Do resting blood pressure, cholesterol, age, sex and heart rate predict presence of hypertension?

Loading the data set:

The data set used in this study has been obtained from the kaggle link: https://www.kaggle.com/datasets/prosperchuks/health-dataset?select=hypertension_data.csv. After downloading the data set it was uploaded to a github repository so that it can be called into Rstudio environment while keeping the work’s reproducibility. In order to load the data set into Rstudio we will use read.csv() function from base R to read the URL of the stored repository

hyper_t <- read.csv("https://raw.githubusercontent.com/Umerfarooq122/Data_sets/main/hypertension_data.csv")

Now in order to see if the data set has been loaded properly with all the columns we can use head() function from Base R which can display the first six row of the data set.

knitr::kable(head(hyper_t))

We can see that the data set has been loaded properly into our Rstudio environment and now we can go ahead and analyze the data set but before starting to analyze we have to bear in mind that our data set might not be in a clean form to work with so we’ll have to wrangle and transform our data set to make it analyze worthy.

Wrangling and Transforming:

First, we will look at the structure of the data set, Since we will be carrying out logistic regression so first we will look at the types of data in each variable/column. In order to do that we will use str() function.

str(hyper_t)

## 'data.frame':    26083 obs. of  14 variables:
##  $ age     : num  57 64 52 56 66 51 42 38 72 47 ...
##  $ sex     : num  1 0 1 0 0 1 0 0 0 0 ...
##  $ cp      : int  3 2 1 1 0 0 1 1 2 2 ...
##  $ trestbps: int  145 130 130 120 120 140 140 120 172 150 ...
##  $ chol    : int  233 250 204 236 354 192 294 263 199 168 ...
##  $ fbs     : int  1 0 0 0 0 0 0 0 1 0 ...
##  $ restecg : int  0 1 0 1 1 1 0 1 1 1 ...
##  $ thalach : int  150 187 172 178 163 148 153 173 162 174 ...
##  $ exang   : int  0 0 0 0 1 0 0 0 0 0 ...
##  $ oldpeak : num  2.3 3.5 1.4 0.8 0.6 0.4 1.3 0 0.5 1.6 ...
##  $ slope   : int  0 0 2 2 2 1 1 2 2 2 ...
##  $ ca      : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ thal    : int  1 2 2 2 2 1 2 3 3 2 ...
##  $ target  : int  1 1 1 1 1 1 1 1 1 1 ...

As we can see that a lot of columns has numeric and integer data type which is true for some columns but other columns like sex,cp,fbs,exang,slope,ca,thal and target have a factor data type. So we will need to fix that. But before changing data type of any columns we need to look out for any missing values in those rows. we will is.na() to see any missing values. According to our previous findings in proposal there in total 25 missing values in the data set:

sum(is.na(hyper_t))

## [1] 25

And if we check column wise all of those missing values are in sex column

knitr::kable(hyper_t[is.na(hyper_t$sex),])

Now we can see that apart from age column in the data set every other variable/column has the same value for each of those missing values so we can ignore those rows and since they are only 25 out 26k (way below 5%) observations so we can easily impute it from our data set.

hyper_t <- hyper_t[!(is.na(hyper_t$sex)),]

After imputation lets quickly confirm that our data set is free from any missing values using sum() and is.na() functions:

sum(is.na(hyper_t))

## [1] 0

Now we do not have any missing values in our data set so the next step is to manage the data type of the columns. The source of our data set does gives us the information about data type of columns and according to the source of data set, columns like sex, cp, fbs, exang, slope, ca, thal and target have a factor data type. So let’s change that first and we can change the factors like 0 and 1 to F(female) and M (male), in sex column, respectively:

hyper_t[hyper_t$sex == 0,]$sex <- "F" # Replacing 0 by F
hyper_t[hyper_t$sex == 1,]$sex <- "M" # Replacing 1 by M


hyper_t$sex <- as.factor(hyper_t$sex)
hyper_t$cp <- as.factor(hyper_t$cp)
hyper_t$fbs <- as.factor(hyper_t$fbs)
hyper_t$restecg <- as.factor(hyper_t$restecg)
hyper_t$exang <- as.factor(hyper_t$exang)
hyper_t$slope <- as.factor(hyper_t$slope)
hyper_t$thal <- as.factor(hyper_t$thal)


hyper_t$target <- ifelse(test = hyper_t$target == 0, yes = "Non-Hypertension", no = "Hypertension")
hyper_t$target <- as.factor(hyper_t$target)

After changing the type of columns now lets recall str() function again to see if everything in our data frame is according to the way they were explained in the source

str(hyper_t)

