mt.rawp2adjp            package:multtest            R Documentation

_A_d_j_u_s_t_e_d _p-_v_a_l_u_e_s _f_o_r _s_i_m_p_l_e _m_u_l_t_i_p_l_e _t_e_s_t_i_n_g _p_r_o_c_e_d_u_r_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

    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:


          _B_o_n_f_e_r_r_o_n_i Bonferroni single-step adjusted p-values for
               strong control of the FWER. 

          _H_o_l_m Holm (1979) step-down adjusted p-values for strong
               control of the FWER.

          _H_o_c_h_b_e_r_g Hochberg (1988) step-up adjusted p-values for 
               strong control of the FWER (for raw (unadjusted)
               p-values satisfying the Simes inequality). 

          _S_i_d_a_k_S_S Sidak single-step adjusted p-values for strong
               control of the FWER (for positive orthant dependent test
               statistics). 

          _S_i_d_a_k_S_D Sidak step-down adjusted p-values for strong control
               of the FWER (for positive orthant dependent test
               statistics). 

          _B_H Adjusted p-values for the Benjamini & Hochberg (1995)
               step-up FDR-controlling procedure (independent and
               positive regression dependent test statistics).

          _B_Y Adjusted p-values for the Benjamini & Yekutieli (2001)
               step-up FDR-controlling procedure (general dependency
               structures).

          _A_B_H 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.

          _T_S_B_H 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.

_V_a_l_u_e:

     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).

_A_u_t_h_o_r(_s):

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

_R_e_f_e_r_e_n_c_e_s:

     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. <URL:
     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.

_S_e_e _A_l_s_o:

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

_E_x_a_m_p_l_e_s:

     # 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)

