fwer2gfwer {multtest} | R Documentation |
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.
fwer2gfwer(adjp, k = 0) fwer2tppfp(adjp, q = 0.05) fwer2fdr(adjp, method = "both", alpha = 0.05)
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). |
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 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.
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
.
Katherine S. Pollard, http://lowelab.ucsc.edu/katie/
with design contributions from Sandrine Dudoit and Mark J. van der Laan.
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). 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). 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). 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. http://www.bepress.com/ucbbiostat/paper121
MTP
, MTP-class
, MTP-methods
, mt.minP
, mt.maxT
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")