CSci 3003: Introduction to Computing in Biology Lab Assignment #7 solution


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Lab 7: Statistical analysis of gene expression data in R

Goals of this lab:
● Practice using R to load/analyze data.
● Learn about statistical analyses of gene expression data.

This lab will focus on statistical analysis of gene expression data using both microarray and
RNA-seq datasets. Specifically, we will investigate genes whose expression is different between
estrogen receptor (ER) positive and ER negative breast cancer tumors. The ER status reflects
whether a tumor will be responsive to hormone therapies and is often used as an important
diagnostic in determining the course of treatment. In this lab, we will examine gene expression
differences between breast cancer tumor samples using both microarray and RNA-Seq
expression data.

Part I: Understanding the breast cancer study

This week’s lab will focus on understanding two expression datasets, loading the data into R,
and performing some manipulations on the data. Before we begin doing statistical analyses of
the gene expression data, it is important that you take some time to understand the study. We
will be examining expression data generated from microarrays as well as from RNA-Seq.

datasets were generated from two studies (cited at the end of this document), and the data have
been uploaded to the NCBI Gene Expression Omnibus and the NCBI Short Read Archive.

Examine the studies, GSE20711 and SRP005601, by clicking the following links:

Answer the following questions:
a) What was the purpose of each study and what experiments did the authors do to answer
the question they were interested in?
b) How many gene expression samples are in each dataset?
c) What two sets of tumor samples did the authors profile for gene expression?
d) How large are the raw data files for each study?

● hint: GSE20711: GSE20711_RAW.tar
● hint: SRP005601: see “Related SRA Data – Runs”

Part II: Loading and manipulating expression data in R

We have provided prepared data files for each experiment that can be downloaded from the
Canvas Website.

Write a script that will do the following:
a) Load the microarray gene expression files into R matrices using the read.table()
function. We will want to use a matrix to interact with the data, so create a matrix from
data frame you just made using the as.matrix() function. In the matrix, we want each
column name to be a tumor ID and each row name to be a gene name.

● BC_MicroArray.txt – Microarray expression data: 32,864 probes (genes) x 90
samples (the values are log-transformed intensities from an Affymetrix array)
● BC_MicroArray_status.txt – The status labels for the samples (ER+ or ER-)

b) Write a short series of commands that will check the structure of the data matrices
you’ve just loaded. The microarray data should contain values for 32,864 probes (genes)
by 90 samples.
c) Print the data for the BRCA1 gene for all samples.

d) Print the values for the first 10 genes for the first ER+ sample (GSM519791) in the
microarray dataset.
e) Compute the mean and standard deviation of the expression data for the BRCA1 gene
across all samples.

f) Compute the mean and standard deviation of the expression of all genes in the first ER+
sample (GSM519791).
g) Print the list of 10 genes with the highest expression values in order of decreasing
expression based on the first ER+ sample (GSM519791).
h) Create a vector called ERpos_samples that contains the GSM names of all ER+

i) Create a vector called ERneg_samples that contains the names of all ER- samples.
j) Use the vectors created in Parts (h) and (i) to compute a new vector
expr_difference, which contains the difference in the mean expression for each
gene between the ER+ and ER- sample groups.

Positive values in this vector should
indicate where mean ER+ expression is greater than mean ER- expression, and
negative values should indicate where ER- < ER+ expression (Hint: matrices can be indexed by name and there are functions that compute means on matrix rows and columns). k) Using the expr_difference vector you just created, print the gene that has the largest positive difference (i.e. ER+ > ER-) and the largest negative difference (i.e. ER+
< ER-) in mean expression between the ER+ and ER- groups. (Hint: you may find the
names function useful here).

Part III: Statistical analysis of microarray gene expression data

For this part of the lab, we will find a subset of the genes that are differentially expressed using
the t-test. The purpose of the t-test is to statistically assess a gene’s difference in expression
across two groups of samples (in this case, ER+ and ER-), and answer the yes/no question “is
this difference significant?”

To perform a t-test to determine if one gene’s differential expression is significant, you must first
calculate a t-statistic. For a single gene, this is:
where X1
is the mean of the ER+ expression levels for that gene, X2
is the mean ERexpression level, N1
and N2
are the number of samples per group (ER+/-), sx1
is the variance of
the ER+ expression values for that gene and sx2
is the variance of the gene’s ER- expression.

a) Create a vector of t-statistics measuring the difference in expression for each gene
between the ER+ and ER- samples (this vector should be 32864 x 1 or 1 x 32864). (Hint:
the functions mean(), var(), and length() or dim() will be useful).

b) Use the hist() function to plot a histogram of t-statistics. (Hint:
hist(myvect,breaks=100)) will create a histogram of the values in myvect with 100

c) Your goal is to answer the yes/no question of whether or not each gene’s expression value
is significantly different from the random expectation in each sample. To do this, you will
need to compute a p-value that reflects the significance of the t-statistics you just measured.

