The permax Package. May 26, 2004

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1 The permax Package May 26, 2004 Version Author Robert J. Gray Maintainer Robert Gentleman The permax library consists of 7 functions, intended to facilitate certain basic analyses of DNA array data, especially with regard to comparing expression levels between two types of tissue. Title permax Depends R (>= 1.2) License GPL 2 R topics documented: permax permcor permsep plot.expr plot.permax rowperm summary.permax Index 11 permax 2-sample permutation t-tests for high dimensional data For high dimensional vectors of observations, computes t statistics for each attribute, and assesses significance using the permutation distribution of the maximum and minimum over all attributes. permax(data, ig1, nperm=0, logs=true, ranks=false, min.np=1, ig2, WHseed=NULL) 1

2 2 permax data Data matrix or data frame. Each case is a column, and each row is an attribute (the opposite of the standard configuration). ig1 The columns of data corresponding to group 1 nperm logs ranks min.np ig2 WHseed Value The number of random permutations to use in computing the p-values. The default is to use the entire permutation distribution, which is only feasible if the sample sizes are fairly small If logs=true (the default), then logs of the values in data are used in the statistics. If ranks=t, then within row ranks are used in place of the values in data in the t statistics. This is equivalent to using the Wilcoxon statistic. Default is ranks=f data will be subset to only rows with at least min.np values larger than min(data) in the columns in ig1 and ig2 The columns of data corresponding to group 2. The default is to include all columns not in ig1 in group 2. When both ig1 and ig2 are given, columns not in either are excluded from the tests. Initial random number seed (a vector of 3 integers). If missing, an initial seed is generated from the runif() function. Not needed if all permutations are calculated. For DNA array data, this function is designed to identify the genes which best discriminate between two tissue types. 2-sample t statistics are computed for each gene using logs (default), raw values, or ranks. Upper and lower p-values (p.upper, p.lower) are computed by comparing each statistic to the permutation distribution of the maximum and minimum (largest negative) statistic over all genes. The pind component of the output gives the p-value for the permutation distribution of each individual gene. It is strongly recommended that different seeds be used for different runs, and ideally the final seed from one run, attr(output, seed.end ), would be used as the initial seed in the next run. Output is a data.frame of class permax, with columns stat: the standardized test statistics for each row pind: individual permutation p-values (2-sided) p2: 2-sided p-value using the distribution of the max overall rows p.lower: 1-sided p-value for lower levels in group 1 p.upper: 1-sided p-value for higher levels in group 1 nml: # permutations where this row was the most significant for p.lower nmr: # permutations where this row was the most sig for p.upper m1, m2: means of groups 1 and 2 (means of logs if logs=t) s1, s2: std deviations of groups 1 and 2 (of logs if logs=t) np1,np2: # values > min(data) in groups 1 and 2 mdiff: difference of means (if logs=t the difference of geometric means) mrat: ratio of means (if logs=t ratio of geometric means) Also, if nperm>0, then output includes attributes seed.start giving the initial random number seed, and seed.end giving the value of the seed at the end. These can be accessed with the attributes() and attr() functions. summary.permax, plot.permax, permcor, permsep.

3 permcor 3 #generate make believe data set.seed(1292) ngenes < m1 <- rnorm(ngenes,4,1) m2 <- rnorm(ngenes,4,1) exp1 <- cbind(matrix(exp(rnorm(ngenes*5,m1,1)),nrow=ngenes), matrix(exp(rnorm(ngenes*10,m2,1)),nrow=ngenes)) exp1[exp1<20] <- 20 sub <- exp1>20 & exp1<150 exp1[sub] <- ifelse(runif(length(sub[sub]))<.5,20,exp1[sub]) dimnames(exp1) <- list(paste('x',format(1:ngenes,justify='l'),sep=''), paste('sample',format(1:ncol(exp1),justify='l'),sep='')) dimnames(exp1) <- list(paste('x',1:ngenes,sep=''), paste('sample',1:ncol(exp1),sep='')) exp1 <- round(exp1) uu <- permax(exp1,1:5) summary(uu,nl=5,nr=5) # 5 most extreme in each direction permcor permutation tests for correlations in high dimensional data For high dimensional vectors of observations, computes the correlation coefficient for each attribute with a specified vector of values, and assesses significance using the permutation distribution of the maximum and minimum over all attributes. permcor(data, phen, nperm=1000, logs=true, ranks=false, min.np=1, WHseed=NULL) data phen nperm logs ranks min.np WHseed Data matrix or data frame. Each case is a column, and each row is an attribute (the opposite of the standard configuration). A vector of values (the ideal phenotype pattern). The correlations of each row of data with phen will be computed. The number of random permutations to use in computing the p-values. The default is If nperm is < 0, the entire permutation distribution will be used, which is only feasible if the sample size is fairly small If logs=true (the default), then logs of the values in data are used in computing correlations (the actual values of phen are used, though). If ranks=t, then within row ranks are used in place of the values in data in the correlations. The actual values of phen are still used. Default is ranks=false. data will be subset to only rows with at least min.np values larger than min(data). Initial random number seed (a vector of 3 integers). If missing, an initial seed is generated from the runif() function. Not needed if all permutations are calculated.

