Understanding and visualizing a distance matrix

My PhD student has just received the data from a set of RNA samples analysed using a gene array. We discussed what should be done first to analyse these experiments. A good first step is to look at the distance between the samples and do unsupervised hierarchical clustering of all the samples to see how the biological replicates gather together. This represents an unbiased way to do some quality control for your experiments. Rather than just trying to identify different genes, we use all the data to determine if replicates gather together, if we have any outliers and to find patterns in the data. 

The first step is the generation of a distance matrix. A distance matrix tells us the difference between lists of numbers. If we put together a group of samples, then the distance matrix compares all of the samples. We discussed the purpose of the data matrix and visualising the matrix. I've written the following R script that tries to explain the concept. Mel helped me develop the script to visualise it using a script from this very informative Stack Overload post. 

Here is the a visualisation of a distance matrix using published data (Webber et al, 2014): 

Visualisation of distance matrix using data from Webber et al, 2014 

This distance matrix is used to do the hierarchical clustering that is plotted out here and shown here: 

Clustering samples using data from Webber et al, 2014.

# Trying to explain the concept of distance
# simple example 1: one digit different by 2 between two samples
samp1 <- c(0, 1, 2, 3, 4, 5, 6, 7, 8)
samp2 <- c(0, 1, 2, 3, 4, 5, 6, 7, 10)
dist(rbind(samp1, samp2))
# the dist() function compares each of the numbers in order along the two rows of the matrix. 
# answer is in this case is 2, as one number in the list is different by 2 to another. 

# simple example 2: one digit different by 72 between two samples
samp1 <- c(0, 1, 2, 3, 4, 5, 6, 7, 8)
samp2 <- c(0, 1, 2, 3, 4, 5, 6, 7, 80)
dist(rbind(samp1, samp2))
# answer is 72

# a little more complicated: two digits different
samp1 <- c(0, 1, 2, 3, 4, 5, 6, 7, 8)
samp2 <- c(0, 10, 2, 3, 4, 5, 6, 7, 80)
dist(rbind(samp1, samp2))
# now the answer is 72.56
# why? 
# well because of the equation used by the default method. 
# the default for the dist() function is euclidean 
# the equation for this is dist = sqrt(sum(x_i - y_i)^2)
# in this case, this calculates as sqrt(9^2 + 72^2)
# why the sqrt and the sum - in part so that the negatives and the positive differences don't cancel each other out.

# you can use other methods of calculating distance
help(dist)

# another is the "maximum" which just gives us the largest difference between the two arrays
# "Maximum distance between two components of x and y"
samp1 <- c(0, 1, 2, 3, 4, 5, 6, 7, 8)
samp2 <- c(0, 10, 2, 30, 4, 5, 6, 7, 80)
dist(rbind(samp1, samp2), method="maximum")
# in this case 72

# a third is the "manhattan" which sum of the absolute distances between the vectors
# "Absolute distance between the two vectors"
samp1 <- c(0, 1, 2, 3, 4, 5, 6, 7, 8)
samp2 <- c(0, 10, 2, 3, 4, 5, 6, 7, 80)
dist(rbind(samp1, samp2), method="manhattan")
# the answer now is 81

# now just envisage a more complicated situation when there are lots more numbers
# more than two samples and numbers that are higher and lower. 

# let's take a couple of examples from some data we analysed previously:

# http://www.mcponline.org/content/13/4/1050.full
# supplementary data is here: http://www.mcponline.org/content/suppl/2014/02/06/M113.032136.DC1/mcp.M113.032136-5.xlsx
# install if necessary:
# install.packages("readxl")
library(readxl)

# this is the link to the data
link <- "http://www.mcponline.org/content/suppl/2014/02/06/M113.032136.DC1/mcp.M113.032136-6.xlsx"

# the download.file() function downloads and saves the file with the name given
download.file(url=link,destfile="file.xlsx", mode="wb")

# then we can open the file and extract the data using the read_excel() function. 
data<- read_excel("file.xlsx")

View(data)

