mt.rawp2adjp {multtest} | R Documentation

## Adjusted p-values for simple multiple testing procedures

### Description

This function computes adjusted p-values for simple multiple testing procedures from a vector of raw (unadjusted) p-values. The procedures include the Bonferroni, Holm (1979), Hochberg (1988), and Sidak procedures for strong control of the family-wise Type I error rate (FWER), and the Benjamini & Hochberg (1995) and Benjamini & Yekutieli (2001) procedures for (strong) control of the false discovery rate (FDR). The less conservative adaptive Benjamini & Hochberg (2000) and two-stage Benjamini & Hochberg (2006) FDR-controlling procedures are also included.

### Usage

    mt.rawp2adjp(rawp, proc=c("Bonferroni", "Holm", "Hochberg", "SidakSS", "SidakSD",
    "BH", "BY","ABH","TSBH"), alpha = 0.05)

### Arguments

`rawp` | A vector of raw (unadjusted) p-values for each hypothesis under consideration. These could be nominal p-values, for example, from t-tables, or permutation p-values as given in `mt.maxT` and `mt.minP`. If the `mt.maxT` or `mt.minP` functions are used, raw p-values should be given in the original data order, `rawp[order(index)]`.

`proc`

A vector of character strings containing the names of the multiple testing procedures for which adjusted p-values are to be computed. This vector should include any of the following: `"Bonferroni"`, `"Holm"`, `"Hochberg"`, `"SidakSS"`, `"SidakSD"`, `"BH"`, `"BY"`, `"ABH"`, `"TSBH"`.
Adjusted p-values are computed for simple FWER- and FDR- controlling procedures based on a vector of raw (unadjusted) p-values by one or more of the following methods:

Bonferroni
  Bonferroni single-step adjusted p-values for strong control of the FWER.
Holm
  Holm (1979) step-down adjusted p-values for strong control of the FWER.
Hochberg
  Hochberg (1988) step-up adjusted p-values for strong control of the FWER (for raw (unadjusted) p-values satisfying the Simes inequality).
SidakSS
  Sidak single-step adjusted p-values for strong control of the FWER (for positive orthant dependent test statistics).
SidakSD
  Sidak step-down adjusted p-values for strong control of the FWER (for positive orthant dependent test statistics).
BH
  Adjusted p-values for the Benjamini & Hochberg (1995) step-up FDR-controlling procedure (independent and positive regression dependent test statistics).
BY
  Adjusted p-values for the Benjamini & Yekutieli (2001) step-up FDR-controlling procedure (general dependency structures).
ABH
  Adjusted p-values for the adaptive Benjamini & Hochberg (2000) step-up FDR-controlling procedure. This method ammends the original step-up procedure using an estimate of the number of true null hypotheses obtained from p-values.
TSBH
  Adjusted p-values for the two-stage Benjamini & Hochberg (2006) step-up FDR-controlling procedure. This method ammends the original step-up procedure using an estimate of the number of true null hypotheses obtained from a first-pass application of `"BH"`. The adjusted p-values are a-dependent, therefore `alpha` must be set in the function arguments when using this procedure.

`alpha` | A nominal type I error rate, or a vector of error rates, used for estimating the number of true null hypotheses in the two-stage Benjamini & Hochberg procedure (`"TSBH"`). Default is 0.05.

### Value

A list with components:

`adjp` | A matrix of adjusted p-values, with rows corresponding to hypotheses and columns to multiple testing procedures. Hypotheses are sorted in increasing order of their raw (unadjusted) p-values.
`index` | A vector of row indices, between 1 and `length(rawp)`, where rows are sorted according to their raw (unadjusted) p-values. To obtain the adjusted p-values in the original data order, use `adjp[order(index),]`.
`h0.ABH` | The estimate of the number of true null hypotheses as proposed by Benjamini & Hochberg (2000) used when computing adjusted p-values for the `"ABH"` procedure (see Dudoit et al., 2007).
`h0.TSBH` | The estimate (or vector of estimates) of the number of true null hypotheses as proposed by Benjamini et al. (2006) when computing adjusted p-values for the `"TSBH"` procedure. (see Dudoit et al., 2007).

### Author(s)

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

### References

Y. Benjamini and Y. Hochberg (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Statist. Soc. B. Vol. 57: 289-300.

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 and D. Yekutieli (2001). The control of the false discovery rate in multiple hypothesis testing under dependency. Annals of Statistics. Vol. 29: 1165-88.

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.

S. Dudoit, J. P. Shaffer, and J. C. Boldrick (2003). Multiple hypothesis testing in microarray experiments. Statistical Science. Vol. 18: 71-103.

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.

Y. Ge, S. Dudoit, and T. P. Speed (2003). Resampling-based multiple testing for microarray data analysis. TEST. Vol. 12: 1-44 (plus discussion p. 44-77).

Y. Hochberg (1988). A sharper Bonferroni procedure for multiple tests of significance, Biometrika. Vol. 75: 800-802.

S. Holm (1979). A simple sequentially rejective multiple test procedure. Scand. J. Statist.. Vol. 6: 65-70.

### See Also

`mt.maxT`, `mt.minP`, `mt.plot`, `mt.reject`, `golub`.

### Examples

    # 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 procedure
    res1<-mt.maxT(smallgd,classlabel)
    rawp<-res1$rawp[order(res1$index)]

    # Permutation adjusted p-values for simple multiple testing procedures
    procs<-c("Bonferroni","Holm","Hochberg","SidakSS","SidakSD","BH","BY","ABH","TSBH")
    res2<-mt.rawp2adjp(rawp,procs)

[Package multtest version 2.0.0 Index]