Quantum Heart Prediction
Elvira Khwatenge
2025-03-30
R Markdown
This is an analysis of a heart disease prediction dataset. The goal is to explore the data, build a predictive model, and evaluate its performance.
Data Loading and Preprocessing
First, we load the necessary libraries and read the data.
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(caret)## Loading required package: lattice
##
## Attaching package: 'caret'
##
## The following object is masked from 'package:purrr':
##
## liftdata <- read.csv("Heart Prediction Quantum Dataset.csv")
head(data)## Age Gender BloodPressure Cholesterol HeartRate QuantumPatternFeature
## 1 68 1 105 191 107 8.362241
## 2 58 0 97 249 89 9.249002
## 3 44 0 93 190 82 7.942542
## 4 72 1 93 183 101 6.495155
## 5 37 0 145 166 103 7.653900
## 6 50 1 114 271 73 8.631604
## HeartDisease
## 1 1
## 2 0
## 3 1
## 4 1
## 5 1
## 6 0str(data)## 'data.frame': 500 obs. of 7 variables:
## $ Age : int 68 58 44 72 37 50 68 48 52 40 ...
## $ Gender : int 1 0 0 1 0 1 1 0 0 1 ...
## $ BloodPressure : int 105 97 93 93 145 114 156 156 116 121 ...
## $ Cholesterol : int 191 249 190 183 166 271 225 236 266 255 ...
## $ HeartRate : int 107 89 82 101 103 73 73 61 114 96 ...
## $ QuantumPatternFeature: num 8.36 9.25 7.94 6.5 7.65 ...
## $ HeartDisease : int 1 0 1 1 1 0 1 0 0 0 ...sum(is.na(data))## [1] 0Data Processing
preprocess the data by converting categorical variables to factors, checking for outliers, and scaling numerical features.
data$Gender <- as.factor(data$Gender)
data$HeartDisease <- as.factor(data$HeartDisease)
summary(data)## Age Gender BloodPressure Cholesterol HeartRate
## Min. :30.00 0:266 Min. : 90.0 Min. :150.0 Min. : 60.00
## 1st Qu.:43.00 1:234 1st Qu.:111.0 1st Qu.:183.8 1st Qu.: 73.00
## Median :55.00 Median :132.0 Median :221.0 Median : 89.00
## Mean :54.86 Mean :132.9 Mean :221.5 Mean : 88.77
## 3rd Qu.:66.25 3rd Qu.:155.0 3rd Qu.:258.0 3rd Qu.:104.00
## Max. :79.00 Max. :179.0 Max. :299.0 Max. :119.00
## QuantumPatternFeature HeartDisease
## Min. : 6.165 0:200
## 1st Qu.: 7.676 1:300
## Median : 8.323
## Mean : 8.317
## 3rd Qu.: 8.936
## Max. :10.785boxplot(data$Age, main="Age",col="orange", border="black")
boxplot(data$BloodPressure, main="BloodPressure",col="violet", border="black")
boxplot(data$Cholesterol, main="Cholesterol",col="navy", border="black")
boxplot(data$HeartRate, main="HeartRate",col="red", border="black")
boxplot(data$QuantumPatternFeature, main="QuantumPatternFeature",col="brown", border="black")
Q1 <- quantile(data$Cholesterol, 0.25)
Q3 <- quantile(data$Cholesterol, 0.75)
IQR <- Q3 - Q1
lower_bound <- Q1 - 1.5 * IQR
upper_bound <- Q3 + 1.5 * IQR
data <- data[data$Cholesterol >= lower_bound & data$Cholesterol <= upper_bound, ]
numerical_features <- c("Age", "BloodPressure", "Cholesterol", "HeartRate", "QuantumPatternFeature")
data[numerical_features] <- scale(data[numerical_features])
head(data)## Age Gender BloodPressure Cholesterol HeartRate QuantumPatternFeature
## 1 0.9176386 1 -1.0550933 -0.6953369 1.04689080 0.04875145
## 2 0.2190708 0 -1.3579112 0.6269431 0.01343493 1.01301086
## 3 -0.7589240 0 -1.5093202 -0.7181348 -0.38846458 -0.40762679
## 4 1.1970657 1 -1.5093202 -0.8777203 0.70240551 -1.98150828
## 5 -1.2479214 0 0.4589963 -1.2652852 0.81723394 -0.72149462
## 6 -0.3397833 1 -0.7144232 1.1284976 -0.90519252 0.34165582
## HeartDisease
## 1 1
## 2 0
## 3 1
## 4 1
## 5 1
## 6 0###Exploratory Data Analysis (EDA)
perform EDA to understand the relationships between variables.