# the data has 762 observations. 

# we can only calculate distances in a matrix where all the values are the same mode - e.g numbers
# convert data frame (data) into a matrix 
# only want a subset of the data - the data from the samples. 
data.m <- as.matrix(data[2:7])
# transpose the data because a distance matrix works in rows
data.m.t <- t(data.m)

# calculate the distances and put the calculations into an object called distances
distances <- dist(data.m.t)

# convert this distances object into a matrix. 
distances.m <- data.matrix(distances)

# you can look at this object.
View(distances.m)

# we can extract the size of the object and the titles
dim <- ncol(distances.m)
names <- row.names(distances.m)

# now to create the visualisation of the difference matrix. 
# first the coloured boxes
image(1:dim, 1:dim, distances.m, axes = FALSE, xlab = "", ylab = "")

# now label the axis
axis(3, 1:dim, names, cex.axis = 0.8, las=3)
axis(2, dim:1, names, cex.axis = 0.8, las=1)

# add the values of the differences
text(expand.grid(1:6, 6:1), sprintf("%0.1f", distances.m), cex=1)

# this example lacks subltety
# the exo samples are very close together and the cell samples are quite far apart.
# it explains why the cluster analysis is so dramatic. 

# export this image as a tiff file with width of 1000 seems to work well. 
# some of the other formats don't work as well. 

# to make the cluster dendrogram object using the hclust() function
hc <- hclust(distances) 
# plot the cluster diagram
# some interesting groups in the data
plot(hc, 
     xlab =expression(bold("All Samples")), 
     ylab = expression(bold("Distance")))
# replicates cluster together well. 



The visualisation was inspired by this:

• http://stackoverflow.com/questions/3081066/what-techniques-exists-in-r-to-visualize-a-distance-matrix

If you have feedback on this script, please leave a comment. 

Downloading and manipulating published proteomic data...

Update: 1 July 2025 - so a lot has happened in 10 years. This includes people moving jobs, promotions and the reorganisation of data on published website. 

Jason moved to Swansea University. 

Aled was promoted to Professor at Cardiff University 

Tim moved to the University of Westminister. 

----

There are many ways to get data into R. I want to illustrate a method of downloading published data within R, opening the data (an Excel file) and then doing visualisations and manipulations. 

I have chosen a paper from Molecular and Cellular Proteomics which uses aptamers to detect multiple proteins in exosomes and cells. 

The data was generated by colleagues that were working in the School of Medicine at Cardiff University including the first author - Dr Jason Webber, a Prostate Cancer UK funded Research Fellow and senior author, Professor Aled Clayton, a Senior Lecturer in Cancer & Genetics at Velindre Hospital. Dr Tim Stone was key to the data analysis. The protein detection method is from a company called SomaLogic. 

The first step was downloading the file from the Molecular and Cellular Proteomics website. I used the download.file() function. This saves the file into your current directory. This was opened using the readxl package (by Hadley Wickham) using the read_excel() function. 

I drew some graphs as I explored and manipulated the data. These are interspersed with the script below.  The visualisations included boxplots and a cluster diagram. 

I wanted to draw a volcano plot which expresses the fold change against the significant of the change (p-value). I couldn't do that with the data supplied so I had to reverse the transformation and calculate the fold change again. 

Here is the volcano plot:

Comparison of changes in exosomes compared cells. Proteins over-expressed in exosomes are on the right. Proteins over-expressed in cells are on the left. 

The plot indicates that there are more proteins over-expressed in cells (on the left) compared to exosomes (on the right). 

Update: 1 July 2025 - orignally, I was able to download the data directly from the Molecular and Cellular Proteomics website. However, at some point, they reorganised their site and put all the data into a zip file. This means that downloading it requires multiple steps outside of R. To make this analysis more stand alone, I have down loaded the data from this zip file and uploaded the spreadsheet onto my Github site. This means that the script will download and analyse the data. 