4 4 permcor Value For DNA array data, this function is designed to identify the genes with the largest positive and negative correlations with the phenotype in phen. Upper and lower p-values (p.upper, p.lower) are computed by comparing each correlation to the permutation distribution of the maximum and minimum (largest negative) correlations over all genes. The pind component of the output gives the p-value for the permutation distribution of each individual gene. If phen is a vector of 1 s for the columns in group 1 and 0 s for the other columns, then the p-values from permcor() should be the same as from permax() (to within simulation precision if random permutations are used). permax() is substantially more efficient in this setting. The functions summary.permax() and plot.permax() can be used with the output of permcor(). It is strongly recommended that different seeds be used for different runs, and ideally the final seed from one run, attr(output, seed.end ), would be used as the initial seed in the next run. Output is a data.frame of class c( permcor, permax ), with columns stat: the Pearson correlation coeffcients for each row of data pind: individual permutation p-values (2-sided) p2: 2-sided p-value using the distribution of the max overall rows p.lower: 1-sided p-value for lower levels in group 1 p.upper: 1-sided p-value for higher levels in group 1 nml: # permutations where this row was the most significant for p.lower nmr: # permutations where this row was the most sig for p.upper np: # values > min(data) in each row Also, if nperm>0, then output includes attributes seed.start giving the initial random number seed, and seed.end giving the value of the seed at the end. These can be accessed with the attributes() and attr() functions. permax, summary.permax, plot.permax. set.seed(1292) ngenes < m1 <- rnorm(ngenes,4,1) m2 <- rnorm(ngenes,4,1) exp1 <- cbind(matrix(exp(rnorm(ngenes*5,m1,1)),nrow=ngenes), matrix(exp(rnorm(ngenes*10,m2,1)),nrow=ngenes)) exp1[exp1<20] <- 20 sub <- exp1>20 & exp1<150 exp1[sub] <- ifelse(runif(length(sub[sub]))<.5,20,exp1[sub]) dimnames(exp1) <- list(paste('x',format(1:ngenes,justify='l'),sep=''), paste('sample',format(1:ncol(exp1),justify='l'),sep='')) dimnames(exp1) <- list(paste('x',1:ngenes,sep=''), paste('sample',1:ncol(exp1),sep='')) exp1 <- round(exp1) #see the permax help file for the definition of exp1 u8 <- permcor(exp1,1:15) summary(u8,nr=4,nl=4) u10 <- permcor(exp1[,c(1:3,5:8)],c(1,1,1,0,0,0,0),nperm=0)

5 permsep 5 summary(u10,nl=4,nr=4) permsep Permutation analysis for complete separation Given two groups of samples of high dimensional attribute vectors (eg DNA array expression levels), determines the number of attributes which completely separate the two groups (all values in one group strictly larger than in the other), and a permutation p-value for this quantity. permsep(data, ig1, nperm=0, ig2, WHseed=NULL) data Data matrix or data frame. Each case is a column, and each row is an attribute (the opposite of the standard configuration). ig1 The columns of data corresponding to group 1 nperm ig2 WHseed The number of random permutations to use in computing the p-values. The default is to use the entire permutation distribution, which is only feasible if the sample sizes are fairly small The columns of data corresponding to group 2. The default is to include all columns not in ig1 in group 2. When both ig1 and ig2 are given, columns not in either are excluded. Initial random number seed (a vector of 3 integers). If missing, an initial seed is generated from the runif() function. Not needed if all permutations are calculated. Prints a vector giving the # genes with complete separation (all in one group larger than all in the other, the proportion of permutations with this many or more genes with complete separation (p-value) ( permutation actually means a distinct rearrangement of columns into 2 groups), the average number of genes per permutation with complete separation, and the proportion of permutations with any genes with complete separation. The value returned is a list with components ics = a vector indicating (with 1) which rows of data have complete separation, and dtcs = a vector containing the printed output. Also, if nperm>0, then the output includes attributes seed.start giving the initial random number seed, and seed.end giving the value of the seed at the end. These can be accessed with the attributes and attr functions.

