1) Basics of R

1.1) Basic Steps

• R can be accessed by clicking an icon or entering the command “R” at the system command line, also refered to as Terminal

• This produces a console window or causes R to start up as an interactive program at the current terminal window

• R works fundamentally by a question-and-answer model: enter a line with a command and press Enter

• Then the program does something relevant

1.1) Basic Steps (continued)

• In this course, we will use RStudio and a file format called R Markdown, which allows us to code using not only R, but bash and Python, two other languages we may refer to as the course progresses

1.2) Library ISwR

• This notebook used the book Introductory Statistics with R, by Peter Dalgaard as a reference

• For the book, R library ISwR (Introductory Statistics with R) can be freely downloaded

• All examples in the book used as reference should run provided that ISwR library is not only installed by also loaded into the current search path

1.2) Library ISwR (continued)

• Library can be installed and loaded by typing the following command into an R chunk

install.packages("ISwR")
library("ISwR")

1.3) Plot Random Numbers

• For a first impression of what R can do, let´s try plotting a graph

• Need to insert the R chunk and use the plot function

1.3) Plot Random Numbers (continued)

plot(rnorm(1000))

1.4) A Potent Calculator

• R can process simple and complex arithmetic expression and produce a result for the user

2 + 2

## [1] 4

• R can also be used to do other standard calculations. Here is how to calculate e to the power of -2

exp(-2)

## [1] 0.1353353

1.4) A Potent Calculator (continued)

• Other than the R chunks, these calculations can be made using the RStudio Console

• In RStusio, when using the R Markdown format (.Rmd), we can insert R, Bash (terminal) and Python chunks

• Proceed to illustrate that in the RStudio IDE

1.5) Assignments

• Assignments are made based on the necessity to store the results of calculations and use these results in downstream processing steps in an entire algorithm or pipeline

• Like other languages, R has symbolic variables: names that can be used to represent values

• To assign the value 2 to variable x, we can enter the following command

x <- 2

• The character <- is called the assignment operator

1.5) Assignments (continued)

• There is no immediate visible result, but from now on, x has the value 2 and can be used in subsequent arithmetic operations

• We can “ask” R which value is stores in the x variable

x

## [1] 2

1.6) Operations after assignment of variable

• Below, our variable x, is used to perform other calculations

x

## [1] 2

• Addition

x + x

## [1] 4

1.6) Operations after assignment of variable (continued)

• Multiplication

5*x

## [1] 10

• Potentiation

x^3 

## [1] 8

1.7) Vectorized Arithmetic

• It is not useful to use one number at a time to run statistics

• One strenght of R is that it can handle entire data vectors as single objects

• A data vector is an array of numbers and a vector variable can be constructed like this

weight <- c(60, 72, 57, 90, 95, 72)

## To look at the vector variable, just type its name again
weight

## [1] 60 72 57 90 95 72

1.7) Vectorized Arithmetic (continued)

• You can do calculations with vectors just like ordinary numbers, so long as they have the same length

• One exception to this rule that we will see will be when we use the mean of weigths of persons (represented by xbar)

• In that case, the mean will be one single number, which will be subtracted from each sample value

1.7) Vectorized Arithmetic (continued)

• Suppose the weight vector indicates the weight of men in kilograms

• One simple formula to indicate whether a person is obese or not, is the body mass index (BMI)

• BMI is calculated by dividing the person´s weight by the square of their height, in meters

1.7) Vectorized Arithmetic (continued)

• Therefore, in R, we need to have a vector with the height values to calculate the bmi vector, containing the body-mass index for the individuals indicated in the weight vector

height <- c(1.75, 1.80, 1.65, 1.90, 1.74, 1.91)
bmi <- weight/height^2
bmi

## [1] 19.59184 22.22222 20.93664 24.93075 31.37799 19.73630

1.8) Calculate the Mean of the variable weight

• The mean is calculated by the sum of the observations divided by the total number of observations

\(\overline{x}\) = \(\sum x_i\) /n

1.8) Calculate the Mean of the variable weight (continued)

• Let´s calculate the mean of the variable weight

sum(weight)

## [1] 446

sum(weight)/length(weight)