Here is the script with some other plots along the way:

START

# pull down a file from the internet, do some analysis and draw a graph...

# choose Jason Webber's MCP Paper...

# http://www.mcponline.org/content/13/4/1050.full

# the data can be downloaded using this link with give zip file. 

# It isn't necessary to do that for this script. 

# install if necessary:

# install.packages(c("ggplot2", "readxl")) 

library(ggplot2)

library(readxl)

# this is the link to the data

link <- "https://github.com/brennanpincardiff/RforBiochemists/raw/master/R_for_Biochemists_101/data/mcp.M113.032136-6.xlsx"

# the download.file() function downloads and saves the file with the name given

download.file(url=link,destfile="file.xlsx", mode="wb")

# then we can open the file and extract the data using the read_excel() function. 

data<- read_excel("file.xlsx")

View(data)

# plot the data - always an important first step!

boxplot(data[2:7], 

        las =2, # las = 2 turns the text around to show sample names

        ylab = expression(bold("expression")),

        main="Boxplot of expression data")  

Two types of sample - exosomes (n=3) and cells (n=3).

# do a cluster analysis to quality control the different groups

# convert to matrix first

data.m <- as.matrix(data[2:7])

dim(data.m)   # gives the dimensions of the matrix

# ans: 762   6

# calculate the distances using the dist() function. 

# various methods are possible - default is Euclidean. 

distances <- dist(data.m)

summary(distances) # have a look at the object

# make the cluster dendrogram object using the hclust() function

hc <- hclust(distances) 

# plot the cluster diagram

# some interesting groups in the data

plot(hc, 

     xlab =expression(bold("All Samples")), 

     ylab = expression(bold("Distance")))

# ah, not what I intended. 

# it clustered the proteins NOT the samples. 

# transpose the data and try again...

data.m.t <- t(data.m)

dim(data.m.t)

# ans = 6  762 - so that has worked. 

# repeat cluter analysis

# calculate the distances using the dist() function. 

# various methods are possible - default is Euclidean. 

distances <- dist(data.m.t)

summary(distances)

# make the cluster dendrogram object using the hclust() function

hc <- hclust(distances) 

# plot the cluster diagram

# some interesting groups in the data

plot(hc, 

     xlab =expression(bold("All Samples")), 

     ylab = expression(bold("Distance")))

# replicates cluster together well. 

# the adjusted P value are in a column entiteld: BH - P.value

# this is a little awkward so rename this and Fold Change column:

colnames(data)[9] <- "P.Value"

colnames(data)[10] <- "Fold.Change"

plot(data$P.Value ~ data$Fold.Change)

# this works but we would like to turn it into a volcano plot 

# with log2 at the bottom and -p-value. 

# we can't log fold changes as half of them are negative numbers 

# we need to re-calculate the raw data

# reverse the log2 transformation. 

# mean the values & calculate fold change in decimal format (no +/-)

data$exo1 <- 2^data$exoRFU1

data$exo2 <- 2^data$exoRFU2

data$exo3 <- 2^data$exoRFU3

data$cell1 <- 2^data$cellRFU1

data$cell2 <- 2^data$cellRFU2

data$cell3 <- 2^data$cellRFU3

# calculate means of the replicates

data$exoMean <- rowMeans(data[,13:15])

data$cellMean <- rowMeans(data[,16:18])

# always good to visualise the data:

plot(log2(data$exoMean)~log2(data$cellMean))

# calculate fold change exo/cell

data$FoldChange <- data$exoMean/data$cellMean

plot(log2(data$FoldChange)) # transform for plotting

# make column in data.frame with transformed data

data$Log2.Fold.Change <- log2(data$FoldChange)

## Identify the genes that have a p-value < 0.05

data$threshold = as.factor(data$P.Value < 0.05)

## Construct the volcano plot object using ggplot

g <- ggplot(data=data, 

            aes(x=Log2.Fold.Change, y =-log10(P.Value), 

                colour=threshold)) +

  geom_point(alpha=0.4, size=1.75) +

  xlim(c(-6, 6)) +

  xlab("log2 fold change") + ylab("-log10 p-value") +

  theme_bw() +

  theme(legend.position="none") + 

  ggtitle("Volcano Plot comparing protein expression in exosomes vs cells ")  # add a title

  

g # show the plot 

END of script

So I think that the threshold of p<0.05 is too low for this volcano plot. It's relatively easy to change and would make a good exercise. Perhaps a threshold of p<0.00001 would be better. 