6 6 plot.expr For each gene there will be 0, 1 or 2 rearrangements with complete separation, depending on the number of unique values and the sizes of the two groups. Adding these numbers over genes and dividing by the number of rearrangements gives the average number per permutation. The value returned averages only over the rearrangements actually used, though. It is strongly recommended that different seeds be used for different runs, and ideally the final seed from one run, attr(output, seed.end ), would be used as the initial seed in the next run. permax ngenes < m1 <- rnorm(ngenes,4,1) m2 <- rnorm(ngenes,4,1) exp1 <- cbind(matrix(exp(rnorm(ngenes*5,m1,1)),nrow=ngenes), matrix(exp(rnorm(ngenes*10,m2,1)),nrow=ngenes)) exp1[exp1<20] <- 20 sub <- exp1>20 & exp1<150 exp1[sub] <- ifelse(runif(length(sub[sub]))<.5,20,exp1[sub]) dimnames(exp1) <- list(paste('x',format(1:ngenes,justify='l'),sep=''), paste('sample',format(1:ncol(exp1),justify='l'),sep='')) dimnames(exp1) <- list(paste('x',1:ngenes,sep=''), paste('sample',1:ncol(exp1),sep='')) exp1 <- round(exp1) uuu <- permsep(exp1,1:5) plot.expr Color image plot of gene expression levels Represents values in the rows of a matrix as colored rectangles in an image plot plot.expr(x, logs=true, ig1=null, ig2=null, clmn.lab=dimnames(x)[[2]], row.lab=dimnames(x)[[1]], clmn.off=null, row.off=null,...) x logs ig1 matrix or data.frame containing the values to be plotted. If logs=true, then log values are used. The columns of x for cases in group 1 (see ) ig2 The columns in group 2. By default, all the columns not in group 1.

7 plot.expr 7 clmn.lab Labels for the columns in the array. row.lab Labels for the rows in the array. clmn.off Offset for printing the column labels (<0 to put labels outside the plot). row.off Offset for printing the row labels (<0 to put labels outside the plot).... Additional arguments to image and text (see par) none Values within a row are centered and normalized to have variance 1. If ig1 is not given, then the values are centered to have mean 0. If ig1 is given, the values are centered so the means of the columns in ig1 and ig2 are equal in magnitude and opposite in direction. The plot is thus useful for comparing within rows, but differences in colors between rows have no meaning. A graphics device supporting image plots must be initialized prior to calling this function. Under Splus 3.4 for unix, the following command (without the line breaks) initializes the X window motif plot window to use 30 colors from blue (lowest levels) to yellow (highest levels) for the image plots (in this scheme a value half way between the lowest and highest values would be a medium intensity gray). motif( -xrm sgraphmotif.colorschemes : background : black; lines : yellow cyan magenta green MediumBlue red; text : white yellow cyan magenta green MediumBlue red; images : blue 30 yellow ) Side Effects An image plot is created on the current graphics device plot.permax set.seed(1292) ngenes < m1 <- rnorm(ngenes,4,1) m2 <- rnorm(ngenes,4,1) exp1 <- cbind(matrix(exp(rnorm(ngenes*5,m1,1)),nrow=ngenes), matrix(exp(rnorm(ngenes*10,m2,1)),nrow=ngenes)) exp1[exp1<20] <- 20 sub <- exp1>20 & exp1<150 exp1[sub] <- ifelse(runif(length(sub[sub]))<.5,20,exp1[sub]) dimnames(exp1) <- list(paste('x',format(1:ngenes,justify='l'),sep=''), paste('sample',format(1:ncol(exp1),justify='l'),sep='')) dimnames(exp1) <- list(paste('x',1:ngenes,sep=''), paste('sample',1:ncol(exp1),sep='')) exp1 <- round(exp1) plot.expr(exp1[1:20,])