## 'data.frame':    26058 obs. of  14 variables:
##  $ age     : num  57 64 52 56 66 51 42 38 72 47 ...
##  $ sex     : Factor w/ 2 levels "F","M": 2 1 2 1 1 2 1 1 1 1 ...
##  $ cp      : Factor w/ 4 levels "0","1","2","3": 4 3 2 2 1 1 2 2 3 3 ...
##  $ trestbps: int  145 130 130 120 120 140 140 120 172 150 ...
##  $ chol    : int  233 250 204 236 354 192 294 263 199 168 ...
##  $ fbs     : Factor w/ 2 levels "0","1": 2 1 1 1 1 1 1 1 2 1 ...
##  $ restecg : Factor w/ 3 levels "0","1","2": 1 2 1 2 2 2 1 2 2 2 ...
##  $ thalach : int  150 187 172 178 163 148 153 173 162 174 ...
##  $ exang   : Factor w/ 2 levels "0","1": 1 1 1 1 2 1 1 1 1 1 ...
##  $ oldpeak : num  2.3 3.5 1.4 0.8 0.6 0.4 1.3 0 0.5 1.6 ...
##  $ slope   : Factor w/ 3 levels "0","1","2": 1 1 3 3 3 2 2 3 3 3 ...
##  $ ca      : Factor w/ 5 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ thal    : Factor w/ 4 levels "0","1","2","3": 2 3 3 3 3 2 3 4 4 3 ...
##  $ target  : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...

Now we can see that we have columns bearing integers, numeric and factors with different levels as mentioned in the source of data set. Our data set is not ready for analysis and modeling:

Age

describe(hyper_t$age)

##    vars     n  mean    sd median trimmed   mad min max range  skew kurtosis
## X1    1 26058 55.66 15.19     56   55.74 17.79  11  98    87 -0.04    -0.74
##      se
## X1 0.09

As we can that our mean age is around 55-56 years with minimum of 11 and maximum of 98 years old. we can see the distribution more clearly by plotting a graph:

ggplot()+
  geom_histogram(data = hyper_t, mapping = aes(x=age, fill = target), color = "black", bins = 30)+
  geom_vline(xintercept=mean(hyper_t$age), color='red')+labs(x="Age", y="Count",title ="Distribution plot of Age")+theme_bw()

So we can see that we have a nice distribution of age ranging from young to very old people even though our mean is on the higher side but we will still further look into age as a factor causing hypertension. We can also create a contingency table using xtabs() function. The contingency table gives the number of cases in each subgroup. For instance, if we apply xtabs()function to target and age column it will give us the number of people having and not having hypertension in each age subgroup as shwon below:

knitr::kable(xtabs(~target+age, data = hyper_t))

#xtabs(~target+age, data = hyper_t)

First row in the contingency table represents ages of patient or respondents. Similarly, second and third rows represent number of patient in that age group not having and having hypertension, respectively.

Sex:

Sex could arguably be another factor that might affect hyper tension. Over here before putting sex in our model we will need to check out for the distribution among male and female patients. Since we change the values of 0 and 1 to “F” and “M”, respectively so instead of plotting lets quickly have a look at contingency table.

knitr::kable(xtabs(~ target + sex, data=hyper_t))

So we can see that gender/sex, even though could arguably be a factor in causing hypertension since male and female body have different response to different medical condition, but we can not use this data set to predict hypertension based on sex/gender since the data has been artificially set in a way that it has equal number of male and female respondents and equal number of responses for both gender in favor of having hypertension and not having hypertension.

In this particular study we will later on use logistic regression which talks about logs odd and logs of the odd ratios and if we do a manual calculations to check out log of odds of female and male having hypertension so we get the same answer:

female.log.odds <- log(5892/7137)
female.log.odds

## [1] -0.191697

Similarly for males:

male.log.odds <- log(5892/7137)
male.log.odds

## [1] -0.191697

So we can see that we get same answer for both and if we check out the log of the odd ratio we get a zero as shown below:

male.log.odds.ratio <- log((5892/7137)/(5892/7137))
male.log.odds.ratio

## [1] 0

logs odd and log of the odds will be explained later one when we apply simple logistic regression but for now we will not include gender/sex into our analysis:

Resting systolic blood pressure:

Systolic blood pressure is another significant factor that can cause hypertension. Most of the time someone with a high blood pressure is automatically considered hypertensive, in fact high blood pressure is another word for hypertension but today we will see if its just a high resting systolic blood pressure or is there more to it. We can quickly check out the summary using describe() function:

describe(hyper_t$trestbps)