## [1] 74.33333

1.9) Calculate the Standard-Deviation of the variable weight

• Standard-deviation can be calculated with the following equation

\[ SD = \sqrt{(\sum (x_i - \overline{x})^2)/(n-1)}\]

1.9) Calculate the Standard-Deviation of the variable weight (continued)

• xbar, the mean of variable weight, can be calculated using the sum and length of variable weight

xbar <- sum(weight)/length(weight)
xbar

## [1] 74.33333

1.9) Calculate the Standard-Deviation of the variable weight (continued)

• Now we can calculate the difference of each replicate in the weight variable and the mean of the weight variable, one by one

weight - xbar

## [1] -14.333333  -2.333333 -17.333333  15.666667  20.666667  -2.333333

1.9) Calculate the Standard-Deviation of the variable weight (continued)

• Notice how R uses xbar, which has length one, to calculate the new weight - xbar data vector

• xbar is recycled and subracted from every element in the weight variable (weight data vector)

1.10) Calculation of the Standard Deviation

• Calculate the squared deviations

(weight - xbar)^2

## [1] 205.444444   5.444444 300.444444 245.444444 427.111111   5.444444

• Calculate the sum of squared deviations

sum((weight - xbar)^2)

## [1] 1189.333

Calculate the standard deviation

sqrt(
  sum(
    (weight - xbar)^2/
      (length(weight)-1)
)
)

## [1] 15.42293

1.11) Standard Statistical Procedures

• It is a standard medical practice to access whether a person is obese or not using validated scientific criteria

• As a simple procedure to show this concept, let’s assume that an individual with a normal weight should have a BMI in the range 20-25

• We want to know if our data deviates from the normal range of BMI

• In R, this can be done using a statistical test called t-test

• You do not need to understand what a t-test is, just remember that is is used to evaluate the distribution of sample values compared to the normal distribution

• You can use a one-sample t-test to assess whether the six persons’ BMI can be assumed to have mean 22.5 given that they come from a normal distribution

• You can do that using the function t.test

1.11) Standard Statistical Procedures: t-test

t.test(
  bmi,
  mu = 22.5
)

## 
##  One Sample t-test
## 
## data:  bmi
## t = 0.34488, df = 5, p-value = 0.7442
## alternative hypothesis: true mean is not equal to 22.5
## 95 percent confidence interval:
##  18.41734 27.84791
## sample estimates:
## mean of x 
##  23.13262

1.12) Plot Graphics

• Let’s now plot a scatterplot of the height and weight of individuals

1.12) Plot Graphics Modifying the plotting character

• You will frequently want to modify drawing of your graphs in various ways

• One way is usig the parameter “plotting character”, pch

1.13) Plot an expected Line for weights at BMI of 22.5

• The term for weight at BMI of 22.5 is:

22.5*(height)^2

• This term can be used to compute the line of expected weights at a BMI of 22.5 using the lines() function

1.13) Plot an expected Line for weights at BMI of 22.5 (continued)

• As a note, we can’t use the lines() function without first creating a plot in R.

plot(height, weight, pch =2)
hh <- c(1.65, 1.70, 1.75, 1.80, 1.85, 1.90)
lines(hh, 22.5 * (hh)^2)

1.14) Vectors

• The weight and height vectors are called numeric vectors

• Besides numeric vectors, there are numeric and character vectors

• In the next chunk, we access the iris data, and look at a summary of the dataset

data(iris)
summary(iris)

##   Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
##  Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  
##  1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  
##  Median :5.800   Median :3.000   Median :4.350   Median :1.300  
##  Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  
##  3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  
##  Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  
##        Species  
##  setosa    :50  
##  versicolor:50  
##  virginica :50  
##                 
##                 
## 

