+
+
+
+
+
+Assignment 1
+You only need to write lines of code for each question. When answering questions that ask you to identify or interpret something, the length of your response doesn’t matter. For example, if the answer is just ‘yes,’ ‘no,’ or a number, you can just give that answer without adding anything else.
+We will go through comparable code and concepts in the live learning session. If you run into trouble, start by using the help help() function in R, to get information about the datasets and function in question. The internet is also a great resource when coding (though note that no outside searches are required by the assignment!). If you do incorporate code from the internet, please cite the source within your code (providing a URL is sufficient).
+Please bring questions that you cannot work out on your own to office hours, work periods or share with your peers on Slack. We will work with you through the issue.
+You will need to install PLINK and run the analyses. Please follow the OS-specific setup guide in SETUP.md . PLINK is a free, open-source whole genome association analysis toolset, designed to perform a range of basic, large-scale analyses in a computationally efficient manner.
+
+Question 1: Data inspection
+Before fitting any models, it is essential to understand the data. Use R or bash code to answer the following questions about the gwa.qc.A1.fam, gwa.qc.A1.bim, and gwa.qc.A1.bed files, available at the following Google Drive link: https://drive.google.com/drive/folders/11meVqGCY5yAyI1fh-fAlMEXQt0VmRGuz?usp=drive_link . Please download all three files from this link and place them in 02_activities/data/.
+
+
fam_file <- "../data/gwa.qc.A1.fam"
+ bim_file <- "../data/gwa.qc.A1.bim"
+ bed_file <- "../data/gwa.qc.A1.bed"
+
+
+ fam_data <- read.table (fam_file, header = FALSE )
+cat ("Number of samples:" , nrow (fam_data), " \n " )
+
+
Number of samples: 4000
+
+
+
+
V1 V2 V3 V4 V5 V6
+1 0 A2001 0 0 1 -0.6944381
+2 1 A2002 0 0 1 1.8538454
+3 2 A2003 0 0 1 2.0826368
+4 3 A2004 0 0 1 2.7387147
+5 4 A2005 0 0 1 1.3411404
+6 5 A2006 0 0 1 0.4167786
+
+
bim_data <- read.table (bim_file, header = FALSE )
+cat ("Number of SNPs:" , nrow (bim_data), " \n " )
+
+
Number of SNPs: 101083
+
+
+
+
V1 V2 V3 V4 V5 V6
+1 1 rs3737728 0 1011278 A G
+2 1 rs1320565 0 1109721 T C
+3 1 rs3813199 0 1148140 A G
+4 1 rs11804831 0 1184667 C T
+5 1 rs3766178 0 1468043 C T
+6 1 rs3128342 0 1476697 A C
+
+
+
+
Loading required package: survival
+
+
+
Loading required package: Matrix
+
+
plink_data <- read.plink (
+ bed = bed_file,
+ bim = bim_file, # pass path, NOT the data frame
+ fam = fam_file # pass path, NOT the data frame
+ )
+
+ geno_matrix <- plink_data$ genotypes
+cat ("Genotype matrix dimensions (samples x SNPs):" , dim (geno_matrix), " \n " )
+
+
Genotype matrix dimensions (samples x SNPs): 4000 101083
+
+
+
+Read the .fam file. How many samples does the dataset contain?
+
+
+
ffam_file <- "../data/gwa.qc.A1.fam"
+ bim_file <- "../data/gwa.qc.A1.bim"
+ bed_file <- "../data/gwa.qc.A1.bed"
+
+
+
# Read the data file
+ data <- read.table ("../data/gwa.qc.A1.fam" , header = FALSE )
+
+# Display number of rows
+nrow (data)
+
+
# Display first few rows
+head (data)
+
+
V1 V2 V3 V4 V5 V6
+1 0 A2001 0 0 1 -0.6944381
+2 1 A2002 0 0 1 1.8538454
+3 2 A2003 0 0 1 2.0826368
+4 3 A2004 0 0 1 2.7387147
+5 4 A2005 0 0 1 1.3411404
+6 5 A2006 0 0 1 0.4167786
+
+
+
+(ii) What is the 'variable type' of the response variable (i.e.Continuous or binary)?