Useful resources (updated 1 July 2025)

• Here is a script about making multiple volcano plots
• More information about volcano plots on Wikipedia. 
• This Enhanced Volcano package looks interesting but I haven't played with it myself. 

Temperature time course

Tracking changes over time is a very useful way of understanding and analysing your system. This applies whether your system is biological or otherwise. As part of my hobby of baking bread, I have built a brick oven in my garden. I have installed thermocouples that allow me to measure the temperature at the top and the bottom of my oven. To investigate the performance of my oven, I have recorded temperatures when I fired the oven in May, June and August of this year.

The data for this is available on github and is downloaded as part of the script.

I have written a script to download, manipulate and graph the data. 

The manipulations required were:

• turning my date and time into a date an time object that R could understand
• subtracting the start time to calculate the elapsed time
• the elapsed time was seconds which was converted to hours
• the time was then converted to a number to allow for graphing by ggplot
• the data was melted into a format for ggplot

Within the script needs to be applied separately to each of the three months of data. This can be done easily by changing the read.table() function to the appropriate file. 

By doing this, I graph and analyse the data in the same way making the graphs easier to compare. Here are the three graphs:

Here is the script for generating these graphs:

library(reshape2)

library(ggplot2)

library(RCurl) # allows us to download data through urls 

# URL for May data:

May <- getURL("https://raw.githubusercontent.com/brennanpincardiff/RforBiochemists/master/data/ovenTempMay.tsv")

# URL for Jun data:

Jun <- getURL("https://raw.githubusercontent.com/brennanpincardiff/RforBiochemists/master/data/ovenTempJun.tsv")

# URL for Aug data: 

Aug <- getURL("https://raw.githubusercontent.com/brennanpincardiff/RforBiochemists/master/data/ovenTempAug.tsv")

# put the URLs together in a vector

urls <- c(May, Jun, Aug)

months <- c("May", "Jun", "Aug")

# do it in a loop to apply to each of the three data sets

for(i in 1:3){

# read in the data for the relevant month - it's a tab separated file 

    data <- read.table(text = urls[i], stringsAsFactors=FALSE, sep = "\t", header = TRUE)

    

    

# convert the data and time into a format that R will understand. make it into a POSIXct object. 

# so as not to mess with the original data put it in a new column called time.P 

# because my dates are separted by slashes "/", I need to tell R about the format. 

    data$time.P <- as.POSIXct(data$time, format = "%d/%m/%Y %H:%M")

    

# the first value is the start.time for this temperature profile. 

    start.time <- data$time.P[1]

    

# calculate the elapsed time 

# substract the start time from each value. 

# This returns the time in seconds

    data$e.time.sec <- data$time.P - start.time

# convert this into an hour time and change back into a number for graphing purposes. 

    data$e.time.hour.num <- as.numeric(data$e.time.sec/3600)

    

    

 # take out the data we need for the plot

    data.subset <- as.data.frame(data$e.time.hour.num)

    colnames(data.subset)[1] <- "e.time.hour.num"

    data.subset$top <- data$top

    data.subset$bot <- data$bot

    

# melt it into a format for ggplot using melt() function

   data.subset.melt <- melt(data.subset, 
                           id.vars = "e.time.hour.num")

# put in nice column names
  colnames(data.subset.melt) <- c("elapsed.time", "place", "temp")
  
# make the graph object
  p <- ggplot(data.subset.melt, aes(x=elapsed.time, 
                                    y= temp, 
                                    colour = factor(place, labels = c("Top", "Bottom")))) + 