2.1) The iris data-frame

• Another form to look at the iris data-frame is typing its name

iris

##     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 1            5.1         3.5          1.4         0.2     setosa
## 2            4.9         3.0          1.4         0.2     setosa
## 3            4.7         3.2          1.3         0.2     setosa
## 4            4.6         3.1          1.5         0.2     setosa
## 5            5.0         3.6          1.4         0.2     setosa
## 6            5.4         3.9          1.7         0.4     setosa
## 7            4.6         3.4          1.4         0.3     setosa
## 8            5.0         3.4          1.5         0.2     setosa
## 9            4.4         2.9          1.4         0.2     setosa
## 10           4.9         3.1          1.5         0.1     setosa
## 11           5.4         3.7          1.5         0.2     setosa
## 12           4.8         3.4          1.6         0.2     setosa
## 13           4.8         3.0          1.4         0.1     setosa
## 14           4.3         3.0          1.1         0.1     setosa
## 15           5.8         4.0          1.2         0.2     setosa
## 16           5.7         4.4          1.5         0.4     setosa
## 17           5.4         3.9          1.3         0.4     setosa
## 18           5.1         3.5          1.4         0.3     setosa
## 19           5.7         3.8          1.7         0.3     setosa
## 20           5.1         3.8          1.5         0.3     setosa
## 21           5.4         3.4          1.7         0.2     setosa
## 22           5.1         3.7          1.5         0.4     setosa
## 23           4.6         3.6          1.0         0.2     setosa
## 24           5.1         3.3          1.7         0.5     setosa
## 25           4.8         3.4          1.9         0.2     setosa
## 26           5.0         3.0          1.6         0.2     setosa
## 27           5.0         3.4          1.6         0.4     setosa
## 28           5.2         3.5          1.5         0.2     setosa
## 29           5.2         3.4          1.4         0.2     setosa
## 30           4.7         3.2          1.6         0.2     setosa
## 31           4.8         3.1          1.6         0.2     setosa
## 32           5.4         3.4          1.5         0.4     setosa
## 33           5.2         4.1          1.5         0.1     setosa
## 34           5.5         4.2          1.4         0.2     setosa
## 35           4.9         3.1          1.5         0.2     setosa
## 36           5.0         3.2          1.2         0.2     setosa
## 37           5.5         3.5          1.3         0.2     setosa
## 38           4.9         3.6          1.4         0.1     setosa
## 39           4.4         3.0          1.3         0.2     setosa
## 40           5.1         3.4          1.5         0.2     setosa
## 41           5.0         3.5          1.3         0.3     setosa
## 42           4.5         2.3          1.3         0.3     setosa
## 43           4.4         3.2          1.3         0.2     setosa
## 44           5.0         3.5          1.6         0.6     setosa
## 45           5.1         3.8          1.9         0.4     setosa
## 46           4.8         3.0          1.4         0.3     setosa
## 47           5.1         3.8          1.6         0.2     setosa
## 48           4.6         3.2          1.4         0.2     setosa
## 49           5.3         3.7          1.5         0.2     setosa
## 50           5.0         3.3          1.4         0.2     setosa
## 51           7.0         3.2          4.7         1.4 versicolor
## 52           6.4         3.2          4.5         1.5 versicolor
## 53           6.9         3.1          4.9         1.5 versicolor
## 54           5.5         2.3          4.0         1.3 versicolor
## 55           6.5         2.8          4.6         1.5 versicolor
## 56           5.7         2.8          4.5         1.3 versicolor
## 57           6.3         3.3          4.7         1.6 versicolor
## 58           4.9         2.4          3.3         1.0 versicolor
## 59           6.6         2.9          4.6         1.3 versicolor
## 60           5.2         2.7          3.9         1.4 versicolor
## 61           5.0         2.0          3.5         1.0 versicolor
## 62           5.9         3.0          4.2         1.5 versicolor
## 63           6.0         2.2          4.0         1.0 versicolor
## 64           6.1         2.9          4.7         1.4 versicolor
## 65           5.6         2.9          3.6         1.3 versicolor
## 66           6.7         3.1          4.4         1.4 versicolor
## 67           5.6         3.0          4.5         1.5 versicolor
## 68           5.8         2.7          4.1         1.0 versicolor
## 69           6.2         2.2          4.5         1.5 versicolor
## 70           5.6         2.5          3.9         1.1 versicolor
## 71           5.9         3.2          4.8         1.8 versicolor
## 72           6.1         2.8          4.0         1.3 versicolor
## 73           6.3         2.5          4.9         1.5 versicolor
## 74           6.1         2.8          4.7         1.2 