hist(data$Age, main="Age Distribution", xlab="Age", col="skyblue", border="white")
hist(data$BloodPressure, main="Blood Pressure Distribution", xlab="Blood Pressure", col="lightgreen", border="white")
hist(data$Cholesterol, main="Cholesterol Distribution", xlab="Cholesterol", col="lightcoral", border="white")
hist(data$HeartRate, main="Heart Rate Distribution", xlab="Heart Rate", col="lightgoldenrod", border="white")
hist(data$QuantumPatternFeature, main="Quantum Pattern Feature Distribution", xlab="Quantum Pattern Feature", col="lavender", border="white")
# Bar plots with colors
plot(data$Gender, main="Gender Distribution", ylab="Frequency", col=c("pink", "lightblue"))
plot(data$HeartDisease, main="Heart Disease Distribution", ylab="Frequency", col=c("lightgreen", "salmon"))
# Scatter plots with colors
plot(data$Age, data$HeartDisease, main="Age vs Heart Disease", xlab="Age", ylab="Heart Disease", col=ifelse(data$HeartDisease == 1, "red", "blue"), pch=19)
plot(data$BloodPressure, data$HeartDisease, main="Blood Pressure vs Heart Disease", xlab="Blood Pressure", ylab="Heart Disease", col=ifelse(data$HeartDisease == 1, "red", "blue"), pch=19)
plot(data$Cholesterol, data$HeartDisease, main="Cholesterol vs Heart Disease", xlab="Cholesterol", ylab="Heart Disease", col=ifelse(data$HeartDisease == 1, "red", "blue"), pch=19)
plot(data$HeartRate, data$HeartDisease, main="Heart Rate vs Heart Disease", xlab="Heart Rate", ylab="Heart Disease", col=ifelse(data$HeartDisease == 1, "red", "blue"), pch=19)
plot(data$QuantumPatternFeature, data$HeartDisease, main="Quantum Pattern Feature vs Heart Disease", xlab="Quantum Pattern Feature", ylab="Heart Disease", col=ifelse(data$HeartDisease == 1, "red", "blue"), pch=19)
# Select numeric columns and handle missing values
numerical_features <- c("Age", "BloodPressure", "Cholesterol", "HeartRate", "QuantumPatternFeature")
numeric_data <- data[, numerical_features]
numeric_data <- na.omit(numeric_data)
# Remove columns with zero variance (if any)
numeric_data <- numeric_data[, apply(numeric_data, 2, var) != 0]
# Compute correlation matrix
correlation_matrix <- cor(numeric_data, use = "complete.obs")
# Visualize with corrplot
library(corrplot)## corrplot 0.95 loadedcorrplot(correlation_matrix, method = "color", type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45)
Model Building
Build a logistic regression model to predict heart disease
set.seed(123)
train_index <- createDataPartition(data$HeartDisease, p = 0.7, list = FALSE)
train_data <- data[train_index, ]
test_data <- data[-train_index, ]
# Train the logistic regression model
model <- glm(HeartDisease ~ ., data = train_data, family = "binomial")
# Summarize the model
summary(model)##
## Call:
## glm(formula = HeartDisease ~ ., family = "binomial", data = train_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.7752 0.4391 4.043 5.27e-05 ***
## Age -0.2477 0.2749 -0.901 0.368
## Gender1 0.2093 0.5015 0.417 0.676
## BloodPressure -0.1250 0.2349 -0.532 0.595
## Cholesterol 0.1128 0.2723 0.414 0.679
## HeartRate -0.2070 0.2441 -0.848 0.397
## QuantumPatternFeature -7.6702 1.0599 -7.237 4.60e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 471.11 on 349 degrees of freedom
## Residual deviance: 110.27 on 343 degrees of freedom
## AIC: 124.27
##
## Number of Fisher Scoring iterations: 8# Make predictions on the test data
predictions <- predict(model, newdata = test_data, type = "response")
predicted_classes <- ifelse(predictions > 0.5, 1, 0)
# Evaluate the model
confusionMatrix(as.factor(predicted_classes), test_data$HeartDisease)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 58 8
## 1 2 82
##
## Accuracy : 0.9333
## 95% CI : (0.8808, 0.9676)
## No Information Rate : 0.6
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.8634
##
## Mcnemar's Test P-Value : 0.1138
##
## Sensitivity : 0.9667
## Specificity : 0.9111
## Pos Pred Value : 0.8788
## Neg Pred Value : 0.9762
## Prevalence : 0.4000
## Detection Rate : 0.3867
## Detection Prevalence : 0.4400
## Balanced Accuracy : 0.9389
##
## 'Positive' Class : 0
## Discussion and Interpretation
Data Summary and Preprocessing
At the Initial Data Inspection the dataset consisted of 500 observations with 7 variables, including Age, Gender, BloodPressure, Cholesterol, HeartRate, QuantumPatternFeature, and HeartDisease. No missing values were detected.
