Description

An object of class EBMTP is the output of a particular multiple testing procedure, as generated by the function EBMTP. The object has slots for the various data used to make multiple testing decisions, in particular adjusted p-values.

Objects from the Class

Objects can be created by calls of the form
new('MTP',
statistic = ...., object of class numeric
estimate = ...., object of class numeric
sampsize = ...., object of class numeric
rawp = ...., object of class numeric
adjp = ...., object of class numeric
reject = ...., object of class matrix
rawdist = ...., object of class matrix
nulldist = ...., object of class matrix
nulldist.type = ...., object of class character
marg.null = ...., object of class character
marg.par = ...., object of class matrix
label = ...., object of class numeric
falsepos = ...., object of class matrix
truepos = ...., object of class matrix
errormat = ...., object of class matrix
EB.h0M = ...., object of class numeric
prior = ...., object of class numeric
prior.type= ...., object of class character
lqv = ...., object of class numeric
Hsets = ...., object of class matrix
index = ...., object of class matrix
call = ...., object of class call
seed = ...., object of class integer
)

Slots

statistic

Object of class numeric, observed test statistics for each hypothesis, specified by the values of the MTP arguments test, robust, standardize, and psi0.

estimate

For the test of single-parameter null hypotheses using t-statistics (i.e., not the F-tests), the numeric vector of estimated parameters corresponding to each hypothesis, e.g. means, differences in means, regression parameters.

sampsize

Object of class numeric, number of columns (i.e. observations) in the input data set.

rawp

Object of class numeric, unadjusted, marginal p-values for each hypothesis.

adjp

Object of class numeric, adjusted (for multiple testing) p-values for each hypothesis (computed only if the get.adjp argument is TRUE).

reject

Object of class 'matrix', rejection indicators (TRUE for a rejected null hypothesis), for each value of the nominal Type I error rate alpha.

rawdist

The numeric matrix for the estimated nonparametric non-null test statistics distribution (returned only if keep.rawdist=TRUE and if nulldist is one of 'boot.ctr', 'boot.cs', or 'boot.qt'). This slot must not be empty if one wishes to call update to change choice of bootstrap-based null distribution.

nulldist

The numeric matrix for the estimated test statistics null distribution (returned only if keep.nulldist=TRUE). By default (i.e., for nulldist='boot.cs'), the entries of nulldist are the null value shifted and scaled bootstrap test statistics, with one null test statistic value for each hypothesis (rows) and bootstrap iteration (columns).

nulldist.type

Character value describing which choice of null distribution was used to generate the MTP results. Takes on one of the values of the original nulldist argument in the call to MTP, i.e., 'boot.cs', 'boot.ctr', 'boot.qt', or 'ic'.

marg.null

If nulldist='boot.qt', a character value returning which choice of marginal null distribution was used by the MTP. Can be used to check default values or to ensure manual settings were correctly applied.

marg.par

If nulldist='boot.qt', a numeric matrix returning the parameters of the marginal null distribution(s) used by the MTP. Can be used to check default values or to ensure manual settings were correctly applied.

falsepos

A matrix with rows equal to the number of hypotheses and columns the number of samples of null test statistics (B) indicating the number of guessed false positives when using the corresponding value of the observed test statistic as a cut-off. Not returned unless keep.falsepos=TRUE.

truepos

A matrix with rows equal to the number of hypotheses and columns the number of samples of null test statistics (B) indicating the number of guessed true positives when using the corresponding value of the observed test statistic as a cut-off. Not returned unless keep.truepos=TRUE.

errormat

The matrix obtained after applying to type I error rate function closure to the matrices in falsepos, and, if applicable, truepos. Not returned unless keep.errormat=TRUE.

EB.h0M

The sum of the local q-values obtained after density estimation. This number serves as an estimate of the proportion of true null hypotheses. Values close to one indicate situations in which type I error control may not be guaranteed by the EBMTP. When prior='EBLQV', this value is used as the prior 'pi' during evaluation of the local q-value function.

prior

The numeric value of the prior 'pi' used when evaluating the local q-value function.

prior.type

Character string returning the value of prior in the original call to EBMTP. One of 'conservative', 'ABH', or 'EBLQV'.

lqv

A numeric vector of length the number of hypotheses with the estimated local q-values used for generating guessed sets of true null hypotheses.

