flip.adjust {flip}

Functions for multiplicity corrections

Description

npc provides overall tests (i.e. weak FWER control), while flip.adjust provides adjusted p-values (i.e. strong FWER control).

Usage

flip.adjust(permTP, method = flip.npc.methods, maxalpha = 1,
  weights = NULL, stdSpace = FALSE, ...)

npc(permTP, comb.funct = c(flip.npc.methods, p.adjust.methods),
  subsets = NULL, weights = NULL, stdSpace = FALSE, ...)

Arguments

permTP

A permutation space (B times m matrix) or an flip.object as produced by flip. Alternatively it can be a flip.object-class resulting, for example from a call of function flip.

method

A method among flip.npc.methods or p.adjust.methods. By default "maxT" is used. See also the section Details.

maxalpha

Adjusted p-values greater than maxalpha are forced to 1. It saves computational time when there are many hypotheses under test.

weights

Optional argument that can be used to give certain variables greater weight in the combined test. Can be a vector or a list of vectors. In the latter case, a separate test will be performed for each weight vector. If both subsets and weights are specified as a list, they must have the same length. In that case, weights vectors may have either the same length as the number of covariates in alternative, or the same length as the corresponding subset vector. Weights can be negative; the sign has no effect unless directional is TRUE. It works for npc and flip.adjust with method= "maxT", "maxTstd" or "minP"

stdSpace

Ask if the permutation distribution of the test statistic should be standardized or not. The default is FALSE. The option is applied only if comb.funct or method is equal to "maxT" or "sumT", it becomes useful when test statistics are of different nature (e.g. chisquare and t-test).

...

further arguments. Among them, tail can be used to set the tail of the alternative for the permTP (see also flip). The arguments statTest, fastSumCombination and linComb are used in objects flipMix and comb.funct= "data.sum","data.linComb","data.pc" or "data.trace".

comb.funct

A combining function flip.npc.methods (all but "kfwer"): "Fisher", "Liptak", "MahalanobisT" , "MahalanobisP" (i.e. related to Hotelling T2), "minP" (i.e. Tippet), "maxT", "sumT" (i.e. direct) , "sumT2" (sum of T^2). "Fisher" combining function is the default. See also the section Details.

subsets

Optional argument that can be used to test one or more subsets of variables. Can be a vector of column names or indices of a flip.object-class (names(flipObject)), or a list of such vectors. In the latter case, a separate test will be performed for each subset. Only for comb.funct %in% c("data.sum","data.linComb","data.pc","data.trace") the names refers to the columns of Y data colnames(flipObject@data$Y) .

Details

npc combines the p-values using the combining functions (and the method) described in Pesarin (2001). It makes use of the join space of the permutations. This is usually derived from a call of flip function or flipMixWithin.

Very shortly: "Fisher" =-sum log(p-values) "Liptak" =sum qnorm(p-values) "MahalanobisT" = Mahalanobis distance of centered matrix permTP (or permTP@permT ) "MahalanobisP" = same as above, but using scores defined by qnorm(p-values) (tails are forced to be one-sided) "minP" = "Tippett" = min(p-values) \ "maxT" = max(test statistics) "maxTstd" = max(standardized test statistics) "sumT" = sum (test statistics) "sumTstd" = sum (standardized test statistics) "sumT2" = sum (test statistics)^2. The followings have to be used carefully and only with objects from function flipMix: "data.sum" = sum of all columns of Y, "data.linComb" = sum of all columns of Y (includes a vector or matrix linComb among the arguments), "data.pc" = extracts the first Principal component from the covariance matrix (you may also include a vector whichPCs indicating which PCs you want to consider)\ "data.trace" = Extends the Pillai Trace, use parametric bootstrap to asses the significance."kfwer" = can be only used with flip.adjust (not in npc). It requires an extra parameter k (k=11 by default).

flip.adjust adjusts the p-value for multiplicity (FamilyWise Error Rate -FWER- and kFWER). When method is equal to "maxT", "maxTstd" (i.e. max T on scale(permTP)) or "minP" (i.e. Tippett) it performs the step-down method of Westfall and Young (1993). For any other element of flip.npc.methods (i.e. "Fisher", "Liptak", "sumT" (i.e. direct) or "sumT2" (sum of T^2)) a call to npc together with a closed testing procedure is used (it make use of cherry:closed). When method is any among p.adjust.methods the function stats:p.adjust or -if weights are provided- someMTP:p.adjust.w is used. To perform control of the kFWER use flip.adjust with method="kfwer" and extra parameter k.

Value

The function returns an object of class flip.object-class (and the use of getFlip(obj,"Adjust").

Author(s)

livio finos, Florian Klinglmueller and Aldo Solari.

References

Pesarin (2001) Multivariate Permutation Tests with Applications in Biostatistics. Wiley, New York.

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

Examples

Y=data.frame(matrix(rnorm(50),10,5))
names(Y)=LETTERS[1:5]
Y[,1:2]=Y[,1:2]+1.5
res = flip(Y,perms=10000)

########npc
p2=npc(res) # same as p2=npc(res,"Fisher")
summary(p2)
p2=npc(res,"minP")
summary(p2)
p2=npc(res,"Fisher",subsets=list(c1=c("A","B"),c2=names(Y)))
summary(p2)
p2=npc(res,"Fisher",subsets=list(c1=c("A","B"),c2=names(Y)),weights=1:5)
summary(p2)


res=flip.adjust(res, method="maxT")

#res=flip.adjust(res,"BH")
##same as
#p.adjust(res,"BH")

## now try
getFlip(res,"Adjust")