3. R for data analysis

3 steps to Basic Data Analysis

  • In this short section, we show how the data manipulation steps we have just seen can be used as part of an analysis pipeline:
  1. Reading in data
    • read.table()
    • read.csv(), read.delim()
  2. Analysis
    • Manipulating & reshaping the data
      • perhaps dealing with “missing data”
    • Any maths you like
    • Diagnostic Plots
  3. Writing out results
    • write.table()
    • write.csv()

A simple walkthrough

  • We have data from 100 patients that given consent for their data to use in future studies
  • A researcher wants to undertake a study involving people that are overweight
  • We will walkthrough how to filter the data and write a new file with the candidates for the study

The Working Directory (wd)

  • Like many programs R has a concept of a working directory
  • It is the place where R will look for files to execute and where it will save files, by default
  • For this course we need to set the working directory to the location of the course scripts
  • In RStudio use the mouse and browse to the directory where you saved the Course Materials

  • Session → Set Working Directory → Choose Directory…

0. Locate the data

Before we even start the analysis, we need to be sure of where the data are located on our hard drive

  • Functions that import data need a file location as a character vector
  • The default location is the working directory
getwd()
[1] "/Users/dunnin01/work/git/r-intro"
  • If the file you want to read is in your working directory, you can just use the file name
list.files()
  • The file.exists function does exactly what it says on the tin!
    • a good sanity check for your code
file.exists("patient-info.txt")
[1] TRUE
  • Otherwise you need the path to the file
    • you can get this using file.choose()
  • If you unsure about specifying a file path at the command line, this online tutorial will give you hands-on practice

1. Read in the data

  • The data are a tab-delimited file. Each row is a record, each column is a field. Columns are separated by tabs in the text
  • We need to read in the results and assign it to an object (patients)
patients <- read.delim("patient-info.txt")

In the latest RStudio, there is the option to import data directly from the File menu. File -> Import Dataset -> From Csv

  • If the data are comma-separated, then use either the argument sep="," or the function read.csv():
  • You need to make sure you use the correct function
    • can you explain the output of the following lines of code?
tmp <- read.csv("patient-info.txt")
head(tmp)
  • For full list of arguments:
?read.table

1b. Check the data

  • Always check the object to make sure the contents and dimensions are as you expect
  • R will sometimes create the object without error, but the contents may be un-usable for analysis
    • If you specify an incorrect separator, R will not be able to locate the columns in your data, and you may end up with an object with just one column
# View the first 10 rows to ensure import is OK
patients[1:10,]  
  • or use the View() function to get a display of the data in RStudio:
View(patients)