versicolor
## 75           6.4         2.9          4.3         1.3 versicolor
## 76           6.6         3.0          4.4         1.4 versicolor
## 77           6.8         2.8          4.8         1.4 versicolor
## 78           6.7         3.0          5.0         1.7 versicolor
## 79           6.0         2.9          4.5         1.5 versicolor
## 80           5.7         2.6          3.5         1.0 versicolor
## 81           5.5         2.4          3.8         1.1 versicolor
## 82           5.5         2.4          3.7         1.0 versicolor
## 83           5.8         2.7          3.9         1.2 versicolor
## 84           6.0         2.7          5.1         1.6 versicolor
## 85           5.4         3.0          4.5         1.5 versicolor
## 86           6.0         3.4          4.5         1.6 versicolor
## 87           6.7         3.1          4.7         1.5 versicolor
## 88           6.3         2.3          4.4         1.3 versicolor
## 89           5.6         3.0          4.1         1.3 versicolor
## 90           5.5         2.5          4.0         1.3 versicolor
## 91           5.5         2.6          4.4         1.2 versicolor
## 92           6.1         3.0          4.6         1.4 versicolor
## 93           5.8         2.6          4.0         1.2 versicolor
## 94           5.0         2.3          3.3         1.0 versicolor
## 95           5.6         2.7          4.2         1.3 versicolor
## 96           5.7         3.0          4.2         1.2 versicolor
## 97           5.7         2.9          4.2         1.3 versicolor
## 98           6.2         2.9          4.3         1.3 versicolor
## 99           5.1         2.5          3.0         1.1 versicolor
## 100          5.7         2.8          4.1         1.3 versicolor
## 101          6.3         3.3          6.0         2.5  virginica
## 102          5.8         2.7          5.1         1.9  virginica
## 103          7.1         3.0          5.9         2.1  virginica
## 104          6.3         2.9          5.6         1.8  virginica
## 105          6.5         3.0          5.8         2.2  virginica
## 106          7.6         3.0          6.6         2.1  virginica
## 107          4.9         2.5          4.5         1.7  virginica
## 108          7.3         2.9          6.3         1.8  virginica
## 109          6.7         2.5          5.8         1.8  virginica
## 110          7.2         3.6          6.1         2.5  virginica
## 111          6.5         3.2          5.1         2.0  virginica
## 112          6.4         2.7          5.3         1.9  virginica
## 113          6.8         3.0          5.5         2.1  virginica
## 114          5.7         2.5          5.0         2.0  virginica
## 115          5.8         2.8          5.1         2.4  virginica
## 116          6.4         3.2          5.3         2.3  virginica
## 117          6.5         3.0          5.5         1.8  virginica
## 118          7.7         3.8          6.7         2.2  virginica
## 119          7.7         2.6          6.9         2.3  virginica
## 120          6.0         2.2          5.0         1.5  virginica
## 121          6.9         3.2          5.7         2.3  virginica
## 122          5.6         2.8          4.9         2.0  virginica
## 123          7.7         2.8          6.7         2.0  virginica
## 124          6.3         2.7          4.9         1.8  virginica
## 125          6.7         3.3          5.7         2.1  virginica
## 126          7.2         3.2          6.0         1.8  virginica
## 127          6.2         2.8          4.8         1.8  virginica
## 128          6.1         3.0          4.9         1.8  virginica
## 129          6.4         2.8          5.6         2.1  virginica
## 130          7.2         3.0          5.8         1.6  virginica
## 131          7.4         2.8          6.1         1.9  virginica
## 132          7.9         3.8          6.4         2.0  virginica
## 133          6.4         2.8          5.6         2.2  virginica
## 134          6.3         2.8          5.1         1.5  virginica
## 135          6.1         2.6          5.6         1.4  virginica
## 136          7.7         3.0          6.1         2.3  virginica
## 137          6.3         3.4          5.6         2.4  virginica
## 138          6.4         3.1          5.5         1.8  virginica
## 139          6.0         3.0          4.8         1.8  virginica
## 140          6.9         3.1          5.4         2.1  virginica
## 141          6.7         3.1          5.6         2.4  virginica
## 142          6.9         3.1          5.1         2.3  virginica
## 143          5.8         2.7          5.1         1.9  virginica
## 144          6.8         3.2          5.9         2.3  virginica
## 145          6.7         3.3          5.7         2.5  virginica
## 146          6.7         3.0          5.2         2.3  virginica
## 147          6.3         2.5          5.0         1.9  virginica
## 148          6.5         3.0          5.2         2.0  virginica
## 149          6.2         3.4          5.4         2.3  virginica
## 150          5.9         3.0          5.1         1.8  virginica

