Heart Disease Predictor

Correlation Matrix

Displays the correlation between variables

This correlation matrix is comparing all columns in the table to see how correlated they are in other. This meaning, that a strong correlation means that there is a significant trend found in relation to another, and then scaling down until you get to neglibible in which they barely affect each other to no correlation where they have no affect at all on each other. Overall for most of the values there was either practically no correlation, a neglegible correlation, or a weak correlation. The highest instances would be described as a moderate correlation(if you take the definition of a moderate correlation to be between 0.5 and 0.7).These instances came in the relationship between ST_Slope and old peak with a correlation of 0.502, and a moderate correlation between heart disease and ST_Slope of 0.599. ST_Slope is measured during a heart test and is supposed to go up when one does exercise. Therefore, an abnormal slope would be either staying flat or trending downward which could be a sign of heart disease. There are then a number of high low correlations coming to either 0.4 up to 0.494. The overall trend was that the bulk of the columns were correlated to each other between the correlation number of the absolute value 0.09 to the absolute value 0.35. There was a wide spread of values being both positive, meaning when one increases, the other can increase, and negative, which means when one value increases the other decreases. There were also some factors with an especially low correlation towards everything, namely RestingECG which had a highest value resulting in a weak correlation of 0.213 but often below 0.1.

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Heart Disease Predictor

Histograms

A graph that shows the count distributions of different variables

The turning point within the dataset is ages forty-six to forty-seven. When you compare the data of the ages of those younger than forty-six to forty-seven, more people do NOT have heart failure. Whereas after ages forty-six to forty-seven, more people had heart failure than people who did not. The peak of the count of people who had heart failure was centered at around ages fifty-four to sixty-three with age ranges of fifty-six to fifty-seven and ages fifty-eight to fifty-nine both having the greatest count of 51 participants having heart failure. The distribution of the graph of people without heart failure is distributed differently. The highest count of people who did NOT have heart failure was 45 participants ages fifty-four to fifty-five. The graph of people without heart failure is less smooth, with a greater change between age ranges.

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Boxplots

Boxplots are a type of visualization that shows the distribution of data

Heart Disease vs Maximum Heartrate

This visualization shows the Maximum heart rate for two groups, one with heart disease, and one without. In the heart disease boxplot, 50% of the data is between 112 and 144.5, and the rest of the data is between 67 and 182 In the group without heart disease, the boxplot shows that 50% of the data is between 134 and 165, and the rest of the data is between 90 and 202 The group without heart disease seems to have a much higher heart rate compared to the group with heart disease. From this data, we can conclude that heart rate might be an important factor in determining if someone has heart disease.

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Pie Charts

Shows a part to whole relationship.

Atypical Angina (ATA) = 0 Non-Anginal Pain (NAP) = 1 Asymptomatic (ASY) = 2 Typical Angina (TA) = 3 Overall, 54% of patients were asymptomatic and experienced no chest pain. The second most prevalent pain was non-anginal pain, followed by atypical angina. A small minority experienced typical angina. In patients with heart disease, an overwhelming majority were asymptomatic, with only 22.86% experiencing any pain. A minority of patients with heart disease had typical angina and atypical angina. However, in patients without heart disease, a third suffered non-anginal pain and another third suffered atypical angina. Asymptomatic chest pain made up a quarter of patients without heart disease, and a minority suffered typical angina. Among both groups, typical angina was the least common type of chest pain. However, a much larger percentage of patients with heart disease were asymptomatic compared to patients without heart disease.

No = 0 Yes = 1 A majority of patients did not experience exercise angina. However, in patients with heart disease, an overwhelming majority (85.2%) experienced exercise angina. In great contrast, about two thirds of patients without heart disease did not experience exercise angina and around a third did. Heart disease could be a factor that contributes to exercise angina, but exercise angina is not necessarily an indicator of heart disease considering a considerable amount of patients without heart disease experienced it as well.

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Scatter plot

Plotting the relationship between all numerical values

This is a scatter matrix which shows the scatter plots comparing all the continuous inputs in the data frame. I think this matrix shows that although heart disease is complicated and nothing is exactly one to one, there are general trends with certain traits that increase risks. For example, in the Age and MaxHR scatter plot, we see that people with heart disease generally trend towards being older and having a lower MaxHR. We can also see that people with a high Oldpeak tend to have heart disease. Some variables also have limited relationships with others. For example, we can see that broadly speaking, the higher the age the higher the resting RestingBP

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Violin Plot

Distribution and density of numerical data.

Interestingly, it seems like cholesterol levels are very similar in all groups. While the values in the male group with heart disease have a larger range than its sibling, the female group's graphs are the opposite. Additionally, the distributions overlap almost entirely, with the heart disease group only being slightly higher in cholesterol levels than the no heart disease group.

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Decision Tree

A decision tree classifier model classifies data as it passes through the nodes in the tree and uses the gini index to determine where to split. In order to optimize the decision tree, I used cv and randomized cv to find the best hyperparameters. Hyperparameters are attributes of models that can be changed to yield more accurate results. Some of the hyperparamaters that can be changed for decision trees include max depth, which controls how many times the tree splits, minimum samples split, which controls the number of samples needed to split an internal node, and minimum samples leaf, which controls the minimum number of samples needed at a leaf. It has a max depth of 54, minimum samples split of 33, minimum samples leaf of 11, and accuracy of 0.84

The confusion matrix above displays the results from the decision tree's training and testing. The top left square represents the number of true positives (Correctly diagnosing the patient with heart disease), the bottom left square represents false positives (Incorrectly diagnosing a patient with heart disease when they do not), top right represents false negatives (Incorrectly saying a patient does not have heart disease when they do), and the bottom represents true negatives (Correctly saying a patient does not have heart disease). Ideally, the number of false negatives and false positives would be as low as possible, which is achieved through optimization.

