Group 8: Project Task 6
2024-05-01
#Vaccine Efficacy in Real-World Scenarios: A Comparative Study of Covid-19 Outcomes in Vaccinated and Unvaccinated Individuals
# Comparing how well vaccines and booster shots protect against COVID-19 variants compared to being unvaccinated
# The objective of this project is to show the results of how effective the vaccine is as well as the boosters. #4Methods
#Describe Variables
#- Mortality Rate: the number of deaths in a given area or period, or from a particular cause.
#- Unvaccinated: not inoculated with a vaccine to provide immunity against a disease.
#- Vaccinated: treat (a person or animal) with a vaccine to produce immunity to a particular infectious disease or pathogen.
#-Vaccinated with booster: A booster is given when a person has completed their vaccine series and the immunity protection against the virus begins to decrease with time
#u1 = mean mortality rate of unvaccinated population
#u2 = mean mortality rate of vaccinated without booster population
#u3 = mean mortality rate of vaccinated with booster population
##Step 1 install and load required libraries
#install.packages(“readxl”)
library(readxl)
library(tidyr)## Warning: package 'tidyr' was built under R version 4.3.3mortality_rate <- read_excel(file.choose())
na.omit(mortality_rate)## # A tibble: 28 × 3
## Unvaccinated Vaccinatedwithbooster Vaccinatedwithoutbooster
## <dbl> <dbl> <dbl>
## 1 2.40 0 0.464
## 2 2.51 0.214 0.444
## 3 2.41 0.117 0.479
## 4 2.48 0.114 0.487
## 5 2.46 0.216 0.555
## 6 2.85 0.184 0.591
## 7 2.85 0.232 0.598
## 8 2.71 0.201 0.622
## 9 2.86 0.292 0.633
## 10 3.24 0.312 0.731
## # ℹ 18 more rows##Step 2 summarize the data
summary(mortality_rate)## Unvaccinated Vaccinatedwithbooster Vaccinatedwithoutbooster
## Min. : 0.6144 Min. :0.0000 Min. :0.1322
## 1st Qu.: 2.1639 1st Qu.:0.1965 1st Qu.:0.4375
## Median : 2.9769 Median :0.2711 Median :0.5944
## Mean : 6.7050 Mean :0.2741 Mean :0.7536
## 3rd Qu.: 9.3795 3rd Qu.:0.3381 3rd Qu.:0.8633
## Max. :33.6421 Max. :0.5331 Max. :3.5275
## NA's :50# Unvaccinated has a mean mortality of 6.71, vaccinated with booster has a mean of 0.27 and vaccinated without booster has a mean of 0.75
list(mortality_rate)## [[1]]
## # A tibble: 78 × 3
## Unvaccinated Vaccinatedwithbooster Vaccinatedwithoutbooster
## <dbl> <dbl> <dbl>
## 1 13.4 NA 0.807
## 2 12.3 NA 0.780
## 3 10.4 NA 0.697
## 4 10.1 NA 0.679
## 5 10.8 NA 0.773
## 6 11.9 NA 0.865
## 7 14.6 NA 0.964
## 8 14.1 NA 0.915
## 9 18.7 NA 1.06
## 10 19.5 NA 0.975
## # ℹ 68 more rows# the mortality rate in this list shows unvaccinated having higher numbers while vaccinated with booster shows much lower rates
##Step3 import and clean the data
mor_rate <- mortality_rate%>%
pivot_longer(cols = c(Vaccinatedwithbooster, Vaccinatedwithoutbooster, Unvaccinated), names_to = "Vaccine_Status",values_to = "Mortality")
# We simplified the data to make it easier to read and follow. We also were able to take out any results that did not contain any numbers.
