Introduction

• Heart diseases increasingly becomes a major risk factor for heart attack and stroke, which constitute the major causes of death’s World wide. Thus, we are looking into the segment of people with and without heart diseases and analyse what are the major factors resulting in Heart Diseases.

• Initially our understanding is that people with high Max Heart Rate and high cholestrol levels are more vulnerable to heart related diseases.

• Here are the parameters through which we carry out our further analysis: 1.chol - Cholestrol Level 2.thalach - Max Heart Rate

Problem Statement

• Does high Maximum Heart Rate and Cholestrol levels prove that people are more vulnerable to heart related diseases ?

Data

• This public health dataset was provided by David Lapp in the Kaggle website, and the reference link is as follows: https://www.kaggle.com/johnsmith88/heart-disease-dataset/metadata

• This open data set dates from 1988 and is last updated in 2019. This is the second version and consists of more than 1000 observations from four databases: Cleveland, Hungary, Switzerland, and Long Beach V.

• Current Dataset is a subset of 5 attributes used for analysis out of the 14 attributes present. The “target” field refers to the presence of heart disease in the patient. It is an integer valued 0 = no disease and 1 = disease.

Data Cont.

• This Dataset contains the following variables:
  • 1.Age
  • 2.Sex
  • 3.Chol - Cholestrol Level
  • 4.Thalach - Maximum Heart Rate Achieved
  • 5.Target - yes or no.
• Out of the above given Attributes the following attributes are factors and the levels are explained as follows:
  • 1.sex 1 stands for male 0 stands for female.
  • 2.target(Prone to heart disease) 0 for no, 1 for yes.
• Explain the scale of numeric variables.(ask)
• Justify everything that you do to preprocess the data.(ask)

Descriptive Statistics and Visualisation

• The Required data has been summarised as shown below in the code, Required Attributes as shown below are converted into the required Factorial format from Number.

#Reading the data from csv file:
Heart_Incidences <- read_csv("C:/Users/Dick Smith/Desktop/Intro 2 Stat/Assignment 3 Data Sets/heart.csv")

#Summarising the Data:
summary(Heart_Incidences)

##       age             sex              chol        thalach     
##  Min.   :29.00   Min.   :0.0000   Min.   :126   Min.   : 71.0  
##  1st Qu.:48.00   1st Qu.:0.0000   1st Qu.:211   1st Qu.:132.0  
##  Median :56.00   Median :1.0000   Median :240   Median :152.0  
##  Mean   :54.43   Mean   :0.6956   Mean   :246   Mean   :149.1  
##  3rd Qu.:61.00   3rd Qu.:1.0000   3rd Qu.:275   3rd Qu.:166.0  
##  Max.   :77.00   Max.   :1.0000   Max.   :564   Max.   :202.0  
##      target      
##  Min.   :0.0000  
##  1st Qu.:0.0000  
##  Median :1.0000  
##  Mean   :0.5132  
##  3rd Qu.:1.0000  
##  Max.   :1.0000

• Checking the Dimensions of the Data:

dim(Heart_Incidences)

## [1] 1025    5

#Checking the classes of the Data:
str(Heart_Incidences)

## Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame': 1025 obs. of  5 variables:
##  $ age    : num  52 53 70 61 62 58 58 55 46 54 ...
##  $ sex    : num  1 1 1 1 0 0 1 1 1 1 ...
##  $ chol   : num  212 203 174 203 294 248 318 289 249 286 ...
##  $ thalach: num  168 155 125 161 106 122 140 145 144 116 ...
##  $ target : num  0 0 0 0 0 1 0 0 0 0 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   age = col_double(),
##   ..   sex = col_double(),
##   ..   chol = col_double(),
##   ..   thalach = col_double(),
##   ..   target = col_double()
##   .. )

• Converting the Required Attributes into Factors:
  • Sex From Number to Factor
  • Target From Number to Factor
  • Also checking for any Missing Values.

  Heart_Incidences$sex <- factor(Heart_Incidences$sex,levels = c(0,1),labels=c("Female","Male"))



#Target From Number to Factor:
Heart_Incidences$target<-factor(Heart_Incidences$target,levels=c(0,1),labels=c("NO","YES"))

#Checking if there are any missing values in the data set: 
sum(is.na(Heart_Incidences))

## [1] 0

Decsriptive Statistics Cont.

• “Heart Disease vulnerability with respect to Max Heart Rate” graph clearly shows that people with max heart rate are more vulnerable to Heart diseases.

• “Heart Disease vulnerability with respect to Cholestrol” graph clearly shows that people with Cholestrol are also vulnerable to Heart Diseases.

• A special segment of code has been used below as shown to remove outliers from the above given boxplot graphs.

#Proportions of Male and Females for Analysis:
prop.table(table(Heart_Incidences$sex))

## 
##    Female      Male 
## 0.3043902 0.6956098

#Proportion of people who are targets of heart disease:
prop.table(table(Heart_Incidences$target))

## 
##        NO       YES 
## 0.4868293 0.5131707

plot_sex_bp<- ggplot(data = Heart_Incidences, aes(x=Heart_Incidences$target, y=Heart_Incidences$chol)) + geom_boxplot(aes(fill=Heart_Incidences$target))
plot_sex_bp+ggtitle("Cholestrol variation with Heart Diesease")+xlab("Heart Disease(Yes or No)")+ylab("cholestrol")

plot_sex_bp<- ggplot(data = Heart_Incidences, aes(x=Heart_Incidences$target, y=Heart_Incidences$thalach)) + geom_boxplot(aes(fill=Heart_Incidences$target))
plot_sex_bp+ggtitle("Max Heart Rate  variation with Heart Disease")+xlab("Heart Disease(Yes or No)")+ylab("Max Heart Rate")