1c. Understanding the object

  • Once we have read the data successfully, we can start to interact with it
  • The object we have created is a data frame:
class(patients)
[1] "data.frame"
  • We can query the dimensions:
ncol(patients)
[1] 10
nrow(patients)
[1] 100
dim(patients)
[1] 100  10
  • The names of the columns are automatically assigned:
colnames(patients)
 [1] "ID"     "Race"   "Sex"    "Smokes" "Height" "Weight" "State"  "Pet"    "Grade"  "Age"   
  • We can use any of these names to access a particular column:
    • and create a vector
    • TOP TIP: type the name of the object and hit TAB: you can select the column from the drop-down list!
patients$ID
  [1] AC/AH/001 AC/AH/017 AC/AH/020 AC/AH/022 AC/AH/029 AC/AH/033 AC/AH/037 AC/AH/044 AC/AH/045 AC/AH/048 AC/AH/049 AC/AH/050
 [13] AC/AH/052 AC/AH/053 AC/AH/057 AC/AH/061 AC/AH/063 AC/AH/076 AC/AH/077 AC/AH/086 AC/AH/089 AC/AH/100 AC/AH/104 AC/AH/112
 [25] AC/AH/113 AC/AH/114 AC/AH/115 AC/AH/127 AC/AH/133 AC/AH/150 AC/AH/154 AC/AH/156 AC/AH/159 AC/AH/160 AC/AH/164 AC/AH/171
 [37] AC/AH/176 AC/AH/180 AC/AH/185 AC/AH/186 AC/AH/192 AC/AH/198 AC/AH/207 AC/AH/208 AC/AH/210 AC/AH/211 AC/AH/213 AC/AH/219
 [49] AC/AH/220 AC/AH/221 AC/AH/225 AC/AH/233 AC/AH/241 AC/AH/244 AC/AH/248 AC/AH/249 AC/SG/002 AC/SG/003 AC/SG/008 AC/SG/009
 [61] AC/SG/010 AC/SG/015 AC/SG/016 AC/SG/046 AC/SG/055 AC/SG/056 AC/SG/064 AC/SG/065 AC/SG/067 AC/SG/068 AC/SG/072 AC/SG/074
 [73] AC/SG/084 AC/SG/095 AC/SG/099 AC/SG/101 AC/SG/107 AC/SG/116 AC/SG/121 AC/SG/122 AC/SG/123 AC/SG/134 AC/SG/139 AC/SG/142
 [85] AC/SG/155 AC/SG/165 AC/SG/167 AC/SG/172 AC/SG/173 AC/SG/179 AC/SG/181 AC/SG/182 AC/SG/191 AC/SG/193 AC/SG/194 AC/SG/197
 [97] AC/SG/204 AC/SG/216 AC/SG/217 AC/SG/234
100 Levels: AC/AH/001 AC/AH/017 AC/AH/020 AC/AH/022 AC/AH/029 AC/AH/033 AC/AH/037 AC/AH/044 AC/AH/045 AC/AH/048 ... AC/SG/234

Word of warning

Like families, tidy datasets are all alike but every messy dataset is messy in its own way - (Hadley Wickham - RStudio chief scientist and author of dplyr, ggplot2 and others)

You will make your life a lot easier if you keep your data tidy and organised. Before blaming R, consider if your data are in a suitable form for analysis. The more manual manipulation you have done on the data (highlighting, formulas, copy-and-pasting), the less happy R is going to be to read it. Here are some useful links on some common pitfalls and how to avoid them

Handling missing values

  • The data frame contains some NA values, which means the values are missing – a common occurrence in real data collection
  • NA is a special value that can be present in objects of any type (logical, character, numeric etc)
  • NA is not the same as NULL:
    • NULL is an empty R object.
    • NA is one missing value within an R object (like a data frame or a vector)
  • Often R functions will handle NAs gracefully:
length(patients$Height)
[1] 100
mean(patients$Height)
[1] NA
  • However, sometimes we have to tell the functions what to do with them.
  • R has some built-in functions for dealing with NAs, and functions often have their own arguments (like na.rm) for handling them:
    • annoyingly, different functions have different argument names to change their behaviour with regards to NA values. Always check the documentation
mean(patients$Height, na.rm = TRUE)
[1] 167.4969
mean(na.omit(patients$Height))
[1] 167.4969

2. Analysis (reshaping data and maths)

  • Our analysis involves identifying patients with extreme BMI
    • we will define this as being two standard deviations from the mean
# Create an index of results:
BMI <- (patients$Weight)/((patients$Height/100)^2)
upper.limit <- mean(BMI,na.rm = TRUE) + 2*sd(BMI,na.rm = TRUE)
upper.limit
[1] 30.9533
  • We can plot a simple chart of the BMI values
    • add a vertical line to indicate the cut-off
    • plotting will be covered in detail shortly..
plot(BMI)
# Add a horizonal line:
abline(h=upper.limit) 