3.1) More Visualization of the iris dataset

We need to cover these basic R functions:

• dim()
• head()
• View()
• class()
• str()

3.2) Visualize iris dataset with basic R functions

• head

head(iris, n = 10)

##    Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1           5.1         3.5          1.4         0.2  setosa
## 2           4.9         3.0          1.4         0.2  setosa
## 3           4.7         3.2          1.3         0.2  setosa
## 4           4.6         3.1          1.5         0.2  setosa
## 5           5.0         3.6          1.4         0.2  setosa
## 6           5.4         3.9          1.7         0.4  setosa
## 7           4.6         3.4          1.4         0.3  setosa
## 8           5.0         3.4          1.5         0.2  setosa
## 9           4.4         2.9          1.4         0.2  setosa
## 10          4.9         3.1          1.5         0.1  setosa

• number of columns and rows

dim(iris)

## [1] 150   5

• the class() function

class(iris)

## [1] "data.frame"

4) More Visualization

4.1) Scatterplot

plot(data=iris, iris$Sepal.Length, iris$Sepal.Width) ## R will complain about this command

## Warning in plot.window(...): "data" is not a graphical parameter

## Warning in plot.xy(xy, type, ...): "data" is not a graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "data" is not a
## graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "data" is not a
## graphical parameter

## Warning in box(...): "data" is not a graphical parameter

## Warning in title(...): "data" is not a graphical parameter

plot(iris$Sepal.Length, iris$Sepal.Width) ## According to the error, this was plotted using a different synthax

4.1) Scatterplot

Plot without warning and message

plot(data=iris, iris$Sepal.Length, iris$Sepal.Width) ## R will complain about this command

plot(iris$Sepal.Length, iris$Sepal.Width) ## According to the error, this was plotted using a different synthax

4.2) Boxplot

boxplot(data=iris, iris$Sepal.Length, iris$Sepal.Width)

5) Data Visualization with specialized libraries

• In R, there are packages designed with the purpose of making good-looking graphics. This is the case with the ggplot2. The chunk below installs the ggplot2 library, loads the library into the R environment and then plots the data present in the iris data-frame.

• You can uncomment the installation line if you need to install it

5.1) Ggplot2

#install.packages("ggplot2")
library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.1.2

ggplot(data=iris, aes(x=Sepal.Length, y=Sepal.Width, color=Species)) + geom_point(size=4)

In our activities to visualize human genomic data, we will use a library called qqman, to visualize the biological association, through a plot known as the Manhattan plot.

5.2) Visualizing GWAS

• The simplest definition of a GWAS is the statistical or significant association between a phenotype (trait) and a genotype. This association can also be called biological association.

• Information about association of SNPs with Huntington’s Disease can be found at the Chaves 2019 Huntington’s disease paper

5.3.1) Package installation

• We need to install and load package qqman

## install.packages("qqman")
library(qqman)

## 

## For example usage please run: vignette('qqman')

## 

## Citation appreciated but not required:

## Turner, (2018). qqman: an R package for visualizing GWAS results using Q-Q and manhattan plots. Journal of Open Source Software, 3(25), 731, https://doi.org/10.21105/joss.00731.

## 

5.3.1) Package installation

• After, we load data-frame to be visualized

• Exact location of text file in your system needs to be determined

GWAS_TABLE <- read.table("../data/chr4.txt", 
                         sep = " ",
                         header = T)

5.3.2) Get information about object with head()

• Use head() function to inspect the data-frame just loaded

head(GWAS_TABLE, n = 10)

##    CHR         SNP     BP         P
## 1    4 chr4:128096 128096 0.0133500
## 2    4 chr4:516586 516586 0.0076260
## 3    4 chr4:523979 523979 0.0024960
## 4    4 chr4:527217 527217 0.0217400
## 5    4 chr4:566177 566177 0.0008988
## 6    4 chr4:578679 578679 0.0162100
## 7    4 chr4:578790 578790 0.0103700
## 8    4 chr4:579307 579307 0.0334600
## 9    4 chr4:580259 580259 0.0190400
## 10   4 chr4:585318 585318 0.0317600