Hsets

A numeric matrix with the same dimension as nulldist, containing the Bernoulli realizations of the estimated local q-values stored in lqv which were used to partition the hypotheses into guessed sets of true and false null hypotheses at each round of (re)sampling. Not returned unless keep.Hsets=TRUE.

label

If keep.label=TRUE, a vector storing the values used in the argument Y. Storing this object is particularly important when one wishes to update EBMTP objects with F-statistics using default marg.null and marg.par settings when nulldist='boot.qt'.

index

For tests of correlation parameters a matrix corresponding to t(combn(p,2)), where p is the number of variables in X. This matrix gives the indices of the variables considered in each pairwise correlation. For all other tests, this slot is empty, as the indices are in the same order as the rows of X.

call

Object of class call, the call to the MTP function.

seed

An integer or vector for specifying the state of the random number generator used to create the resampled datasets. The seed can be reused for reproducibility in a repeat call to MTP. This argument is currently used only for the bootstrap null distribution (i.e., for nulldist="boot.xx"). See ?set.seed for details.

Methods

signature(x = "EBMTP")

[

: Subsetting method for EBMTP class, which operates selectively on each slot of an EBMTP instance to retain only the data related to the specified hypotheses.

as.list

: Converts an object of class EBMTP to an object of class list, with an entry for each slot.

plot

: plot methods for EBMTP class, produces the following graphical summaries of the results of a EBMTP. The type of display may be specified via the which argument.

1. Scatterplot of number of rejected hypotheses vs. nominal Type I error rate.

2. Plot of ordered adjusted p-values; can be viewed as a plot of Type I error rate vs. number of rejected hypotheses.

3. Scatterplot of adjusted p-values vs. test statistics (also known as "volcano plot").

4. Plot of unordered adjusted p-values.

The plot method for objects of class EBMTP does not return the plots associated with which=5 (using confidence regions) or with which=6 (pertaining to cut-offs) as it does for objects of class MTP. This is because the function EBMTP currently only returns adjusted p-values. The argument logscale (by default equal to FALSE) allows one to use the negative decimal logarithms of the adjusted p-values in the second, third, and fourth graphical displays. The arguments caption and sub.caption allow one to change the titles and subtitles for each of the plots (default subtitle is the MTP function call). Note that some of these plots are implemented in the older function mt.plot.

print

: print method for EBMTP class, returns a description of an object of class EBMTP, including sample size, number of tested hypotheses, type of test performed (value of argument test), Type I error rate (value of argument typeone), nominal level of the test (value of argument alpha), name of the EBMTP (value of argument method), call to the function EBMTP.

In addition, this method produces a table with the class, mode, length, and dimension of each slot of the EBMTP instance.

summary

: summary method for EBMTP class, provides numerical summaries of the results of an EBMTP and returns a list with the following three components.

1. rejections: A data.frame with the number(s) of rejected hypotheses for the nominal Type I error rate(s) specified by the alpha argument of the function MTP.

2. index: A numeric vector of indices for ordering the hypotheses according to first adjp, then rawp, and finally the absolute value of statistic (not printed in the summary).

3. summaries: When applicable (i.e., when the corresponding quantities are returned by MTP), a table with six number summaries of the distributions of the adjusted p-values, unadjusted p-values, test statistics, and parameter estimates.

EBupdate

: update method for EBMTP class, provides a mechanism to re-run the MTP with different choices of the following arguments - nulldist, alternative, typeone, k, q, alpha, smooth.null, bw, kernel, prior, keep.nulldist, keep.rawdist, keep.falsepos, keep.truepos, keep.errormat, keep.margpar. When evaluate is 'TRUE', a new object of class EBMTP is returned. Else, the updated call is returned. The EBMTP object passed to the update method must have either a non-empty rawdist slot or a non-empty nulldist slot (i.e., must have been called with either 'keep.rawdist=TRUE' or 'keep.nulldist=TRUE').