# colour = factor and the labels allows us to customize the legend

        geom_line(size=1) +

        geom_point() +

        labs(color = "Place") + # customizes the legend title

        scale_colour_manual(values=c("black","red")) +

        ylab("Temperature") + # y-label

        xlab("Elapsed time (hours)") + # x-label

        ylim(0,400) +

        scale_x_continuous(limits=c(0, 48), 

                           breaks=c(0,1,4,8,12, 24, 48)) +

        theme_bw()

# position the legend  

    p <- p + theme(legend.position=c(1,1), # move to the top right

                   legend.justification=c(1,1), # move it in a bit

                   legend.text=element_text(size = 12), # increase size of text

                   legend.title=element_text(size = 12)) # and the title

    

    p <- p + theme(axis.title.y = element_text(size = 14 )) + 

      theme(axis.text = element_text(size = 12))

    

# add the appropriate title

    p <- p + ggtitle(paste0("Oven Temp (", months[i], " Firing)")) 

# print the object - you have to do this because of the loop

    print(p)

}

Helpful resources, I used to prepare this script:

• http://www.noamross.net/blog/2014/2/10/using-times-and-dates-in-r---presentation-code.html
• http://www.markhneedham.com/blog/2014/07/20/r-ggplot-dont-know-how-to-automatically-pick-scale-for-object-of-type-difftime-discrete-value-supplied-to-continuous-scale/
• http://stackoverflow.com/questions/7531868/how-to-rename-a-single-column-in-a-data-frame-in-r
• http://docs.ggplot2.org/current/scale_continuous.html
• http://stackoverflow.com/questions/14441729/read-a-csv-from-github-into-r
• http://stackoverflow.com/questions/23897027/pass-multiple-variables-into-ggtitle-r
• https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-do-lattice_002ftrellis-graphics-not-work_003f

Opening an image of a leukemia cell in R

Updated 16th May 2016: The image is now on Github so link points there.

I have been exploring the possibility of using R to open and analyse some images. This was first prompted by a delegate that attended our R for Biochemists Training Day organised through the Biochemical Society.

Our search revealed the Bioconductor package, EBImage which allows the opening of .jpg files using R. This allowed me to extract the fluorescence values that I had from this image which I prepared with a colleague, Dr Elisabeth Walsby. Beth stained the cell and I did the confocal microscopy. Here is the nice picture of a chronic lymphocytic leukaemia cell stained for a protein (red colour) and for DNA (blue).

I can open this image with R using the readImage() function that comes as part of the EBImage package. When I display the image using the display() command, it opens a new browser window. It has various functionality to explore the image shown here:

The most useful aspect of this approach is the ability to extract the fluorescence values to use to make nice plots in R. This uses the imageData() function which works like this:

• imageData(img)[, 512, 3]  - access a vector with all the x values across one y value (pixel number 512) and extracts the third colour for the image. 

I've used EBImage to extract values and to generate this graph which shows the fluorescence of the pixels across the middle of the cell:

Here is the script with some plots that I generated along the way:

# EBImage - a Bioconductor package for analysing images

source("http://bioconductor.org/biocLite.R")

biocLite("EBImage")

library("EBImage")

library(ggplot2)

# the image is on Github
img <- readImage("https://raw.githubusercontent.com/brennanpincardiff/RforBiochemists/master/data/images/cllCell.jpg")
# the object created is a Large Image (24 Mb in this case!)

display(img)

# opens a window in a web browser and allows you to look at the image

print(img)

# shows some of the structure of the Large Image object.

dim(img)

# [1] 1024 1024    3   

# corresponds to x and y pixels of the image and then the number of colours for each pixel

# why do we want to do this?

# so that we can extract data out of the image and draw nice graphs. 

# to extract a value out of the Large Image use the imageData() function

# if you place the mouse over the image in the web browser, you see the name of the pixel. 

# we can extract the fluorescence value and plot the data

x <- imageData(img)[, 512, 3]