5.3.3) Plotting GWAS data-frame

• In this section we use functions plot() and boxplot() to visualize data-frame

• In the y access, we see genomic coordinates and in the x access, p-valoues of the biological association

• Note that depending on the synthax used for plotting, R may complain

• Comments not turned off

plot(data=GWAS_TABLE, GWAS_TABLE$BP, GWAS_TABLE$P) ## R complains

## Warning in plot.window(...): "data" is not a graphical parameter

## Warning in plot.xy(xy, type, ...): "data" is not a graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "data" is not a
## graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "data" is not a
## graphical parameter

## Warning in box(...): "data" is not a graphical parameter

## Warning in title(...): "data" is not a graphical parameter

• Turn off comments

plot(data=GWAS_TABLE, GWAS_TABLE$BP, GWAS_TABLE$P) ## R complains

5.3.4) Plotting GWAS data-frame

plot(GWAS_TABLE$BP, GWAS_TABLE$P) ## R does not complain

5.4) Boxplot

• Boxplot

boxplot(data=GWAS_TABLE, GWAS_TABLE$BP, GWAS_TABLE$P)

5.5) Boxplot

• Compare the chromosomal coordinates and the values of the p-values in the boxplot above

• The chunk below allows one to ommit NA values in data-frame

GWAS_TABLE_Ommit <- na.omit(GWAS_TABLE)

A seguir, criamos uma variável que armazena as posições das SNPs a serem realçadas em verde no Manhattan plot. Estas SNPs são mutações biológica e estatisticamente associadas à Doença de Huntington no gene de uma sortilina, localizada em proximidade física ao gene da proteína huntingtina mutada, a qual é a causadora medeliana (segue as leis de segregação genética de Mendel) da Doença de Huntington.