During Data Type Conversion the Gender and HeartDisease variables were converted to factor variables for appropriate analysis.
Outliers in the Cholesterol variable were removed to ensure data quality.
Numerical features were scaled to standardize their ranges for model performance.
Exploratory Data Analysis (EDA)
Histograms
The age histogram shows a relatively normal distribution of ages, with a slight right skew, indicating a higher proportion of middle-aged and older individuals.
The bimodal blood pressure distribution suggests two distinct groups, possibly representing normal and high blood pressure populations.
The right-skewed distribution indicates that most individuals have normal cholesterol levels, but a notable subset has higher levels.
The normal distribution indicates that most individuals have heart rates within the typical range.
Quantum Pattern Feature/multimodal Distribution suggests distinct subgroups within the population relevant to heart disease prediction.
Bar Plots
The distribution of males and females in the dataset is critical for understanding potential gender-based risk differences.
Heart Disease Distribution Illustrates the prevalence of heart disease in the sample, providing insight into the overall burden of the disease.
Scatter plots of Age, BloodPressure, Cholesterol, HeartRate, and QuantumPatternFeature versus HeartDisease use color-coding to visualize relationships. Patterns or clusters reveal risk factors or predictive indicators.
Correlation Matrix- heatmap visualizes correlations between numerical features, with stronger correlations indicating potential multicollinearity, which affects model interpretation and feature selection.
Model Building- Logistic Regression
Coefficients
Intercept: 1.7752
Age: -0.2477 (p = 0.368)
Gender1: 0.2093 (p = 0.676)
BloodPressure: -0.1250 (p = 0.595)
Cholesterol: 0.1128 (p = 0.679)
HeartRate: -0.2070 (p = 0.397)
QuantumPatternFeature: -7.6702 (p < 0.001)
Interpretation:
The QuantumPatternFeature is highly significant (p < 0.001), indicating a strong relationship with heart disease.
Other variables such as Age, Gender, BloodPressure, Cholesterol, and HeartRate are not statistically significant in this model (p > 0.05).
Model Evaluation (Confusion Matrix)
Accuracy: 93.33%
Sensitivity: 96.67%
Specificity: 91.11%
Results Interpretation
Demographic and Health Indicators
A slightly right-skewed distribution suggests more middle-aged and older individuals, which aligns with typical heart disease demographics. Blood Pressure/Bimodal distribution could indicate a mix of individuals with normal and high blood pressure, requiring further stratified analysis.Right-skewness suggests a need for targeted cholesterol management strategies. Normal distribution suggests heart rates are generally within expected ranges. Quantum Pattern Feature/ Multimodal distribution suggests subgroups requiring further investigation to understand patterns related to heart disease.
Gender and Heart Disease Distribution
Knowing the proportions of males and females helps understand potential gender-specific risk factors. Heart Disease Distribution Indicates overall disease burden, useful for resource allocation and public health planning.
Relationships Between Variables and Heart Disease
Color-coding aids in visualizing relationships between variables and heart disease in correlation matrix, highlights potential risk factors.Correlation Matrix helps identify multicollinearity, informing model adjustments for more accurate predictions.
Model Performance
The logistic regression model shows high accuracy (93.33%), sensitivity (96.67%), and specificity (91.11%), demonstrating strong predictive capability. The highly significant QuantumPatternFeature suggests it is a crucial predictor of heart disease within this model.
Implications
For Academia- Validate QuantumPatternFeature in other datasets, explore interactions, and test other models like Random Forests or Neural Networks.
For Industry- Develop diagnostic tools incorporating the QuantumPatternFeature, and create personalized health monitoring devices.
For Policy Makers- Implement targeted interventions for high-risk groups identified by the model, focusing on QuantumPatternFeature and traditional risk factors.
Caveats
The model is based on a specific dataset and may not generalize to other populations.
Some features might be correlated, affecting coefficient interpretation.Some variables lack statistical significance (p > 0.05), requiring cautious interpretation.