## Step 4 data visualization
boxplot(Mortality ~ Vaccine_Status, data = mor_rate,
main = "Mortality_rate_analysis_based_on_vaccine_status", xlab = "Vaccine_Status",
ylab = "Mortality Rate")
# The first box plot which is unvaccinated shows a right skewed box and shows outlliers
# the second box vaccinated with booster shows that it is symmetric with no outliers
# the third box vaccinated without booster shows a right skewed box with 6 outliers
# This shows that the mortality rate in vaccinated with booster is the lowest rate
##analytical approach(anova) to test the significance of hypothesis
# Test data through levenetest, shapiro test and bartlette test#install.packages("car")
library(car)## Warning: package 'car' was built under R version 4.3.3## Loading required package: carData## Warning: package 'carData' was built under R version 4.3.3leveneTest(mor_rate$Mortality, mor_rate$Vaccine_Status, data = mor_rate)## Warning in leveneTest.default(mor_rate$Mortality, mor_rate$Vaccine_Status, :
## mor_rate$Vaccine_Status coerced to factor.## Levene's Test for Homogeneity of Variance (center = median: mor_rate)
## Df F value Pr(>F)
## group 2 18.022 7.285e-08 ***
## 181
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# passes lavene test
#install.packages("dplyr")
library(dplyr)## Warning: package 'dplyr' was built under R version 4.3.3##
## Attaching package: 'dplyr'## The following object is masked from 'package:car':
##
## recode## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionVaccination Rates
mor_rate %>%
group_by(Vaccine_Status) %>%
summarise(shapiro.test = shapiro.test(Mortality)$p.value)## # A tibble: 3 × 2
## Vaccine_Status shapiro.test
## <chr> <dbl>
## 1 Unvaccinated 1.18e-11
## 2 Vaccinatedwithbooster 9.16e- 1
## 3 Vaccinatedwithoutbooster 3.79e-12# - Unvaccinated and vaccinated without booster groups show significant deviation from normality (p < 0.001).
# - Mortality rates in the vaccinated group with boosters do not significantly deviate from normal (p > 0.05).
# passes shaporp test
bartlett.test(mor_rate$Mortality~mor_rate$Vaccine_Status, data = mor_rate)##
## Bartlett test of homogeneity of variances
##
## data: mor_rate$Mortality by mor_rate$Vaccine_Status
## Bartlett's K-squared = 452.25, df = 2, p-value < 2.2e-16# - The Bartlett test suggests that the differences in mortality rates between vaccine status groups have uneven spreads (p < 0.001).
# - This means we should be careful when comparing these groups because their differences in variance could affect our results.
# passes bartlett Anova
###anova <- aov( Vaccine_Status~ mortality_rate, data = mor_rate)
###summary(anova)
# - The analysis shows that the type of vaccine status affects mortality rates (p < 0.001).
# - This means there are differences in mortality rates between the groups with different vaccine statuses.
# - We may need to check which groups specifically differ from each other.
###plot(anova,2)
# This pot show sthe residuals and the graph shows the majority of the data following the line
# with the exception of a few outliers
#install.packages("stats")library(stats)
result<- pairwise.t.test(mor_rate$Mortality, mor_rate$Vaccine_Status, p.adjust.method = "bonferroni")
print(result)##
## Pairwise comparisons using t tests with pooled SD
##
## data: mor_rate$Mortality and mor_rate$Vaccine_Status
##
## Unvaccinated Vaccinatedwithbooster
## Vaccinatedwithbooster 3.5e-07 -
## Vaccinatedwithoutbooster 1.3e-10 1
##
## P value adjustment method: bonferroni# - Vaccinated individuals with booster shots have significantly lower mortality rates compared to those without booster shots.
# - Vaccinated individuals, even without boosters, have significantly lower mortality rates compared to the unvaccinated.
#u1≠u2≠u3
#We can conclude that the mortality rate between unvaccinated, vaccinated with the booster and vaccinated with are not the same
#They have different means and the p value 0.00 is < 0.05 so we Reject HO!
#vaccinated with the booster had the lowest mortality rate out of the three