A p-value represents the probability that the observed t-statistic was derived from samples
where there was no significant difference in the means of the two groups. Thus, a small pvalue reflects a case in which the gene is very likely differentially expressed between the
two sets of samples. Typically, a cutoff of 0.05 is used; genes with less than a 0.05 p-value
are called significantly differentially expressed.

Modify the code you created above to also compute a vector of p-values, one for each gene.
(Hint: you will need to use the pt() function here, which computes the integral under the tdistribution for you; N = N1+N2) Because we want to test for positive and negative
differences between the two groups at the same time, we will use a two-sided t-test, which
computes the integral under the t-distribution for the ranges − ∞→−|t
stat| and |t

Remember, this is how we compute the probability of observing, under the null hypothesis
that the gene is not differentially expressed, a value at least as extreme as the one you
observed (on either side of the t-distribution). You can compute this probability using built-in
R functions as follows:
pval = 2 * pt(-abs(tstat),N-2)
where N is the total number of tumor samples (both ER+ and ER-).

(pval = pt(tstat,N-2) is appropriate for performing a one-sided t-test)
d) Extra credit (2pts):
● Explain in detail why this works for computing the p-value for a one-sided test (1pt):
pval = pt(-abs(tstat),N-2);
● Explain in detail why this works for computing the p-value for a two-sided test (1pt):
pval = 2 * pt(-abs(tstat),N-2);

e) Using the results you computed for parts 1-3, answer the following questions by writing short
sections of R code:

i.) Print a list of significantly differentially expressed genes (p-value < 0.05), sorted in
order of their significance (from smallest to largest). Include the gene name, the t-
statistic, and the corresponding p-value in your list. Hint: either the order function,
or the sort function with the index.return=TRUE option, will be useful.

ii.) How many genes are significantly differentially expressed at a p-value < 0.05? How
many genes are significantly differentially expressed at a Bonferroni-corrected pvalue < 0.05?
iii.) How many genes are significantly differentially expressed and more highly in ER+
tumors relative to ER- tumors?
iv.) How many genes are significantly differentially expressed and more lowly in ER+
tumors relative to ER- tumors?

v.) Select a gene from the top 10 most significantly differentially expressed and describe
what’s known about its function ( will be useful).

Part IV: Using R Packages to Process RNA-Seq Data

As we discussed in class, RNA-Seq technology is the current technology of choice for
measuring gene expression profiles. Typical RNA-Seq datasets contain hundreds of millions of
raw sequencing reads that need to be processed with specialized methods in order to perform
statistical analysis.

Fortunately, corresponding advances in computational and statistical
approaches have paralleled this leap in experimental technology. A few well-established
analysis “pipelines” are now responsible for processing most RNA-Seq data generated today.
Here, we have processed an RNA-Seq breast cancer data set comparing ER+ and ER- gene
expression differences into raw read counts.

This allows you to run a comparable differential
expression test based on RNA-Seq data. In this portion of the lab, you will download and run an
R package that will identify differentially expressed genes related to ER+/- status.
Open the provided script, Part4.R, and run the code.

You will need to modify/add code for
parts b and f. For the remaining parts, study the code that accomplishes each of the following:
a) Run the code to download and install DESeq2

b) Add code to read in RNA-Seq files:
● BC_RNAseq.txt – RNA-Seq expression count data (18517 genes X 7 samples)
● BC_RNAseq_status.txt – RNA-Seq expression sample status labels (ER+ or ER-)

c) Convert status table into a factor and create DESeq2 Count Data Set
d) Normalize for size effects and estimate dispersion of the data
e) Calculate differential expression

f) Print the most significant 100 genes based on their adjusted p-value using False
Discovery Rate control. What is the corresponding FDR for these 100 genes?
g) Extra credit (2pts): how many of the top 500 most significantly differentially expressed
genes overlap between the microarray and RNA-Seq analyses? Comment on the
degree of overlap—is this what you expected? Note: you will need to clean the RNAseqderived gene names before matching them to the microarray-derived gene names.

Submit to Canvas:

When you’re finished with the lab, make a report of any questions you answered plus any
requested output, and gather the scripts that you modified. Submit your homework files using
the online Canvas submit tool.


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