fwer2gfwer             package:multtest             R Documentation

_F_u_n_c_t_i_o_n _t_o _c_o_m_p_u_t_e _a_u_g_m_e_n_t_a_t_i_o_n _M_T_P _a_d_j_u_s_t_e_d _p-_v_a_l_u_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     Augmentation multiple testing procedures (AMTPs) to control the
     generalized family-wise error rate (gFWER), the tail probability
     of the proportion of false positives (TPPFP), and false discovery
     rate (FDR) based on any initial procudeure controlling the
     family-wise error rate (FWER). AMTPs are obtained by adding
     suitably chosen null hypotheses to the set of null hypotheses
     already rejected by an initial FWER-controlling MTP. A function
     for control of FDR given any TPPFP controlling procedure is also
     provided.

_U_s_a_g_e:

     fwer2gfwer(adjp, k = 0)

     fwer2tppfp(adjp, q = 0.05)

     fwer2fdr(adjp, method = "both", alpha = 0.05)

_A_r_g_u_m_e_n_t_s:

    adjp: Numeric vector of adjusted p-values from any FWER-controlling
          procedure.

       k: Maximum number of false positives.

       q: Maximum proportion of false positives.

  method: Character string indicating which FDR controlling method
          should be used. The options are "conservative" for a
          conservative, general method, "restricted" for a less
          conservative, but restricted method, or "both" (default) for
          both.

   alpha: Nominal level for an FDR controlling procedure (can be a
          vector of levels).

_D_e_t_a_i_l_s:

     The gFWER and TPPFP functions control Type I error rates defined
     as tail probabilities for functions g(Vn,Rn) of the numbers of
     Type I errors (Vn) and rejected hypotheses (Rn). The gFWER and
     TPPFP correspond to the special cases g(Vn,Rn)=Vn (number of false
     positives) and g(Vn,Rn)=Vn/Rn (proportion of false positives among
     the rejected hypotheses), respectively. 

     Adjusted p-values for an AMTP are simply shifted versions of the
     adjusted p-values of the original FWER-controlling MTP. For
     control of gFWER (Pr(Vn>k)), for example, the first 'k' adjusted
     p-values are set to zero and the remaining p-values are the
     adjusted p-values of the FWER-controlling MTP shifted by k. One
     can therefore build on the large pool of available
     FWER-controlling procedures, such as the single-step and step-down
     maxT and minP procedures.

     Given a FWER-controlling MTP, the FDR can be conservatively
     controlled at level 'alpha' by considering the corresponding TPPFP
     AMTP with 'q=alpha/2' at level 'alpha/2', so that
     Pr(Vn/Rn>alpha/2)<=alpha/2. A less conservative procedure
     ('general=FALSE') is obtained by using an AMTP controlling the
     TPPFP with 'q=1-sqrt(1-alpha)' at level '1-sqrt(1-alpha)', so that
     Pr(Vn/Rn>1-sqrt(1-alpha))<=1-sqrt(1-alpha). The first, more
     general method can be used with any procedure that asymptotically
     controls FWER. The second, less conservative method requires the
     following additional assumptions: (i) the true alternatives are
     asymptotically always rejected by the FWER-controlling procedure,
     (ii) the limit of the FWER exists, and (iii) the FWER-controlling
     procedure provides exact asymptotic control. See <URL:
     http://www.bepress.com/sagmb/vol3/iss1/art15/> for more details.
     The method implemented in 'fwer2fdr' for computing rejections
     simply uses the TPPFP AMTP 'fwer2tppfp' with 'q=alpha/2' (or
     1-sqrt(1-alpha)) and rejects each hypothesis for which the TPPFP
     adjusted p-value is less than or equal to alpha/2 (or
     1-sqrt(1-alpha)). The adjusted p-values are based directly on the
     FWER adjusted p-values, so that very occasionally a hypothesis
     will have the indicator that it is rejected in the matrix of
     rejections, but the adjusted p-value will be slightly greater than
     the nominal level. The opposite might also occur occasionally.

_V_a_l_u_e:

     For 'fwer2gfwer' and 'fwer2tppfp', a numeric vector of AMTP
     adjusted p-values. For 'fwer2fdr', a list with two components: (i)
     a numeric vector (or a 'length(adjp)' by 2 matrix if
     'method="both"') of adjusted p-values for each hypothesis, (ii) a
     'length(adjp)' by 'length(alpha)' matrix (or 'length(adjp)' by
     'length(alpha)' by 2 array if 'method="both"') of indicators of
     whether each hypothesis is rejected at each value of the argument
     'alpha'.

_A_u_t_h_o_r(_s):

     Katherine S. Pollard with design contributions from Sandrine
     Dudoit and Mark J. van der Laan.

_R_e_f_e_r_e_n_c_e_s:

     M.J. van der Laan, S. Dudoit, K.S. Pollard (2004), Augmentation
     Procedures for Control of the Generalized Family-Wise Error Rate
     and Tail Probabilities for the Proportion of False Positives,
     Statistical Applications in Genetics and Molecular Biology, 3(1). 
     <URL: http://www.bepress.com/sagmb/vol3/iss1/art15/>

     M.J. van der Laan, S. Dudoit, K.S. Pollard (2004), Multiple
     Testing. Part II. Step-Down Procedures for Control of the
     Family-Wise Error Rate, Statistical Applications in Genetics and
     Molecular Biology, 3(1). <URL:
     http://www.bepress.com/sagmb/vol3/iss1/art14/>

     S. Dudoit, M.J. van der Laan, K.S. Pollard (2004), Multiple
     Testing. Part I. Single-Step Procedures for Control of General
     Type I Error Rates, Statistical Applications in Genetics and
     Molecular Biology, 3(1). <URL:
     http://www.bepress.com/sagmb/vol3/iss1/art13/>

     Katherine S. Pollard and Mark J. van der Laan, "Resampling-based
     Multiple Testing: Asymptotic Control of Type I Error and
     Applications to Gene Expression Data" (June 24, 2003). U.C.
     Berkeley Division of Biostatistics Working Paper Series. Working
     Paper 121. <URL: http://www.bepress.com/ucbbiostat/paper121>

_S_e_e _A_l_s_o:

     'MTP', 'MTP-class', 'MTP-methods', 'mt.minP', 'mt.maxT'

_E_x_a_m_p_l_e_s:

     data<-matrix(rnorm(200),nr=20)
     group<-c(rep(0,5),rep(1,5))
     fwer.mtp<-MTP(X=data,Y=group)
     fwer.adjp<-fwer.mtp@adjp
     gfwer.adjp<-fwer2gfwer(adjp=fwer.adjp,k=c(1,5,10))
     compare.gfwer<-cbind(fwer.adjp,gfwer.adjp)
     mt.plot(adjp=compare.gfwer,teststat=fwer.mtp@statistic,proc=c("gFWER(0)","gFWER(1)","gFWER(5)","gFWER(10)"),col=1:4,lty=1:4)
     title("Comparison of Single-step MaxT gFWER Controlling Methods")