  • It is also useful to save the variable we have computed as a new column in the data frame
round(BMI,1)
  [1] 22.9 25.1 26.4 30.6 26.5 27.9 26.3 25.6 23.4 28.2 28.2   NA 30.0 27.9 24.5 22.0 25.6 31.5 23.8   NA 23.5 26.7 31.4   NA
 [25] 24.6   NA 24.8 29.2   NA 24.1 25.1 28.0 29.4 28.2 23.6 26.4   NA 25.0 27.7 27.0 25.6 26.7 24.5 26.1 23.1 28.2 26.9   NA
 [49] 25.4 25.9   NA 24.8 28.2   NA 30.4 26.8 26.0 25.2 26.9 31.7 25.6   NA 26.7 27.8 28.4   NA 31.5 27.0 30.0 26.5 25.2   NA
 [73] 26.7 25.8   NA 27.6 29.1 26.6 26.6 26.9 27.6 26.4 27.8   NA 27.8 25.8 27.7 28.7 24.2 24.6 28.3 24.8 27.8 21.4 28.0 26.0
 [97] 26.2 26.4 27.7   NA
patients$BMI <- round(BMI,1)
head(patients)
  • To actually select the candidates we can use a logical expression to test the values of the BMI vector being greater than the upper limit
    • if the second line looks a bit weird, remember that <- is doing an assignment. Thevalue we are assigning to our new variable is the logical (TRUE or FALSE) vector given by testing each item in BMI against the upper.limit
BMI > upper.limit
  [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE    NA FALSE FALSE FALSE FALSE FALSE  TRUE FALSE    NA
 [21] FALSE FALSE  TRUE    NA FALSE    NA FALSE FALSE    NA FALSE FALSE FALSE FALSE FALSE FALSE FALSE    NA FALSE FALSE FALSE
 [41] FALSE FALSE FALSE FALSE FALSE FALSE FALSE    NA FALSE FALSE    NA FALSE FALSE    NA FALSE FALSE FALSE FALSE FALSE  TRUE
 [61] FALSE    NA FALSE FALSE FALSE    NA  TRUE FALSE FALSE FALSE FALSE    NA FALSE FALSE    NA FALSE FALSE FALSE FALSE FALSE
 [81] FALSE FALSE FALSE    NA FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE    NA
candidates <- BMI > upper.limit

We have seen that a logical vector can be used to subset a data frame

  • However, in our case the result looks a bit funny
  • Can you think why this might be?
patients[candidates,]

The which function will take a logical vector and return the indices of the TRUE values

  • This can then be used to subset the data frame
which(BMI > upper.limit)
[1] 18 23 60 67
candidates <- which(BMI > upper.limit)

3. Outputting the results

  • We write out a data frame of candidates (patients with BMI more than standard deviations from the mean) as a ‘comma separated values’ text file (CSV):
write.csv(patients[candidates,], file="selectedSamples.csv")
  • The output file is directly-readable by Excel
  • It’s often helpful to double check where the data has been saved. Use the get working directory function:
getwd()      # print working directory
list.files() # list files in working directory

To recap, the set of R commands we have used is:-

patients <- read.delim("patient-info.txt")
BMI <- (patients$Weight)/((patients$Height/100)^2)
upper.limit <- mean(BMI,na.rm = TRUE) + 2*sd(BMI,na.rm = TRUE)
plot(BMI)
# Add a horizonal line:
abline(h=upper.limit) 

patients$BMI <- round(BMI,1)
candidates <- which(BMI > upper.limit)
write.csv(patients[candidates,], file="selectedSamples.csv")

Exercise: Exercise 3

  • A separate study is looking for patients that are underweight and also smoke;
  • Modify the condition in our previous code to find these patients
  • e.g. having BMI that is 2 standard deviations less than the mean BMI
  • Write out a results file of the samples that match these criteria, and open it in a spreadsheet program
### Your Answer Here ### 
---
title: "Introduction to Solving Biological Problems Using R - Day 1"
author: Mark Dunning, Suraj Menon and Aiora Zabala. Original material by Robert Stojnić,
  Laurent Gatto, Rob Foy, John Davey, Dávid Molnár and Ian Roberts
date: '`r format(Sys.time(), "Last modified: %d %b %Y")`'
output:
  html_notebook:
    toc: yes
    toc_float: yes
---

