The Bum Class

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

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 signficance.

Value

Graphical functions (hist and image) invisibly return the object on which they were invoked.
The cutoffSignficant 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 selectSignficant 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 signficant 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:

The 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 COLOR.EXPECTED and COLOR.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 rarther than the uniform component of the mixture. Significance is specified either by the false discovery rate (when by = 'FDR' or by = 'FalseDiscovery') or by the posterior probability (when by = '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 <kcoombes@mdanderson.org>

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

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')

#cleanup
rm(a, b, be, alpha, GAMMA, sens, spec, fake.data)