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# Stroke Risk Prediction: Exploratory Data Analysis and Model Evaluation

In this comprehensive analysis, we delve into the critical task of predicting stroke risk by examining the association between various covariates and stroke occurrence. Through exploratory data analysis, we investigate key factors such as BMI, average glucose levels, hypertension, and smoking status to uncover their significance. We employ three distinct models—Linear Regression, Decision Tree, and a Neural Network—to assess their predictive capabilities. The results showcase the effectiveness of these models, offering valuable insights into stroke risk assessment and highlighting the importance of data-driven healthcare decisions.

## Assignment Problem Description: Predicting Stroke Risk

In this data analysis assignment, we aim to predict whether a person is at risk of experiencing a stroke based on various covariates. We employ three different models: Linear Regression, Random Forest, and a Convolutional Neural Network. The dataset is split into two groups in a 4:1 ratio, and the accuracy of each model is assessed by training them on the training dataset and evaluating their performance on the test dataset.

### BMI Analysis

We began our exploratory data analysis by plotting the BMI for individuals who have experienced a stroke and those who have not. The boxplot revealed no significant difference between the two groups.

• Boxplot showing the BMI of individuals who experienced a stroke and those who didn’t

### Average Glucose Level Comparison

Next, we compared the average glucose levels between the two groups. While the median levels were similar, there was a notable difference in variance between the groups, indicating a potential association between stroke and blood sugar levels.

• Boxplot comparing the avg. glucose level between the two groups

### Hypertension and Stroke

We analyzed the relationship between hypertension and stroke by creating a contingency table and conducting a chi-squared test. The results showed a significant association between having hypertension and experiencing a stroke.

Yes(Hypertension) No
Yes(Stroke) 66 183
No 432 4429

Table 1: Association between hypertension and stroke

### Smoking Status and Stroke

Similarly, we assessed the relationship between smoking status and stroke using a contingency table and a chi-squared test. The test statistics revealed a statistically significant relationship between smoking and experiencing a stroke.

No(Stroke) Yes
formerly smoked 815 70
Never smoked 1802 90
smokes 747 42
unknown 1497 47

Table 2: Relationship between smoking status and having a stroke

### Analysis and Evaluation

After conducting exploratory data analysis, we proceeded to build and evaluate predictive models.

### Linear Regression

We trained a linear regression model and identified that age, hypertension, heart disease, and average glucose level were significant variables based on the p-values of the coefficients. The adjusted R-squared value indicated that only 7% of the outcome's variation was explained linearly by the covariates. Testing the model on the test dataset resulted in an accuracy of 0.83.

oep. va riable: stroke R-squared: 0.076
Model: OLS Adj. R-squared : 0.072
Method: Least Squares F-statistic: 20.08
Da te : Sun, 19 Har 2923 Prob (F-statistic): 3.07e-S6
Time ' 92:18:4& Log-Likelihood 99,626
No. Observations:Of Residuals: 3927 AIC: -199
Of Mode\: Covariance Type: 3916 BIC: -1852 .
coef std err t P>|t [0.025 0.975]
const -0.0929 0.019 -4.769 0.000 -0.131 -0.055
age 0.0025 0.000 10.831 0.000 0.002 0.003
hypertension 0.0392 0.011 3.562 0.000 0.018 0.061
heart_disease 0.0464 0.015 3.140 0.002 0.017 0.075
avg_glucose_level 0.0004 7.16e-05 5.085 0.000 0.000 0.001
bmi -0.0006 0.000 -1.348 0.178 -0.001 0.000
gender_ Male 0.0017 0.006 0.277 0.782 -0.010 0.014
gender_Other -0.0269 0.189 -0.143 0.887 -0.397 0.343
ever_married_Yes -0.0245 0.009 -2.731 0.006 -0.042 -0.007
work_type_Never_worked 0.0290 0.045 0.648 0.517 -0.059 0.117
work_type_Private 0.0099 0.009 1.073 0.283 -0.008 0.028
work_type_Self-employed -0.0140 0.011 -1.223 0.221 -0.036 0.008
work_type_children 0.0528 0.016 3.352 0.001 0.022 0.084
Residence_type_Urban 0.0035 0.006 0.581 0.561 -0.008 0.015
smoking_status_formerly: smoked 0.0072 0.010 0.711 0.477 -0.013 0.027
smoking_status_never smoked 0.0019 0.008 0.224 0.823 -0.014 0.018
smoking_status_smoke 0.0099 0.010 0.954 0.340 -0.010 0.030
Omnibus: 3307.510 Durbin-Watson: 2.020
Prob(Omnibus): 0.000 Jarque-Bera (JB): 60531.132
Skew: 4.174 Prob(JB): 0.00
Kurtosis: 20.328 Cond. No. 7.85e+03
• Linear Regression Model in Python to Train the Dataset

### Decision Tree

We utilized a decision tree model to predict stroke risk. After fitting the model on the test dataset, we achieved an accuracy of 0.91, which outperformed the linear regression model. The regression diagnostics are show by the plot

• Regression Diagnostics

### Neural Network

A neural network model with two hidden layers and 64 cells was employed, and it was trained for 100 epochs. The model achieved a Mean Absolute Error (MAE) of 0.11 and an accuracy of 0.89, falling between the decision tree and linear regression models in terms of performance.

### Appendix

``` import numpy as np import os import pandas as pd from sklearn.model_selection import train_test_split import statsmodels.api as sm from sklearn.linear_model import LinearRegression import tensorflow as tf from tensorflow.keras.datasets import mnist from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Conv2D, MaxPooling2D, Flatten, Dense import tensorflow as tf from tensorflow import keras df=pd.read_csv("healthcare-dataset-stroke-data.csv") df.columns df=df.drop('id',axis=1) df.columns df=df.dropna() X=df[['gender', 'age', 'hypertension', 'heart_disease', 'ever_married', 'work_type', 'Residence_type', 'avg_glucose_level', 'bmi', 'smoking_status']] y=df['stroke'] lm = LinearRegression() X_train = pd.get_dummies(data=X_train, drop_first=True) X_test = pd.get_dummies(data=X_test, drop_first=True) X_test['gender_Other']=[0]*982 new_order=['age', 'hypertension', 'heart_disease', 'avg_glucose_level', 'bmi', 'gender_Male', 'gender_Other', 'ever_married_Yes', 'work_type_Never_worked', 'work_type_Private', 'work_type_Self-employed', 'work_type_children', 'Residence_type_Urban', 'smoking_status_formerly smoked', 'smoking_status_never smoked', 'smoking_status_smokes'] X_test=X_test[new_order] X_train1 = sm.add_constant(X_train) # add intercept term model = sm.OLS(y_train, X_train1) results = model.fit() print(results.summary()) lm.fit(X_train, y_train) lm.fit(X_train, y_train) y1=lm.predict(X_test) for i in range(982): if y1[i]>.1: y1[i]=1 else: y1[i]=0 sum(m)/982 clf.fit(X_train, y_train) y_pred = clf.predict(X_test) accuracy = accuracy_score(y_test, y_pred) mean = X_train.mean(axis=0) std = X_train.std(axis=0) X_train = (X_train - mean) / std X_test = (X_test - mean) / std model = keras.Sequential([ keras.layers.Dense(64, activation='relu', input_shape=(X_train.shape[1],)), keras.layers.Dense(64, activation='relu'), keras.layers.Dense(1) ]) model.compile(optimizer='adam', loss='mse', metrics=['mae']) history = model.fit(X_train, y_train, epochs=100, validation_split=0.2) test_loss, test_mae = model.evaluate(X_test, y_test) print('Test MAE:', test_mae) ```