# 3. R for data analysis

##3 steps to Basic Data Analysis

- In this short section, we show how the data manipulation steps we have just seen can be used as part of an analysis pipeline:

1. Reading in data
    + `read.table()`
    + `read.csv(), read.delim()`
2. Analysis
    + Manipulating & reshaping the data
        + perhaps dealing with "missing data"
    + Any maths you like
    + Diagnostic Plots
3. Writing out results
    + `write.table()`
    + `write.csv()`
  
## A simple walkthrough

- We have data from 100 patients that given consent for their data to use in future studies
- A researcher wants to undertake a study involving people that are overweight
- We will walkthrough how to filter the data and write a new file with the candidates for the study    
    
##The Working Directory (wd)


- Like many programs R has a concept of a working directory 
- It is the place where R will look for files to execute and where it will
save files, by default
- For this course we need to set the working directory to the location
of the course scripts
- In RStudio use the mouse and browse to the directory where you saved the Course Materials

- ***Session → Set Working Directory → Choose Directory...***

## 0. Locate the data

Before we even start the analysis, we need to be sure of where the data are located on our hard drive

- Functions that import data need a file location as a character vector
- The default location is the ***working directory***
```{r}
getwd()
```

- If the file you want to read is in your working directory, you can just use the file name

```{r eval=FALSE}
list.files()
```

- The `file.exists` function does exactly what it says on the tin!
    + a good sanity check for your code

```{r}
file.exists("patient-info.txt")
```

- Otherwise you need the *path* to the file
    + you can get this using **`file.choose()`**
    
- If you unsure about specifying a file path at the command line, this [online tutorial](http://rik.smith-unna.com/command_line_bootcamp/?id=vczhybjhtyt) will give you hands-on practice
    
##1. Read in the data

- The data are a tab-delimited file. Each row is a record, each column is a field. Columns are separated by tabs in the text
- We need to read in the results and assign it to an object (`patients`)

```{r}
patients <- read.delim("patient-info.txt")

```

In the latest RStudio, there is the option to import data directly from the File menu. ***File*** -> ***Import Dataset*** -> ***From Csv***

- If the data are comma-separated, then use either the argument `sep=","` or the function `read.csv()`:
- You need to make sure you use the correct function
    + can you explain the output of the following lines of code?

```{r }
tmp <- read.csv("patient-info.txt")
head(tmp)
```
- For full list of arguments:
```{r}
?read.table
```

##1b. Check the data
- *Always* check the object to make sure the contents and dimensions are as you expect
- R will sometimes create the object without error, but the contents may be un-usable for analysis
    + If you specify an incorrect separator, R will not be able to locate the columns in your data, and you may end up with an object with just one column
    
```{r}
# View the first 10 rows to ensure import is OK
patients[1:10,]  
```


- or use the `View()` function to get a display of the data in RStudio:
```{r}
View(patients)
```

##1c. Understanding the object

- Once we have read the data successfully, we can start to interact with it
- The object we have created is a *data frame*:
```{r}
class(patients)
```

- We can query the dimensions:

```{r}
ncol(patients)
nrow(patients)
dim(patients)
```


- The names of the columns are automatically assigned:

```{r}
colnames(patients)
```

- We can use any of these names to access a particular column:
    + and create a vector
    + TOP TIP: type the name of the object and hit TAB: you can select the column from the drop-down list!
```{r}
patients$ID

```

## Word of warning


![](images/tolstoy.jpg)



![](images/hadley.jpg)

> Like families, tidy datasets are all alike but every messy dataset is messy in its own way - (Hadley Wickham - RStudio chief scientist and author of dplyr, ggplot2 and others)

You will make your life a lot easier if you keep your data **tidy** and ***organised***. Before blaming R, consider if your data are in a suitable form for analysis. The more manual manipulation you have done on the data (highlighting, formulas, copy-and-pasting), the less happy R is going to be to read it. Here are some useful links on some common pitfalls and how to avoid them