+
+
+
data <- read.table (fam_file, header = FALSE )
+
+
+
+
+
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+ 1
+
+
+
+Read the .bim file. How many SNPs does the dataset contain?
+
+
+
# Read the .bim file
+ bbim_data <- read.table (bim_file, header = FALSE )
+# Number of SNPs
+ num_snps <- nrow (bim_data)
+cat ("The dataset contains" , num_snps, "SNPs. \n " )
+
+
The dataset contains 101083 SNPs.
+
+
+
+
+Question 2: Allele Frequency Estimation
+
+Load the genotype matrix for SNPs rs1861, rs3813199, rs3128342, and rs11804831 using additive coding. What are the allele frequencies (AFs) for these four SNPs?
+
+
+
# Load required library
+library (snpStats)
+
+# Read PLINK files
+ plink_data <- read.plink (
+ bed = bed_file,
+ bim = bim_file,
+ fam = fam_file
+ )
+
+# Extract genotype matrix
+ geno_matrix <- plink_data$ genotypes
+
+# Subset SNPs of interest
+ snps_of_interest <- c ("rs1861" , "rs3813199" , "rs3128342" , "rs11804831" )
+ geno_sub <- geno_matrix[, snps_of_interest]
+
+# Convert to numeric (0,1,2)
+ geno_numeric <- as (geno_sub, "numeric" )
+
+# Function to calculate allele frequency
+ calc_af <- function (snp_vector) {
+ sum (snp_vector, na.rm = TRUE ) / (2 * sum (! is.na (snp_vector)))
+ }
+
+# Compute allele frequencies
+ allele_freqs <- apply (geno_numeric, 2 , calc_af)
+
+# Print results
+ allele_freqs
+
+
rs1861 rs3813199 rs3128342 rs11804831
+ 0.9460141 0.9430874 0.6948789 0.8456588
+
+
+
+What are the minor allele frequencies (MAFs) for these four SNPs?
+
+
+
# Function to calculate minor allele frequency
+ calc_maf <- function (snp_vector) {
+ af <- sum (snp_vector, na.rm = TRUE ) / (2 * sum (! is.na (snp_vector))) # allele freq
+ maf <- min (af, 1 - af) # minor allele freq
+ return (maf)
+ }
+
+# Compute MAFs for all SNPs in geno_numeric
+ maf_values <- apply (geno_numeric, 2 , calc_maf)
+
+# Print results
+ maf_values
+
+
rs1861 rs3813199 rs3128342 rs11804831
+0.05398587 0.05691262 0.30512109 0.15434124
+
+
+
+
+Question 3: Hardy–Weinberg Equilibrium (HWE) Test
+
+Conduct the Hardy–Weinberg Equilibrium (HWE) test for all SNPs in the .bim file. Then, load the file containing the HWE p-value results and display the first few rows of the resulting data frame.
+
+
+
hwe_results <- read.table ("../data/gwa_hwe.hwe" , header = TRUE )
+head (hwe_results)
+
+
CHR SNP TEST A1 A2 GENO O.HET. E.HET. P
+1 1 rs3737728 ALL(QT) A G 428/1841/1713 0.4623 0.4479 0.04379
+2 1 rs1320565 ALL(QT) T C 19/589/3368 0.1481 0.1453 0.27340
+3 1 rs3813199 ALL(QT) A G 12/428/3531 0.1078 0.1073 1.00000
+4 1 rs11804831 ALL(QT) C T 81/1061/2820 0.2678 0.2610 0.11340
+5 1 rs3766178 ALL(QT) C T 214/1378/2391 0.3460 0.3506 0.41590
+6 1 rs3128342 ALL(QT) A C 382/1655/1927 0.4175 0.4240 0.33030
+
+
+
+What are the HWE p-values for SNPs rs1861, rs3813199, rs3128342, and rs11804831?