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Random Forest

A random forest classifier is an ensemble of decision trees that work together to classify data. Individually, decision trees are weak models, but are powerful when they work together. Each decision tree in the random forest individually classifies the data, and the outcome with the most votes becomes the final outcome of the model. I used randomized cv to find the best hyperparameters for the model. The hyperparameters of random forest models are similar to decision trees, with the added parameter, max number of estimators which controls the max number of decision trees used in the model.The max number of estimators is 67, the max depth is 90, and the model has an accuracy of 0.89, which is greater than an individual decision tree.

The confusion matrix above displays the results of the random forest's training and testing. Compared to the decision tree, the number of false negatives and false positives is lower.

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Adaboost

Adaboost is an example of ensemble learning, where several basic algorithms are combined to make one more optimized algorithm. For example, with a decision tree, instead of hoping one decision tree can correctly guess a result, ensemble learning will take multiple decision trees and combine them together to create a stronger algorithm. Adaboost is also a sequential learning version of ensemble learning, where every model is made in order, and the newest model learns from the previous model's failures. It does this by "boosting", or reducing the error through methods such as increasing the weights of data that was mislabeled. However, Adaboost is extremely sensitive to noisy data and outliers, which is why it is highly recommended to remove outliers from data with Adaboost. Here, Adaboost was used on our heart disease dataset, with a mean squared error of 0.12 on our testing data, and an overall accuracy score of 0.880 and a precision score of 0.880. This is a decent score for a machine learning model, but when it comes to diagnosis it probably isn't the best and there is certainly a more ideal model.

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Logistic Regression

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The model is a logistic regression and it works by predicting whether someone has heart disease or if they do not. It classifies them into one of these two groups . We changed some parameters such as the weight, training and testing data. I think it performed well in predicting if someone has heart disease and classifying them into two groups. It does this by analyzing relationships between two independent variables. The coefficient of the linear regression model shows the relationship between the variables by multiplying it with a certain value and a higher/lower coefficient indicates which classification the data point would be predicted to be in.

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Support Vector Classifer(SVC)

Confusion Matrix below(top left is correct positive, top right is false positive, bottom left is false negative, and bottom right is correct negative.

Support Vector Classification Model uses two groups of data to categorize new data. It does this by plotting the data onto a graph, and then using a hyperplane to split the data according to the group that the data belongs to. The hyper-parameters that could be fine tuned are the Kernel, the C value, the Gamma value, and the Degree. I decided to use a RandomizedSearchCV to determine the best parameters. When testing, for the best parameters, I ran into some problems. The first problem was how long it took too long to run the program. The program would run for about thirty minutes, and still not find a best fit for the graph. In response, I decided to decrease the amount of variables the RandomizedSearchCV needed to look for, and additionally, the range that each variable could search within. In the end, I decided that testing the C value, the Gamma value, and the Kernel would be most helpful in optimizing the model. According to my values the RandomizedSearchCV determine the best parameters was a Kernel of linear, a Gamma value of 96, and a C value of 9. I ended up getting an accuracy score of 0.72 with 56 true positive, 24 false positives, 27, false negatives, and 77 true negatives.

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Gaussian Naive Bayes

The image you see above is a confusion matrix that displays in the top left correct positive diagnosis, top right incorrect positive diagnose, bottom left incorrect negative diagnosis, bottom right correct negative diagnosis

Gaussian Naive Bayes is for binary classification and assumes that all continuous data has normal distribution, and that all features are independent and equal from each other. The Naive Bayes finds the probability of the predicted outcome(y variable) given the x values and then classifies the point based on whether one of the classifications had a higher probability than the other classification. In order to optimize the function, I stratified the data, which raised the accuracy score from 0.83 to 0.885 while also scaling the data though that did not cause a change in the accuracy score or any of the other measures. The results ending up giving a accuracy score of 0.885, a precision score of 0.878, a recall score of 0.921, and an f1 score of 0.899. This resulted in 8 false negatives and 13 false positives out of 184 points in what I believe can be described as an accurate model. One problem is that there are 8 false negatives(4.3 percent of people) as that puts someones life at risk due to them not getting treated for heart disease.

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K Nearest Neighbors

KNN works through proximity to make classifications or predictions about the grouping of an individual data point. Our KNN model had a accuracy of 86% and a recall of 90%. Above is a confusion matrix depicting the results of our model on the testing data set and it shows that this model has a higher chance of a false positive than a false negative.

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Neural Network

Our neural network for this project had 3 hidden layers. We trained it with a 0.3 validation split for 25 epochs. The result is a model that hovers at around 85-89% accuracy.`

Above is a confusion matrix which shows the predictions versus the actual results on the testing data set. We can see that in 27 cases, the model guessed that the patient had heart disease when they did not and in 15 cases where the model guessed the patient didn't have heart disease when they did.

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Scores

Above is the scores table showing the score results of all of our models. We can see that Adaboost, KNN, and Random Forest performed the best out of all the models while mlp and random forest grid performed the worst.

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Scores

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