# this gives the values for colour 3 for the whole x line at the value of y = 512. 

# this is a list of 1024 numbers which can be plotted

plot(x)  

# the index at the bottom refers to the x values across the whole image. 

# using the web browser, I can choose the line across the middle of the cell

# extract a row of 100 pixels wide from left to right of the middle of the image.

# I chose to extract values from y pixel 425 to 545 which correspond to the middle of the cell

# colour 1

x10.col1 <- as.data.frame(imageData(img)[ ,425:525, 1])

plot(x10.col1$V5)  # plot one of the values

Plot one of the values (V5)

x10.col1$mean <- rowMeans(x10.col1[1:100])

plot(x10.col1$mean) # plot the mean

Plot the mean of 100 pixels

# colour 3

x10.col3 <- as.data.frame(imageData(img)[ ,425:525, 3])

x10.col3$mean <- rowMeans(x10.col3[1:100])

plot(x10.col3$mean, col = "blue")

lines(x10.col1$mean, col = "red")

Plot both colours using Base R

# assemble a data frame to allow us to use ggplot to plot the data..

m <- as.data.frame(x10.col1$mean)

m$col3 <- x10.col3$mean

# change the column names in the data frame

colnames(m) <- c("col1", "col3")

# make the basic ggplot object

p <- ggplot(data=m, aes(x=seq(1, length(col3)))) + 

     geom_line(aes(y = col3), colour = "blue") + 

     geom_line(aes(y = col1), colour = "red")

p  # show the plot

Plot both colours in ggplot2

# focus on just the cell

p <- ggplot(data=m, aes(x=seq(1, length(col3)))) + 

     geom_line(aes(y = col3), colour = "blue") + 

     geom_line(aes(y = col1), colour = "red") + 

     xlim(350,850) # focus on just the cell

p  # have a look

# gives Warning messages but these can be ignored.

Focus on the cell by limiting the x-axis.

# add some titles and a easy theme 

p <- p +  xlab("Distance (pixels)") +   #label x-axis

          ylab("Fluorescence signal") +    #label y-axis

          ggtitle("Histogram of fluoresence of CLL cell") +  #title

          theme_bw()     # a simple theme

p   # show the plot

Add titles and change the theme.

# plot points instead of lines...

q <- ggplot(data=m, aes(x=seq(1, length(col3)))) + 

  geom_point(aes(y = col3), colour = "blue") + 

  geom_point(aes(y = col1), colour = "red") + 

  xlim(350,850) +  

  xlab("Distance (pixels)") +   # label x-axis

  ylab("Fluorescence signal") +    # label y-axis

  ggtitle("Histogram of fluoresence of CLL cell") +  # add a title

  theme_bw()     # a simple theme

q   # show the plot

You have the plot at the top of the page....

Resources: 

• My first link to EBImage: http://www.r-bloggers.com/r-image-analysis-using-ebimage/
• Introduction to EBImage (PDF): http://bioconductor.org/packages/release/bioc/vignettes/EBImage/inst/doc/EBImage-introduction.pdf
• Reference manual for EBImage: http://bioconductor.org/packages/release/bioc/manuals/EBImage/man/EBImage.pdf
• http://www.cookbook-r.com/Graphs/Axes_(ggplot2)/
• http://stackoverflow.com/questions/13837565/how-to-plot-one-variable-in-ggplot

Analysing some citation data in R....

Last week, I showed a graph that detailed the number of publications in my field of study: chronic lymphocytic leukemia - over 17,000 publications with over 4,000 between 2010 and 2014. This inspired me to ask the question of what papers, from 2010 to 2014 were the most cited papers in the field. What were the MUST READ papers?

To do this required me to download citation data and do some analysis. Downloading citation data is not difficult but it does take up a bit of internet time. You don't need to do it yourself to appreciate the graph that I have made or the list of papers that it generated. 

