mt.maxT: Step-down maxT and minP multiple testing procedures
In multtest: Resampling-based multiple hypothesis testing

Description Usage Arguments Details Value Author(s) References See Also Examples

These functions compute permutation adjusted p-values for step-down multiple testing procedures described in Westfall & Young (1993).

1 2	mt.maxT(X,classlabel,test="t",side="abs",fixed.seed.sampling="y",B=10000,na=.mt.naNUM,nonpara="n") mt.minP(X,classlabel,test="t",side="abs",fixed.seed.sampling="y",B=10000,na=.mt.naNUM,nonpara="n")

`X`	A data frame or matrix, with m rows corresponding to variables (hypotheses) and n columns to observations. In the case of gene expression data, rows correspond to genes and columns to mRNA samples. The data can be read using `read.table`.
`classlabel`	A vector of integers corresponding to observation (column) class labels. For k classes, the labels must be integers between 0 and k-1. For the `blockf` test option, observations may be divided into n/k blocks of k observations each. The observations are ordered by block, and within each block, they are labeled using the integers 0 to k-1.
`test`	A character string specifying the statistic to be used to test the null hypothesis of no association between the variables and the class labels. If `test="t"`, the tests are based on two-sample Welch t-statistics (unequal variances). If `test="t.equalvar"`, the tests are based on two-sample t-statistics with equal variance for the two samples. The square of the t-statistic is equal to an F-statistic for k=2. If `test="wilcoxon"`, the tests are based on standardized rank sum Wilcoxon statistics. If `test="f"`, the tests are based on F-statistics. If `test="pairt"`, the tests are based on paired t-statistics. The square of the paired t-statistic is equal to a block F-statistic for k=2. If `test="blockf"`, the tests are based on F-statistics which adjust for block differences (cf. two-way analysis of variance).
`side`	A character string specifying the type of rejection region. If `side="abs"`, two-tailed tests, the null hypothesis is rejected for large absolute values of the test statistic. If `side="upper"`, one-tailed tests, the null hypothesis is rejected for large values of the test statistic. If `side="lower"`, one-tailed tests, the null hypothesis is rejected for small values of the test statistic.
`fixed.seed.sampling`	If `fixed.seed.sampling="y"`, a fixed seed sampling procedure is used, which may double the computing time, but will not use extra memory to store the permutations. If `fixed.seed.sampling="n"`, permutations will be stored in memory. For the `blockf` test, the option `n` was not implemented as it requires too much memory.
`B`	The number of permutations. For a complete enumeration, `B` should be 0 (zero) or any number not less than the total number of permutations.
`na`	Code for missing values (the default is `.mt.naNUM=--93074815.62`). Entries with missing values will be ignored in the computation, i.e., test statistics will be based on a smaller sample size. This feature has not yet fully implemented.
`nonpara`	If `nonpara`="y", nonparametric test statistics are computed based on ranked data. If `nonpara`="n", the original data are used.

These functions compute permutation adjusted p-values for the step-down maxT and minP multiple testing procedures, which provide strong control of the family-wise Type I error rate (FWER). The adjusted p-values for the minP procedure are defined in equation (2.10) p. 66 of Westfall & Young (1993), and the maxT procedure is discussed p. 50 and 114. The permutation algorithms for estimating the adjusted p-values are given in Ge et al. (In preparation). The procedures are for the simultaneous test of m null hypotheses, namely, the null hypotheses of no association between the m variables corresponding to the rows of the data frame X and the class labels classlabel. For gene expression data, the null hypotheses correspond to no differential gene expression across mRNA samples.

A data frame with components

`index`	Vector of row indices, between 1 and `nrow(X)`, where rows are sorted first according to their adjusted p-values, next their unadjusted p-values, and finally their test statistics.
`teststat`	Vector of test statistics, ordered according to `index`. To get the test statistics in the original data order, use `teststat[order(index)]`.
`rawp`	Vector of raw (unadjusted) p-values, ordered according to `index`.
`adjp`	Vector of adjusted p-values, ordered according to `index`.
`plower`	For `mt.minP` function only, vector of "adjusted p-values", where ties in the permutation distribution of the successive minima of raw p-values with the observed p-values are counted only once. Note that procedures based on `plower` do not control the FWER. Comparison of `plower` and `adjp` gives an idea of the discreteness of the permutation distribution. Values in `plower` are ordered according to `index`.

Yongchao Ge, yongchao.ge@mssm.edu,
Sandrine Dudoit, http://www.stat.berkeley.edu/~sandrine.

S. Dudoit, J. P. Shaffer, and J. C. Boldrick (Submitted). Multiple hypothesis testing in microarray experiments.

Y. Ge, S. Dudoit, and T. P. Speed. Resampling-based multiple testing for microarray data hypothesis, Technical Report \#633 of UCB Stat. http://www.stat.berkeley.edu/~gyc

P. H. Westfall and S. S. Young (1993). Resampling-based multiple testing: Examples and methods for p-value adjustment. John Wiley \& Sons.

mt.plot, mt.rawp2adjp, mt.reject, mt.sample.teststat, mt.teststat, golub.

# Gene expression data from Golub et al. (1999)
# To reduce computation time and for illustrative purposes, we condider only
# the first 100 genes and use the default of B=10,000 permutations.
# In general, one would need a much larger number of permutations
# for microarray data.

data(golub)
smallgd<-golub[1:100,] 
classlabel<-golub.cl

# Permutation unadjusted p-values and adjusted p-values 
# for maxT and minP procedures with Welch t-statistics
resT<-mt.maxT(smallgd,classlabel)
resP<-mt.minP(smallgd,classlabel)
rawp<-resT$rawp[order(resT$index)]
teststat<-resT$teststat[order(resT$index)]

# Plot results and compare to Bonferroni procedure
bonf<-mt.rawp2adjp(rawp, proc=c("Bonferroni"))
allp<-cbind(rawp, bonf$adjp[order(bonf$index),2], resT$adjp[order(resT$index)],resP$adjp[order(resP$index)])

mt.plot(allp, teststat, plottype="rvsa", proc=c("rawp","Bonferroni","maxT","minP"),leg=c(0.7,50),lty=1,col=1:4,lwd=2)
mt.plot(allp, teststat, plottype="pvsr", proc=c("rawp","Bonferroni","maxT","minP"),leg=c(60,0.2),lty=1,col=1:4,lwd=2)
mt.plot(allp, teststat, plottype="pvst", proc=c("rawp","Bonferroni","maxT","minP"),leg=c(-6,0.6),pch=16,col=1:4)

# Permutation adjusted p-values for minP procedure with F-statistics (like equal variance t-statistics)
mt.minP(smallgd,classlabel,test="f",fixed.seed.sampling="n")

# Note that the test statistics used in the examples below are not appropriate 
# for the Golub et al. data. The sole purpose of these examples is to 
# demonstrate the use of the mt.maxT and mt.minP functions.

# Permutation adjusted p-values for maxT procedure with paired t-statistics
classlabel<-rep(c(0,1),19)
mt.maxT(smallgd,classlabel,test="pairt")

# Permutation adjusted p-values for maxT procedure with block F-statistics
classlabel<-rep(0:18,2)
mt.maxT(smallgd,classlabel,test="blockf",side="upper")