Additionally, when calling EBupdate for any Type I error rate other than FWER, the typeone argument must be specified (even if the original object did not control FWER). For example, typeone="fdr", would always have to be specified, even if the original object also controlled the FDR. In other words, for all function arguments, it is safest to always assume that you are updating from the EBMTP default function settings, regardless of the original call to the EBMTP function. Currently, the main advantage of the EBupdate method is that it prevents the need for repeated estimation of the test statistics null distribution.

To save on memory, if one knows ahead of time that one will want to compare different choices of bootstrap-based null distribution, then it is both necessary and sufficient to specify 'keep.rawdist=TRUE', as there is no other means of moving between null distributions other than through the non-transformed non-parametric bootstrap distribution. In this case, 'keep.nulldist=FALSE' may be used. Specifically, if an object of class EBMTP contains a non-empty rawdist slot and an empty nulldist slot, then a new null distribution will be generated according to the values of the nulldist= argument in the original call to EBMTP or any additional specifications in the call to update. On the other hand, if one knows that one wishes to only update an EBMTP object in ways which do not involve choice of null distribution, then 'keep.nulldist=TRUE' will suffice and 'keep.rawdist' can be set to FALSE (default settings). The original null distribution object will then be used for all subsequent calls to update.

N.B.: Note that keep.rawdist=TRUE is only available for the bootstrap-based resampling methods. The non-null distribution does not exist for the permutation or influence curve multivariate normal null distributions.

ebmtp2mtp

: coersion method for converting objects of class EBMTP to objects of class MTP. Slots common to both objects are taken from the object of class EBMTP and used to create a new object of class MTP. Once an object of class MTP is created, one may use the method update to perform resampling-based multiple testing (as would have been done with calls to MTP) without the need for repeated resampling.

Author(s)

Houston N. Gilbert, based on the original MTP class and method definitions written by Katherine S. Pollard

References

H.N. Gilbert, K.S. Pollard, M.J. van der Laan, and S. Dudoit (2009). Resampling-based multiple hypothesis testing with applications to genomics: New developments in R/Bioconductor package multtest. Journal of Statistical Software (submitted). Temporary URL: http://www.stat.berkeley.edu/~houston/JSSNullDistEBMTP.pdf.

Y. Benjamini and Y. Hochberg (2000). On the adaptive control of the false discovery rate in multiple testing with independent statistics. J. Behav. Educ. Statist. Vol 25: 60-83.

Y. Benjamini, A. M. Krieger and D. Yekutieli (2006). Adaptive linear step-up procedures that control the false discovery rate. Biometrika. Vol. 93: 491-507.

M.J. van der Laan, M.D. Birkner, and A.E. Hubbard (2005). Empirical Bayes and Resampling Based Multiple Testing Procedure Controlling the Tail Probability of the Proportion of False Positives. Statistical Applications in Genetics and Molecular Biology, 4(1). http://www.bepress.com/sagmb/vol4/iss1/art29/

S. Dudoit and M.J. van der Laan. Multiple Testing Procedures and Applications to Genomics. Springer Series in Statistics. Springer, New York, 2008.

S. Dudoit, H. N. Gilbert, and M. J. van der Laan (2008). Resampling-based empirical Bayes multiple testing procedures for controlling generalized tail probability and expected value error rates: Focus on the false discovery rate and simulation study. Biometrical Journal, 50(5):716-44. http://www.stat.berkeley.edu/~houston/BJMCPSupp/BJMCPSupp.html.

H.N. Gilbert, M.J. van der Laan, and S. Dudoit. Joint multiple testing procedures for graphical model selection with applications to biological networks. Technical report, U.C. Berkeley Division of Biostatistics Working Paper Series, April 2009. URL http://www.bepress.com/ucbbiostat/paper245.

See Also

EBMTP, EBMTP-methods, MTP, MTP-methods, [-methods, as.list-methods, print-methods, plot-methods, summary-methods, mtp2ebmtp, ebmtp2mtp

Examples