+
+
+
+
+
+Attaching package: 'dplyr'
+
+
+
The following objects are masked from 'package:stats':
+
+ filter, lag
+
+
+
The following objects are masked from 'package:base':
+
+ intersect, setdiff, setequal, union
+
+
# Now filter SNPs
+ snps_of_interest <- c ("rs1861" , "rs3813199" , "rs3128342" , "rs11804831" )
+
+ hwe_results %>%
+ filter (SNP %in% snps_of_interest) %>%
+ select (SNP, P)
+
+
SNP P
+1 rs3813199 1.0000
+2 rs11804831 0.1134
+3 rs3128342 0.3303
+4 rs1861 0.2747
+
+
+
+
+Question 4: Genetic Association Test
+
+Conduct a linear regression to test the association between SNP rs1861 and the phenotype. What is the p-value?
+
+
+
# Read in the phenotype from .fam
+ fam_data <- read.table ("../data/gwa.qc.A1.fam" , header = FALSE )
+ geno_matrix <- as (geno_matrix, "numeric" ) # make sure numeric
+
+# Add phenotype to genotype subset
+ geno_df <- as.data.frame (geno_numeric)
+ geno_df$ PHENOTYPE <- fam_data$ V6 # column 6 is phenotype
+
+# Fit linear regression for rs1861
+ model <- lm (PHENOTYPE ~ rs1861, data = geno_df)
+
+# Summary to get p-value
+summary (model)$ coefficients
+
+
Estimate Std. Error t value Pr(>|t|)
+(Intercept) 0.05238114 0.09486224 0.5521811 5.808554e-01
+rs1861 0.97382401 0.04942584 19.7027317 1.617463e-82
+
+
# Extract p-value for rs1861
+ p_value <- summary (model)$ coefficients["rs1861" , "Pr(>|t|)" ]
+
+# Print it
+cat ("SNP: rs1861 \n Linear regression p-value:" , p_value, " \n " )
+
+
SNP: rs1861
+Linear regression p-value: 1.617463e-82
+
+
+
+How would you interpret the beta coefficient from this regression?
+
+
+
summary (model)$ coefficients
+
+
Estimate Std. Error t value Pr(>|t|)
+(Intercept) 0.05238114 0.09486224 0.5521811 5.808554e-01
+rs1861 0.97382401 0.04942584 19.7027317 1.617463e-82
+
+
# Extract beta (estimate) and p-value for rs1861
+ beta <- summary (model)$ coefficients["rs1861" , "Estimate" ]
+ pval <- summary (model)$ coefficients["rs1861" , "Pr(>|t|)" ]
+
+cat ("rs1861: Beta =" , beta, ", p-value =" , pval, " \n " )
+
+
rs1861: Beta = 0.973824 , p-value = 1.617463e-82
+
+
cat ("The beta coefficient for rs1861 is approximately 0.974, indicating that each additional copy of the minor allele is associated with an increase of about 0.974 units in the phenotype under an additive model. \n " )
+
+
The beta coefficient for rs1861 is approximately 0.974, indicating that each additional copy of the minor allele is associated with an increase of about 0.974 units in the phenotype under an additive model.
+
+
+
+Plot the scatterplot of phenotype versus the genotype of SNP rs1861. Add the regression line to the plot.