8 8 plot.permax plot.permax Image plot of the most significant genes (attributes) from a permax analysis Given the output of permax, and the array of expression levels, creates a color image plot of the expression levels of the most significant genes plot.permax(x, data, nl=25, nr=25, logs=true, ig1=null, ig2=null, clmn.lab=dimnames(data)[[2]], row.lab=dimnames(data)[[1]], clmn.off=null, row.off=null,...) x data nl nr logs ig1 A permax object (output from permax) Matrix or data frame of expression levels used as input to permax The nl most significant genes in the lower tail will be plotted The nr most significant genes in the upper tail will be plotted If logs=true, then log values are used. The columns of data for cases in group 1 (see ) ig2 The columns in group 2. By default, all the columns not in group 1. clmn.lab row.lab clmn.off row.off Labels for the columns in the array. Labels for the rows in the array. Offset for printing the column labels (<0 to put labels outside the plot). Offset for printing the row labels (<0 to put labels outside the plot).... Additional arguments to image and text (see par) none Values within a row of data are centered and normalized to have variance 1. If ig1 is not given, then the values are centered to have mean 0. If ig1 is given, the values are centered so the means of the columns in ig1 and ig2 are equal in magnitude and opposite in direction (usually ig1 and ig2 should match the values used in the permax call). The plot is thus useful for comparing within rows, but differences in colors between rows have no meaning. The plot will give the most significant lower tail genes in the top portion (most significant at the top), and the most significant upper tail genes in the bottom portion (most significant at the bottom). This function just selects out the appropriate rows of data, and calls plot.expr(). row.names(data) or dimnames(data)[[1]] must correspond to row.names(z) for the selection to work properly. A graphics device supporting image plots must be initialized prior to calling this function. Under Splus 3.4 for unix, the following command (without the line breaks) initializes the X window motif plot window to use 30 colors from blue (lowest levels) to yellow (highest levels) for the image plots (in this scheme a value half way between the lowest and highest values would be a medium intensity gray).

9 rowperm 9 motif( -xrm sgraphmotif.colorschemes : background : black; lines : yellow cyan magenta green MediumBlue red; text : white yellow cyan magenta green MediumBlue red; images : blue 30 yellow ) Side Effects An image plot is created on the current graphics device permax, plot.expr set.seed(1292) ngenes < m1 <- rnorm(ngenes,4,1) m2 <- rnorm(ngenes,4,1) exp1 <- cbind(matrix(exp(rnorm(ngenes*5,m1,1)),nrow=ngenes), matrix(exp(rnorm(ngenes*10,m2,1)),nrow=ngenes)) exp1[exp1<20] <- 20 sub <- exp1>20 & exp1<150 exp1[sub] <- ifelse(runif(length(sub[sub]))<.5,20,exp1[sub]) dimnames(exp1) <- list(paste('x',format(1:ngenes,justify='l'),sep=''), paste('sample',format(1:ncol(exp1),justify='l'),sep='')) dimnames(exp1) <- list(paste('x',1:ngenes,sep=''), paste('sample',1:ncol(exp1),sep='')) exp1 <- round(exp1) uu <- permax(exp1,1:5) plot(uu,exp1,ig1=1:5,cex=.7) rowperm Generates random permutations within rows of a matrix Given a matrix x, returns a copy of x with a separate random permutations applied within each row. rowperm(x) x a numeric matrix A numeric matrix with each row containing the elements from the corresponding row of x permuted in a random order.

10 10 summary.permax x <- matrix(1:12,3) x # [,1] [,2] [,3] [,4] #[1,] #[2,] #[3,] rowperm(x) # [,1] [,2] [,3] [,4] #[1,] #[2,] #[3,] summary.permax Summarizes the output of permax Finds and prints the most significant genes in the output of permax summary.permax(object, data, nl=25, nr=25,...) object data nl nr A dataframe of class permax (created by permax) The data matrix used as input to permax. If given, the rows of d corresponding to the most significant genes will also be printed. The nl most significant genes in the lower tail will be printed The nr most significant genes in the upper tail will be printed... Supplied for compatibility but not used. If d is given, it must be a data frame with row.names(d) corresponding to row.names(object), or a matrix with dimnames(d)[[1]] corresponding to row.names(object). The purpose of including d is primarily to print the rows of the original data corresponding to the most significant statistics. permax # An example is given in the permax help file

11 Index Topic hplot plot.expr, 6 plot.permax, 8 Topic htest permax, 1 permcor, 3 permsep, 5 Topic print summary.permax, 10 Topic utilities rowperm, 9 attr, 5 attributes, 5 permax, 1 permcor, 3 permsep, 5 plot.expr, 6 plot.permax, 8 print.summary.permax (summary.permax), 10 rowperm, 9 summary.permax, 10 11

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