# install package
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.3.3
R Markdown
Introduction
Background: In recent years, heart disease is one of the leading
causes of death. In this project, we want to analyze patient data to
identify factors associated with heart disease and build a predictive
model.
Research question: Can we predict heart disease based on patient
characteristics?
Data Description
| id |
Identifier |
Patient ID |
| age |
Numeric |
Age of the patient |
| sex |
Categorical |
Sex (0 = female, 1 = male) |
| chol |
Numeric |
Serum cholesterol level |
| trestbps |
Numeric |
Resting blood pressure |
| thalach |
Numeric |
Maximum heart rate achieved |
| target |
Binary |
Heart disease status (0 = no disease, 1 = disease) |
Step 0: read in 3 datasets
dataset 1: demographics (age, sex)
demographics = read.csv("demographics.csv")
head(demographics)
## id age sex
## 1 1 63 1
## 2 2 37 1
## 3 3 41 0
## 4 4 56 1
## 5 5 57 0
## 6 6 57 1
# check whether there is NA in all datasets
sum(is.na(demographics$id))
## [1] 0
any(duplicated(demographics$id))
## [1] FALSE
dataset 2: clinical (chol, trestbps, thalach)
clinical = read.csv("clinical.csv")
head(clinical)
## id chol trestbps thalach
## 1 1 233 145 150
## 2 2 250 130 187
## 3 3 204 130 172
## 4 4 236 120 178
## 5 5 354 120 163
## 6 6 192 140 148
# check whether there is NA in all datasets
sum(is.na(clinical$id))
## [1] 0
any(duplicated(clinical$id))
## [1] FALSE
dataset 3: outcome (target)
outcome = read.csv("outcome.csv")
head(outcome)
## id target
## 1 1 1
## 2 2 1
## 3 3 1
## 4 4 1
## 5 5 1
## 6 6 1
# check whether there is NA in all datasets
sum(is.na(outcome$id))
## [1] 0
any(duplicated(outcome$id))
## [1] FALSE
Step 1: merge these 3 datasets using common key “id”
merged_df <- merge(demographics, clinical, by = "id")
merged_df <- merge(merged_df, outcome, by = "id")
summary(merged_df)
## id age sex chol
## Min. : 1.0 Min. :29.00 Min. :0.0000 Min. :126.0
## 1st Qu.: 76.5 1st Qu.:47.50 1st Qu.:0.0000 1st Qu.:211.0
## Median :152.0 Median :55.00 Median :1.0000 Median :240.0
## Mean :152.0 Mean :54.37 Mean :0.6832 Mean :246.3
## 3rd Qu.:227.5 3rd Qu.:61.00 3rd Qu.:1.0000 3rd Qu.:274.5
## Max. :303.0 Max. :77.00 Max. :1.0000 Max. :564.0
## trestbps thalach target
## Min. : 94.0 Min. : 71.0 Min. :0.0000
## 1st Qu.:120.0 1st Qu.:133.5 1st Qu.:0.0000
## Median :130.0 Median :153.0 Median :1.0000
## Mean :131.6 Mean :149.6 Mean :0.5446
## 3rd Qu.:140.0 3rd Qu.:166.0 3rd Qu.:1.0000
## Max. :200.0 Max. :202.0 Max. :1.0000
sum(is.na(merged_df))
## [1] 0
Step 2: Exploratory data analysis
For quantative variable: we use histogram / boxplot
quant_vars <- c("age", "chol", "trestbps", "thalach")
par(mfrow = c(2, 2)) # 2x2 grid
Histogram
par(mfrow = c(2, 2))
for (col in quant_vars) {
hist(merged_df[[col]],
main = col,
xlab = col)
}
Boxplot
par(mfrow = c(2, 2))
for (col in quant_vars) {
boxplot(merged_df[[col]],
main = col,
xlab = col)
}
For categorical variables: we can use bar plots/tables to
visualize
table
table(merged_df$sex)
##
## 0 1
## 96 207
table(merged_df$target)
##
## 0 1
## 138 165
bar plot
par(mfrow = c(2, 1))
ggplot(merged_df, aes(x = factor(target))) +
geom_bar(fill = "orange") +
labs(
title = "Distribution of target",
x = "target",
y = "Count"
)
ggplot(merged_df, aes(x = factor(sex))) +
geom_bar(fill = "steelblue") +
labs(
title = "Distribution of Gender",
x = "Gender",
y = "Count"
)
Question we are interested in: Is Heart Disease More Common in Males
or Females?
# First, do a visualization
ggplot(merged_df, aes(x = factor(sex), fill = factor(target))) +
geom_bar(position = "dodge") +
labs(
title = "Heart Disease by Gender",
x = "Gender",
y = "Count",
fill = "Heart Disease"
)
Now use the chi2 test: we are interested in
null hypothesis: sex and heart disease are independent
alternative: sex and heart disease are associate
Summary: The small p-value suggests that sex and heart disease are
not independent, indicating a significant association.
Step 3: Model using logistic regression
model <- glm(
target ~ age + factor(sex) + chol + trestbps + thalach ,
data = merged_df,
family = binomial
)
summary(model)
##
## Call:
## glm(formula = target ~ age + factor(sex) + chol + trestbps +
## thalach, family = binomial, data = merged_df)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.344548 1.832916 -0.188 0.8509
## age -0.014453 0.017584 -0.822 0.4111
## factor(sex)1 -1.860719 0.343297 -5.420 5.96e-08 ***
## chol -0.007105 0.002762 -2.572 0.0101 *
## trestbps -0.020107 0.008366 -2.404 0.0162 *
## thalach 0.046981 0.007700 6.101 1.05e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 417.64 on 302 degrees of freedom
## Residual deviance: 316.69 on 297 degrees of freedom
## AIC: 328.69
##
## Number of Fisher Scoring iterations: 4
Conclusion: Sex, Serum cholesterol level, Resting blood pressure,
Maximum heart rate achieved are associated with heart disease.
Step 4: further analysis
exp(coef(model))
## (Intercept) age factor(sex)1 chol trestbps thalach
## 0.7085402 0.9856509 0.1555607 0.9929202 0.9800935 1.0481020
Interpretation:
Sex: Holding other variables constant, males have significantly
lower odds of heart disease compared to females. Specifically, the odds
of heart disease for males are about 84% lower than for females.
Cholesterol: For each one-unit increase in cholesterol, the odds of
heart disease decrease by about 0.7%. This indicates a small but
statistically significant negative association.