#Code used to remove outliers from the boxplots:
outliers <- boxplot(Heart_Incidences$chol, plot=FALSE)$out
Heart_Incidences <- Heart_Incidences[-which(Heart_Incidences$chol %in% outliers),]

plot_sex_bp<- ggplot(data = Heart_Incidences, aes(x=Heart_Incidences$target, y=Heart_Incidences$chol)) + geom_boxplot(aes(fill=Heart_Incidences$target))
plot_sex_bp+ggtitle("Cholestrol variation with Heart Diesease")+xlab("Heart Disease(Yes or No)")+ylab("cholestrol")

outliers <- boxplot(Heart_Incidences$thalach, plot=FALSE)$out
Heart_Incidences <- Heart_Incidences[-which(Heart_Incidences$thalach %in% outliers),]

plot_sex_bp<- ggplot(data = Heart_Incidences, aes(x=Heart_Incidences$target, y=Heart_Incidences$thalach)) + geom_boxplot(aes(fill=Heart_Incidences$target))
plot_sex_bp+ggtitle("Max Heart Rate  variation with Heart Disease")+xlab("Heart Disease(Yes or No)")+ylab("Max Heart Rate")

#knitr::kable(table)

Hypothesis Testing

• We are considering two samples one with heart disease and the other without heart disease and lets see how the cholestrol and max heart rate are affected among these two samples, to predict the vulnerability of people towards heart diseases.
• The dataset is more male dominant as there are more number of males compared to females.
• The variance is unequal.

var(Heart_Incidences$chol[Heart_Incidences$target=="YES"])

## [1] 1921.851

var(Heart_Incidences$chol[Heart_Incidences$target=="NO"])

## [1] 2152.996

t.test(Heart_Incidences$chol~Heart_Incidences$target,
       paired = FALSE,
       var.equal = FALSE,
       alternative = "two.sided")

## 
##  Welch Two Sample t-test
## 
## data:  Heart_Incidences$chol by Heart_Incidences$target
## t = 4.1978, df = 990.04, p-value = 2.938e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   6.373539 17.563614
## sample estimates:
##  mean in group NO mean in group YES 
##          249.1639          237.1954

var(Heart_Incidences$thalach[Heart_Incidences$target=="YES"])

## [1] 371.0126

var(Heart_Incidences$thalach[Heart_Incidences$target=="NO"])

## [1] 479.885

t.test(Heart_Incidences$thalach~Heart_Incidences$target,
       paired = FALSE,
       var.equal = FALSE,
       alternative = "two.sided")

## 
##  Welch Two Sample t-test
## 
## data:  Heart_Incidences$thalach by Heart_Incidences$target
## t = -14.641, df = 969.73, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -21.65517 -16.53632
## sample estimates:
##  mean in group NO mean in group YES 
##          139.5000          158.5957

Hypothesis Testing Result for Cholestrol Level:(ask feedback)

• Assuming that the Mean Cholestrol level for people with Heart Diseases and Mean Cholestrol level for people with no Heart diseases is equal as our \[H_0 \] i.e our Null Hypothesis -Then upon conducting the Welch two sample test it is clear that p-Value is 0.001326 which is < 0.05.
• Therefore we can reject the null hypothesis
• The results of the two-sample t-test assuming Unequal variance found a statistically significant difference between the mean cholestrol levels of people with and without heart diseases t(df=1022.8)=3.2191, p=.00136, 95% CI for the difference in means [4.02 16.600]. The results of the investigation suggest that people with cholestrol have significantly less heart diseases than those without it.

Hypothesis Testing result for Max Heart Rate:(ask feedback)

• Assuming that the Mean Max Heart Rate for people with Heart Diseases and Mean Max Heart Rate level for people with no Heart diseases is equal as our \[H_0 \] i.e our Null Hypothesis -Then upon conducting the Welch two sample test it is clear that p-Value is < 2.2e-16 which is < 0.05.
• Therefore we can reject the null hypothesis and go ahead with our Alternate Hypothesis \[H_A \] which is the Mean Max Heart Rate for people with Heart Diseases and Mean Max Heart Rate level for people with no Heart diseases is not equal
• The results of the two-sample t-test assuming Unequal variance found a statistically significant difference between the mean Max Heart Rate of people with and without heart diseases t(df=976.86)=-14.682 ,p<2.2e-16, 95% CI for the difference in means [-22.02 -16.88]. The results of the investigation suggest that people with Max Heart Rate are significantly more vulnerable to heart diseases compared to those with less Maximun Heart Rate .

Discussion

• Maximum Heart Rate plays a crucial role in Heart diseases than cholestrol levels and people with more Heart Rate are more vulnerable to heart diseases.
• The Data set is Biased as the observations are male dominant and less female data is present compared to males.
• Other Factors like Excersise, Mental Stress etc.. needs to be considered for further future analysis.
  -Maximum Heart Rate of an Individual plays a crucial and vital role in Heart diseases. -[External Reference] : Also When WHI researchers examined data on 129,135 postmenopausal women, they found that those with the highest resting heart rates—more than 76 beats per minute—were 26% more likely to have a heart attack or die from one than those with the lowest resting heart rates—62 beats per minute or less.
• Thus it is pretty much clear that Maximum Heart Rate is one of the prime factors in heart strokes and heart related diseases.

References

-External Refernce on Heart Rates: https://www.health.harvard.edu/heart-health/what-your-heart-rate-is-telling-you