##    vars     n   mean   sd median trimmed   mad min max range skew kurtosis   se
## X1    1 26058 131.59 17.6    130  130.38 14.83  94 200   106 0.72     0.92 0.11

We can see a very good distribution of the resting systolic blood pressure. It ranges from 94 mm of Hg (mercury) to 200 mm of Hg and the mean value is around 131.59 mm of Hg which is a very good indication of having evenly distributed data. We can also plot this data using a histogram.

ggplot()+
  geom_histogram(data = hyper_t, mapping = aes(x=trestbps, fill=target), color = "black", bins = 20)+theme_bw()+
  geom_vline(xintercept=mean(hyper_t$trestbps), color='red')+labs(x="Resting systolic blood pressure", y="Count",title ="Distribution of Resting Blood pressure (systolic)")

To check the distribution of resting blood pressure among hypertensive and non-hypertensive patients we can go ahead and plot a density ridges plot as shown below:

ggplot(hyper_t, aes(x = trestbps, y = target, fill=target)) + geom_density_ridges(alpha = .7)+labs(x="Resting blood pressure(systolic)", y= "", title = "Desnity Ridges Plot of Blood Pressure")+theme_bw()+theme(legend.position = "none")

Similarly on a contingency table:

knitr::kable(xtabs(~target+trestbps, data = hyper_t))

Well if we look at the contingency table we kind of get the idea that even people with low systolic resting blood pressure are hypertensive and as the blood pressure goes up toward normal range the number of hypertensive patients drops and as we crosses the 126 mm of Hg the number of hypertensive patients increases with exceptions. Surprisingly people with higher blood pressure (at 192 and 200) are not hypertensive.

We need to check these exceptions and see if other variable like chest pain, fasting blood sugar, heart rate e.t.c are playing their role. For instance, at 115 mm of Hg there are 262 hypertensive patients so lets check what else do we have at this particular blood pressure:

hyper_115 <- hyper_t|>
  filter(trestbps == 115)

hyper_rest <- hyper_t|>
  filter(trestbps != 115)

Let’s compare the filtered data frame (hyper_115) to rest of the data (hyper_rest):

knitr::kable(describe(hyper_rest))

knitr::kable(describe(hyper_115))

After doing a rough comparison of both data frames(hyper_t and hyper_115) we can see that some parameters has increased significantly. Parameter like mean cholesterol, mean age, mean heart rate e.t.c. Which kind of indicates that there is a lot more to hypertension than just having a high blood pressure.

Fasting blood sugar:

Blood sugar also cause hypertension.Diabetes and high blood pressure are closely related. In addition to having similar risk factors and causes, diabetes can also raise blood pressure. Eventually, the conditions that induce high blood pressure can result from insulin resistance and high blood glucose levels [3]. Lets check out the how many people with hypertension have a high blood pressure

xtabs(~target+fbs, data = hyper_t)

##                   fbs
## target                 0     1
##   Hypertension     12292  1982
##   Non-Hypertension  9860  1924

Another astonishing result, as we witness a lot of people with fasting blood sugar less than 120 mg/ are hypertensive while almost equal amount of people with fasting blood sugar level higher than 120 mg/ are either hypertensive or non-hypertensive. Which is kind of strange considering the research done in the reference shared above.

ggplot(hyper_t, aes(x = fbs, y = target, fill=target)) + geom_bar(stat = "identity")+labs(x="Fasting blood sugar", y= "", title = "Desnity Ridges Plot of Fasting Blood Sugar")+theme_bw()+theme(legend.position = "none")

Cholesterol:

High cholesterol and high blood pressure (hypertension) are related. Your arteries hardens and narrows because of cholesterol plaque and calcium. As a result, pumping blood through them requires significantly more effort from your heart. Consequently, Your blood pressure goes up too [4]. Lets check out the summary statistics of our data for the column cholesterol using describe() function.

describe(hyper_t$chol)

##    vars     n   mean    sd median trimmed   mad min max range skew kurtosis
## X1    1 26058 246.29 51.65    240   243.5 47.44 126 564   438  1.1     4.15
##      se
## X1 0.32

Anything above 240 mg/dl when it comes to total cholesterol is very harmful [4] and as we can see that our mean is a bit on higher side but do have a very good variation in the data ranging from minimum of 126 mg/dl to 564 mg/dl. We are not going to create a contingency table since the range is too high and the table is going to be huge and not easy o understand so instead we will plot a ridge density plot to see how cholesterol is distributed in hypertensive and non hypertensive patients:

ggplot(hyper_t, aes(x = chol, y = target, fill=target)) + geom_density_ridges(alpha=.6, color='black')+labs(x="Cholesterol", y="", title = "Density Ridges Plot of Cholesterol ")+theme_bw()+theme(legend.position = "none")

and a general distribution of cholesterol.