Here is the graph:

Here is the script to draw this graph:

START

# This data file has a list of the PubMed IDs, the year and the citation data 

data <- read.csv("http://science2therapy.com/data/cllCitation2010to2014_20150722.csv", header=T)

str(data)

cit <- data$cit

# not very useful but good practice to plot the data first...

plot(density(cit))

plot(density(cit), log='x')

hist(cit)

# not very useful in ggplot either. 

p <- ggplot(data=data,          # specify the data frame with data

            aes(x=cit)) +       # specify the x and y for the graph

  geom_bar(binwidth = 10)    # it's a bar plot

p   # show the plot

# so lots of the publications with relatively few citations. 

# Do some subsetting to identify highly cited papers. 

# http://www.statmethods.net/management/subset.html

# calculate the mean number of citations 

mean.cit <- mean(data$cit)   # 4.1 for this data set. 

# data frame of publications with no citations

newdata.zero <- subset(data, cit == 0)

# data frame of publications with one citation

newdata.one <- subset(data, cit == 1)

# make a data frame of publications with more than one citations upto the mean 

newdata.greater1 <- subset(data, cit > 1)

newdata.mean <- subset(newdata.greater1, cit < mean.cit)

# make a data frame of publications with more than the mean citations

# up to the mean squared

newdata.greatermean <- subset(data, cit > mean.cit)

newdata.meanSq <- subset(newdata.greatermean, cit < (mean.cit^2))

# make a data frame of publications with more than the mean squared citations

# up to the mean cubed

newdata.greatermeanSq <- subset(data, cit > (mean.cit^2))

newdata.SqtoCube <- subset(newdata.greatermeanSq, cit < (mean.cit^3)) 

# make a data frame of publications with more than the mean cubed citations

newdata.greaterCube <- subset(data, cit > (mean.cit^3))

# assemble these numbers into a vector

count<-c(nrow(newdata.zero), nrow(newdata.one), nrow(newdata.mean), 

         nrow(newdata.meanSq), nrow(newdata.SqtoCube), nrow(newdata.greaterCube))

# simple barplot

barplot(count)

# create a list of labels

lab=c("0","1","2-4","5-16","17-64", ">64")

# assemble a new data frame to plot with ggplot

df <- as.data.frame(count)

df$label <- lab

df$labfac <- factor(df$label, as.character(df$label))

# do a nice histogram of citation frequency in ggplot

p <- ggplot(data=df, aes(y=count)) + 

  geom_bar(aes(x=labfac), data=df, stat="identity") + 

  xlab("Number of citations") +   # label x-axis

  ylab("Number of Papers") +    # label y-axis

  ggtitle("Chronic Lymphocytic Leukemia Papers published 2010 to 2014") +  # add a title

  theme_bw() +      # a simple theme

  expand_limits(y=c(0,2000)) +   # customise the y-axis

  theme(axis.title.y = element_text(size = 14 )) + 

  theme(axis.title.x = element_text(size = 14 )) + 

  theme(axis.text = element_text(size = 12))

p    #show us the plot

END

Thoughts on the citation analysis

The average number of citations per paper was just over 4. 

Only 24 papers were cited more than 64 times. 

Here is a list of the 5 most highly cited papers from 2010 to 2014:

1. Porter, et al 2011 N Engl J Med “Chimeric antigen receptor-modified T cells in chronic lymphoid leukemia.” Cited: 414 times 
2. Stephens et al 2011 Cell “Massive genomic rearrangement acquired in a single catastrophic event during cancer development.” Cited: 333 times 
3. Kalos et al 2011 Sci Transl Med “T cells with chimeric antigen receptors have potent antitumor effects and can establish memory in patients with advanced leukemia.” Cited: 287 times 
4. Puente et al 2011 Nature “Whole-genome sequencing identifies recurrent mutations in chronic lymphocytic leukaemia.” Cited: 228 times 
5. Grupp et al 2013 N Engl J Med “Chimeric antigen receptor-modified T cells for acute lymphoid leukemia.” Cited: 205 times 

Full list of the 24 papers is available as a PDF here.