+
+
+
library (ggplot2)
+library (dplyr)
+
+# Create prediction data (smooth curve)
+ geno_range <- data.frame (
+ rs1861 = seq (0 , 2 , length.out = 100 )
+ )
+
+ geno_range$ predicted <- predict (model, newdata = geno_range)
+
+# Prepare count data (for point sizes)
+ count_data <- geno_df %>%
+ mutate (PHENOTYPE = round (PHENOTYPE)) %>%
+ filter (! is.na (rs1861), ! is.na (PHENOTYPE)) %>%
+ group_by (rs1861, PHENOTYPE) %>%
+ summarise (count = n (), .groups = "drop" )
+
+# Plot
+ p <- ggplot () +
+ geom_point (
+ data = count_data,
+ aes (x = rs1861, y = PHENOTYPE, size = count),
+ color = "blue"
+ ) +
+ geom_line (
+ data = geno_range,
+ aes (x = rs1861, y = predicted),
+ color = "red" ,
+ size = 1.2
+ ) +
+ scale_size_continuous (range = c (2 , 10 )) +
+ labs (
+ title = "Phenotype vs Genotype (rs1861)" ,
+ x = "Genotype (0/1/2)" ,
+ y = "Phenotype" ,
+ size = "Count"
+ ) +
+ coord_cartesian (xlim = c (- 0.5 , 2.5 ), ylim = c (- 0.1 , 1.1 )) +
+ theme_minimal ()
+
+
Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
+ℹ Please use `linewidth` instead.
+
+
+
+
+
+
+
+
+
+
+
+Convert the genotype coding for rs1861 to recessive coding.
+
+
+
# Create a new variable with recessive coding
+ geno_df$ rs1861_rec <- ifelse (geno_df$ rs1861 == 2 , 1 , 0 )
+
+# Check result
+table (geno_df$ rs1861, geno_df$ rs1861_rec)
+
+
+ 0 1
+ 0 15 0
+ 1 398 0
+ 2 0 3551
+
+
+
+Conduct a linear regression to test the association between the recessive-coded rs1861 and the phenotype. What is the p-value?
+
+
+
# Fit linear regression with recessive coding
+ model_rec <- lm (PHENOTYPE ~ rs1861_rec, data = geno_df)
+
+# Extract p-value
+ p_value_rec <- summary (model_rec)$ coefficients["rs1861_rec" , "Pr(>|t|)" ]
+
+# Print result
+cat ("Recessive model p-value:" , p_value_rec, " \n " )
+
+
Recessive model p-value: 2.729298e-79
+
+
+
+Plot the scatterplot of phenotype versus the recessive-coded genotype of rs1861. Add the regression line to the plot.
+
+
+
# Scatterplot
+plot (geno_df$ rs1861_rec, geno_df$ PHENOTYPE,
+ xlab = "Recessive Genotype (rs1861)" ,
+ ylab = "Phenotype" ,
+ main = "Phenotype vs Recessive rs1861" ,
+ pch = 16 )
+
+# Add regression line
+abline (model_rec, col = "red" , lwd = 2 )
+
+
+
+
+
+
+
+
+
+Which model fits better? Justify your answer.
+
+
+
# R-squared for additive model
+summary (model)$ r.squared
+
+
# R-squared for recessive model
+summary (model_rec)$ r.squared
+
+
# Compare model fits
+cat ("The additive model fits slightly better than the recessive model because its R-squared is higher (0.0892 vs 0.0858), even though both p-values are highly significant. \n " )
+
+
The additive model fits slightly better than the recessive model because its R-squared is higher (0.0892 vs 0.0858), even though both p-values are highly significant.
+
+
+
+
+Criteria
+
+
+
+
+
+
+
+
+
+
+
+Data Inspection
+Correct sample/SNP counts and variable type identified.
+Missing or incorrect counts or variable type.
+
+
+Allele Frequency Estimation
+Correct allele and minor allele frequencies computed.
+Frequencies missing or wrong.
+
+
+Hardy–Weinberg Equilibrium Test
+Correct PLINK command and p-value extraction in R.
+PLINK command or extraction incorrect/missing.
+
+
+Genetic Association Test
+Correct regressions, plots, coding, and interpretation.
+Regression, plots, or interpretation missing/incomplete.
+
+
+
+
+
+
+
+