- http://www.datacarpentry.org/spreadsheet-ecology-lesson/
- http://kbroman.org/dataorg/

##Handling missing values

- The data frame contains some **`NA`** values, which means the values are missing – a common occurrence in real data collection
- `NA` is a special value that can be present in objects of any type (logical, character, numeric etc)
- `NA` is not the same as `NULL`:
    - `NULL` is an empty R object. 
    - `NA` is one missing value within an R object (like a data frame or a vector)
- Often R functions will handle `NA`s gracefully:

```{r}
length(patients$Height)
mean(patients$Height)
```

- However, sometimes we have to tell the functions what to do with them. 
- R has some built-in functions for dealing with `NA`s, and functions often have their own arguments (like `na.rm`) for handling them:
    + annoyingly, different functions have different argument names to change their behaviour with regards to `NA` values. *Always check the documentation*

```{r}
mean(patients$Height, na.rm = TRUE)

mean(na.omit(patients$Height))
```

##2. Analysis (reshaping data and maths)

- Our analysis involves identifying patients with extreme BMI
    + we will define this as being two standard deviations from the mean

```{r}
# Create an index of results:
BMI <- (patients$Weight)/((patients$Height/100)^2)
upper.limit <- mean(BMI,na.rm = TRUE) + 2*sd(BMI,na.rm = TRUE)
upper.limit
```


- We can plot a simple chart of the BMI values 
    + add a vertical line to indicate the cut-off
    + plotting will be covered in detail shortly..

```{r}
plot(BMI)
# Add a horizonal line:
abline(h=upper.limit) 
```

- It is also useful to save the variable we have computed as a new column in the data frame

```{r}
round(BMI,1)
patients$BMI <- round(BMI,1)
head(patients)
```

- To actually select the candidates we can use a logical expression to test the values of the BMI vector being greater than the upper limit
    + if the second line looks a bit weird, remember that `<-` is doing an assignment. Thevalue we are assigning to our new variable is the logical (`TRUE` or `FALSE`) vector given by testing each item in `BMI` against the `upper.limit`
    
```{r}
BMI > upper.limit
candidates <- BMI > upper.limit
```

We have seen that a logical vector can be used to subset a data frame

- However, in our case the result looks a bit funny
- Can you think why this might be?

```{r}
patients[candidates,]
```

The `which` function will take a logical vector and return the indices of the `TRUE` values

- This can then be used to subset the data frame

```{r}
which(BMI > upper.limit)
candidates <- which(BMI > upper.limit)
```


## 3. Outputting the results

- We write out a data frame of candidates (patients with BMI more than standard deviations from the mean) as a 'comma separated values' text file (CSV):

```{r}
write.csv(patients[candidates,], file="selectedSamples.csv")
```

- The output file is directly-readable by Excel
- It's often helpful to double check where the data has been saved. Use the *get working directory* function:

```{r eval=FALSE}
getwd()      # print working directory
list.files() # list files in working directory

```


To recap, the set of R commands we have used is:-

```{r}
patients <- read.delim("patient-info.txt")
BMI <- (patients$Weight)/((patients$Height/100)^2)
upper.limit <- mean(BMI,na.rm = TRUE) + 2*sd(BMI,na.rm = TRUE)
plot(BMI)
# Add a horizonal line:
abline(h=upper.limit) 
patients$BMI <- round(BMI,1)
candidates <- which(BMI > upper.limit)
write.csv(patients[candidates,], file="selectedSamples.csv")

```

##Exercise: Exercise 3

- A separate study is looking for patients that are underweight and also smoke; 
  + Modify the condition in our previous code to find these patients
  + e.g. having BMI that is 2 standard deviations *less* than the mean BMI
  + Write out a results file of the samples that match these criteria, and open it in a spreadsheet program


```{r}
### Your Answer Here ### 



```