ggplot()+
  geom_histogram(data = hyper_t, mapping = aes(x=chol, fill=target), color = "black", bins = 20)+theme_bw()+
  geom_vline(xintercept=mean(hyper_t$chol), color='red')+labs(x="Cholesterol", y="Count",title ="Distribution of Cholesterol (systolic)")

Chest pain:

High blood pressure can damage your arteries by making them less elastic, which decreases the flow of blood and oxygen to your heart and leads to heart disease. In addition, decreased blood flow to the heart can cause, chest pain, also called angina [5]. Since we got the data for chest pain in ordinal form so its better to use it because a patient might not have high blood pressure, blood sugar and cholesterol on the day but what if the data collected was on a day when the hypertensive patient were taking proper precaution to keep those indicators down. So in that case we can refer to angina since angina is caused by permanent hypertension.

hyper_t %>%
  group_by(cp) %>%
  summarise(n = n())

## # A tibble: 4 × 2
##   cp        n
##   <fct> <int>
## 1 0     12314
## 2 1      4456
## 3 2      7392
## 4 3      1896

In the above grouped summary we have 12314 patients with asymptomatic chest pain, 4456 patients with typical angina, 7392 patients with atypical angina and 1896 with no angina pain. Let’s create a contingency table and see how many patients with hypertension is having angina:

xtabs(~target+cp, data = hyper_t)

##                   cp
## target                0    1    2    3
##   Hypertension     3384 3680 5860 1350
##   Non-Hypertension 8930  776 1532  546

As we can see that there are a lot of patients who has no symptoms of chest pain are non-hypertensive. Conversely, high number patients with angina and non angina chest pain are hypertensive. If we go back to our previous statement which stated :patient might not have high blood pressure, blood sugar and cholesterol on the day but what if the data collected was on a day when the hypertensive patient were taking proper precaution to keep those indicators down. So in that case we can refer to angina since angina is caused by permanent hypertension Now in order to prove our point lets filter the data for patients who has angina and see if the means of resting blood pressure for those patients is lower than overall mean. If we get a Yes it means that our assumption was right.

hyper_angina <- hyper_t |>
  filter(cp==1)

summarise(hyper_angina, mean = mean(trestbps))

##       mean
## 1 128.2617

So as we can see that mean of resting blood pressure is lower than overall mean, almost around 80% of patients have angina are hypertensive which kind of proves the point that maybe patients with hypertension had lower blood pressure on the day only.

Chest Vessels:

In our data we have one columns that accounts for the number of vessels narrowed more than 50%. The data ranges from 0 to 4.

describe(hyper_t$ca)

##    vars     n mean   sd median trimmed mad min max range skew kurtosis   se
## X1    1 26058 0.72 1.01      0    0.53   0   0   4     4 1.29     0.75 0.01

xtabs(~target+ca, data = hyper_t)

##                   ca
## target                 0     1     2     3     4
##   Hypertension     11252  1870   624   258   270
##   Non-Hypertension  3894  3644  2674  1474    98

ggplot(hyper_t, aes(x = ca, fill=target)) + geom_bar( color='black')+labs(x="Chest Vessels", y="", title = "Chest Vessels plot")+theme_bw()

Maximum Heart rate achieved:

describe(hyper_t$thalach)

##    vars     n   mean    sd median trimmed   mad min max range  skew kurtosis
## X1    1 26058 149.64 22.87    153  150.94 22.24  71 202   131 -0.52    -0.08
##      se
## X1 0.14

ggplot()+
  geom_histogram(data = hyper_t, mapping = aes(x=thalach, fill=target), color = "black", bins = 20)+theme_bw()+
  geom_vline(xintercept=mean(hyper_t$thalach), color='yellow')+labs(x="Maximum heart rate", y="Count",title ="Distribution of Heart rate")

ggplot(hyper_t, aes(x = thalach, y = target, fill=target)) + geom_density_ridges(alpha=.6, color = "black")+labs(x="Maximum heart rate", y="", title = "Density of hypertensive and non hypertensive patients")+theme_bw()+theme(legend.position = "none")

Exercise Induced Angina:

xtabs(~target+exang, data = hyper_t)

##                   exang
## target                 0     1
##   Hypertension     12280  1994
##   Non-Hypertension  5260  6524