5.6) Create vector to highlight genome coordinates in Manhattan plot

SNP_HIGHLIGHT <- c("chr4:3043512","chr4:3043513","chr4:3048207","chr4:3224216",
                   "chr4:3231772","chr4:3233844","chr4:3235081","chr4:3235084",
                   "chr4:3236881","chr4:3236883","chr4:3241845","chr4:3243804",
                   "chr4:3263138","chr4:3265130","chr4:3265710","chr4:3314646",
                   "chr4:3380088","chr4:3409359","chr4:3411110","chr4:3415336",
                   "chr4:3415378","chr4:3438643","chr4:3446091","chr4:3449886",
                   "chr4:3473066","chr4:3476809","chr4:3480439","chr4:3487151",
                   "chr4:3496058","chr4:3496110","chr4:3506933","chr4:3508752",
                   "chr4:3510957","chr4:3512690","chr4:3517746","chr4:3518190",
                   "chr4:3529671","chr4:3532327","chr4:3533066","chr4:3746133",
                   "chr4:3747842","chr4:3748134","chr4:3765305","chr4:3765336",
                   "chr4:3944253","chr4:3944752","chr4:3944888","chr4:3946166",
                   "chr4:3946175","chr4:3969218","chr4:4051294","chr4:4076788",
                   "chr4:4103104","chr4:4103105","chr4:4109198","chr4:4109210",
                   "chr4:4240627","chr4:4242705","chr4:4243668","chr4:4245210",
                   "chr4:4245510","chr4:4245513","chr4:4245591","chr4:4245926",
                   "chr4:4245929","chr4:4246109","chr4:4246433","chr4:4246453",
                   "chr4:4246457","chr4:4246497","chr4:4249414","chr4:4249415",
                   "chr4:4249484","chr4:4271623","chr4:4275306","chr4:4304749",
                   "chr4:4318931","chr4:4318970","chr4:4319564","chr4:4319728",
                   "chr4:4319750","chr4:4322078","chr4:4709657","chr4:4732282",
                   "chr4:4789635","chr4:4822960","chr4:4824890","chr4:4825092",
                   "chr4:4825180","chr4:4865316","chr4:4865321","chr4:5018702",
                   "chr4:5812778","chr4:5814082","chr4:5833660","chr4:5833899",
                   "chr4:5835541","chr4:5851205","chr4:5862752","chr4:5862938",
                   "chr4:5862943","chr4:5901873","chr4:5905499","chr4:5906287",
                   "chr4:6018891","chr4:6019046","chr4:6020190","chr4:6020367",
                   "chr4:6025638","chr4:6025656","chr4:6025766","chr4:6026058",
                   "chr4:6083488","chr4:6204935","chr4:6235553","chr4:6237142",
                   "chr4:6238466","chr4:6239906","chr4:6240929","chr4:6245022",
                   "chr4:6245618","chr4:6245732","chr4:6245915","chr4:6246075",
                   "chr4:6246373","chr4:6246959","chr4:6290594","chr4:6292020",
                   "chr4:6294095","chr4:6298375","chr4:6316092","chr4:6321396",
                   "chr4:6324647","chr4:6324785","chr4:6327669","chr4:6328354",
                   "chr4:6328507","chr4:6333130","chr4:6333559","chr4:6333669",
                   "chr4:6335966","chr4:6435341","chr4:6435486","chr4:6435926",
                   "chr4:6437191","chr4:6437197","chr4:6457121","chr4:6457131",
                   "chr4:6457132","chr4:6568390","chr4:6570032","chr4:6570768",
                   "chr4:6596360","chr4:6613252","chr4:6613462","chr4:6620991",
                   "chr4:6624771","chr4:6626154","chr4:6641969","chr4:6642090",
                   "chr4:6644466","chr4:6644467","chr4:6644468","chr4:6647889",
                   "chr4:6648300","chr4:6662665","chr4:6663319","chr4:6663715",
                   "chr4:6674554","chr4:6678553","chr4:6678599","chr4:6690535",
                   "chr4:6698664","chr4:6698667","chr4:6698706","chr4:6720572",
                   "chr4:6911679","chr4:6985889","chr4:6987394","chr4:7002344",
                   "chr4:7004495","chr4:7004506","chr4:7005196","chr4:7005199",
                   "chr4:7024077","chr4:7024398","chr4:7029430","chr4:7031064",
                   "chr4:7044357","chr4:7044380","chr4:7048842","chr4:7052115",
                   "chr4:7055253","chr4:7064243","chr4:7067765","chr4:7073187",
                   "chr4:7074027","chr4:7677967","chr4:7701947","chr4:7702795",
                   "chr4:7703505","chr4:7703807","chr4:7704795","chr4:7704818",
                   "chr4:7709703","chr4:7712150","chr4:7714490","chr4:7733843",
                   "chr4:7735162","chr4:7735164","chr4:7736103","chr4:7736112")

5.7) Biological Association Visualization: Manhattan Plot

• Finally, we plot the Manhattanh plot graph

manhattan(GWAS_TABLE_Ommit, 
          highlight = SNP_HIGHLIGHT, 
          annotateTop = T, 
          annotatePval = 0.20, 
          genomewideline = -log10(0.0001))

6) References

7) Session Info

sessionInfo()

## R version 4.1.1 (2021-08-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Big Sur 10.16
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] qqman_0.1.8   ggplot2_3.4.2
## 
## loaded via a namespace (and not attached):
##  [1] bslib_0.5.0      compiler_4.1.1   pillar_1.9.0     jquerylib_0.1.4 
##  [5] highr_0.10       tools_4.1.1      digest_0.6.32    jsonlite_1.8.7  
##  [9] evaluate_0.21    lifecycle_1.0.3  tibble_3.2.1     gtable_0.3.3    
## [13] pkgconfig_2.0.3  rlang_1.1.1      cli_3.6.1        rstudioapi_0.14 
## [17] yaml_2.3.7       xfun_0.39        fastmap_1.1.1    withr_2.5.0     
## [21] dplyr_1.1.2      knitr_1.43       generics_0.1.3   sass_0.4.6      
## [25] vctrs_0.6.3      revealjs_0.9     grid_4.1.1       tidyselect_1.2.0
## [29] calibrate_1.7.7  glue_1.6.2       R6_2.5.1         fansi_1.0.4     
## [33] rmarkdown_2.22   farver_2.1.1     magrittr_2.0.3   MASS_7.3-60     
## [37] scales_1.2.1     htmltools_0.5.5  colorspace_2.1-0 labeling_0.4.2  
## [41] utf8_1.2.3       munsell_0.5.0    cachem_1.0.8