)- selectSignificant(object, alpha, by='FDR', ...)
Uses
cutoffSignificant
to determine a logical vector that indicates which of the p-values are significant.- countSignificant(object, alpha, by='FDR', ...)
Uses
selectSignificant
to count the number of significant p-values.
Author(s)
Kevin R. Coombes krc@silicovore.com
References
Pounds S, Morris SW.
Estimating the occurrence of false positives and false negatives in
microarray studies by approximating and partitioning the empirical
distribution of p-values.
Bioinformatics. 2003 Jul 1;19(10):1236-42.
Benjamini Y, Hochberg Y.
Controlling the false discovery rate: a practical and powerful approach
to multiple testing.
J Roy Statist Soc B, 1995; 57: 289-300.
Efron B, Tibshirani R.
Empirical bayes methods and false discovery rates for microarrays.
Genet Epidemiol 2002, 23: 70-86.
See Also
Two classes that produce lists of p-values that can (and often
should) be analyzed using BUM are MultiTtest
and
MultiLinearModel
. Also see BumSummary
.
Examples
showClass("Bum")
fake.data <- c(runif(700), rbeta(300, 0.3, 1))
a <- Bum(fake.data)
hist(a, res=200)
alpha <- (1:25)/100
plot(alpha, cutoffSignificant(a, alpha, by='FDR'),
xlab='Desired False Discovery Rate', type='l',
main='FDR Control', ylab='Significant P Value')
GAMMA <- 5*(10:19)/100
plot(GAMMA, cutoffSignificant(a, GAMMA, by='EmpiricalBayes'),
ylab='Significant P Value', type='l',
main='Empirical Bayes', xlab='Posterior Probability')
b <- summary(a, (0:100)/100)
be <- b@estimates
sens <- be$TP/(be$TP+be$FN)
spec <- be$TN/(be$TN+be$FP)
plot(1-spec, sens, type='l', xlim=c(0,1), ylim=c(0,1), main='ROC Curve')
points(1-spec, sens)
abline(0,1)
image(a)
countSignificant(a, 0.05, by='FDR')
countSignificant(a, 0.99, by='Emp')