Logistic Regression on 10 Year Heart Disease Risk

.title[
# Logistic Regression on 10 Year Heart Disease Risk
]
.author[
### By: Evan Parker, Edward Coleman, Zack Shin, and Johnny Zhang
]
.institute[
### West Chester University of Pennsylvania 
]
.date[
### December 15, 2022 Prepared for STA 490: Capstone Statistics 
]

---

## <center>Agenda</center>

### Dataset Description

### Variable Breakdown

### Final Dataset Creation

### Model Building

### Model Selection

---

# <center>Dataset Description</center>

- 1948: 5,000 research participants, 30-60 y.o.
- Framingham, Massachusetts
- Examined every 2 years
- 1971: Re-roster due to passed away patients
- 4240 observations
- Both demographical and medical information

**From this Analysis:**

We hope to uncover key characteristics of patents that will determine if they will be diagnosed with *Coronary Heart Disease*. This will help medical professionals potentially diagnose patents sooner, saving their lives n the process

---

# <center>List of Variables</center>

- **Male**: Dummy Variable, 0 for Female, 1 for Male
- **Age**: Patient's age in years
- **Education**: 1: Some High School, 2: High School/GED, 3: Some College/Vocational School, 4: College
- **SmokingStatus**: Dummy Variable, 0 for Non-Smoker, 1 for Smoker
- **CigarettesPerDay** Amount of Cigarettes smoked per day
- **BloodPressureMeds** Dummy Variable, 0 for Not Prescribed, 1 for Prescribed
- **StrokeHistory**: Dummy Variable, 0 for No Stroke, 1 for Stroke
- **HighBloodPressure**: Dummy Variable, 0 for no HBP, 1 for HBP
- **Diabetes**: Dummy Variable, 0 for Not Diagnosed, 1 for Diagnosed
- **TotalCholesterol**: Patient's cholesterol levels (mg/dL)
- **SystolicBloodPressure**: Patient's systolic BP (mmHg)
- **DiastolicBloodPressure**: Patient's diastolic BP (mmHg)
- **BMI**: Patient's BMI (kg/m^2)
- **GlucoseLevel**: Patient's glucose level (mg/dL)

**Response**:

- **CoronaryHeartDisease**: Dummy Variable, 0 for Not at Risk, 1 for At Risk

---

# <center>Male</center>

- More females than males
- *0* observations with missing data

---

# <center>Age</center>

- Split observations into age groups of 10 years
- Very few in 70's category, thus combined with 60's
- *0* observations with missing data

]

- Appears to be approximately Normal

]

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# <center>Education</center>

- Most patients did not attend college 
- *105* observations with missing data

---

# <center>Smoking Status</center>

- Almost an even split
- *0* observations with missing data

---

# <center>Cigarettes Per Day</center>

- Split into groups of 10 cigarettes
- Most patients did not smoke
- Of smokers, most fall into *11-20* category
- *29* observations with missing data

]

- Skewed plot due to half of the sample not smoking
- Some high outliers in 60's

]

---

# <center>Blood Pressure Medication</center>

- Large majority are were not prescribed
- *53* observations with missing data

---

# <center>Stroke History</center>

- Large majority did not have a previous stroke
- *0* observations with missing data

---

# <center>High Blood Pressure</center>

- About two-thirds do not have High Blood Pressure
- *0* observations with missing data

---

# <center>Diabetes</center>

- Large majority have not been diagnosed
- *0* observations with missing data

---

# <center>Total Cholesterol</center>

- Quite Normal histogram
- Some high outliers in 600's range
- *50* observations with missing data

---

# <center>Systolic Blood Pressure</center>

- Normal Histogram
- *0* observations with missing data

---

# <center>Diastolic Blood Pressure</center>

- Normal Histogram
- *0* observations with missing data

---

# <center>BMI</center>

- Normal Histogram
- Few high outliers in 50's and 60's
- *19* observations with missing data

---

# <center>BPM</center>

- Normal Histogram
- *1* observation with missing data

---

# <center>Glucose</center>

- Normal Histogram, potential right tail
- Some high outliers in 200's and 300's
- *388* observations with missing data

---

# <center>Coronary Heart Disease</center>

- Most patients were not at risk of Coronary Heart Disease
- *0* observations with missing data

---

# <center>Missing Data</center>

- **EducationLevel**, **CigarettesPerDay**, **BloodPressureMeds**, **TotalCholesterol**, **BPM**, and **GlucoseLevel** are all missing data
- Patients not want to disclose information, medical professions did not test

**Our Attempt**

- Create a temporary data set with only complete observations, run regression to create a predictive model
- Variables were not highly correlated correlated, meaning linear regression was not accurate
- Instead, replace missing values with mode of variable

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# <center>Variable Recoding</center>

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# <center>PCA's</center>

]

]

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# <center>Our Final Dataset is Complete!</center>

- Replaced Missing Values
- Re-coded Variables
- Added PCA 1 and PCA 2

**Analysis**:

- Since **CHDRisk** is a dummy variable, analysis will be a *logistic regression analysis*

---

# <center>Model 1: All Predictors</center>

CHDRisk = Male + Age + Education + 
SmokingStatus + CigaretesPerDay + BloodPressureMedication + StrokeHistory + 
HighBloodPressure + Diabetes + TotalCholesterol + SystolicBloodPressure + DiastolicBloodPressure + 
BMI + BPM + GlucoseLevel + PCA1 + PCA2

---

# <center>Model 2: Categorical Predictors</center>

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# <center>Model 1 vs Model 2</center>

Because *Model 2* is a nested model of *Model 1*, we run a likelihood ratio test

- Statistically significant p-value
- *Model 1* performs better than *Model 2*
- Numerical Variables are important for Coronary Heart Disease diagnoses

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# <center>Model 3: Numerical Predictors</center>

CHDRisk = TotalCholesterol + SystolicBloodPressure + DiastolicBloodPressure + 
BMI + BPM + GlucoseLevel + PCA1 + PCA2

---

# <center>Model 1 vs Model 3</center>

Because *Model 3* is a nested model of *Model 1*, we run a likelihood ratio test

- Statistically significant p-value
- *Model 1* performs better than *Model 3*
- Categorical Variables are important for Coronary Heart Disease diagnoses

---

# <center>Final Model</center>

<center>Model 1 is the best model!</center>

**CHDRisk** = 1.271 − 0.4996(**Male.Male**) − 0.1659(**Age.40's**) − 0.3964(**Age.50's**) − 0.5961(**Age.60+**) + 0.1894(**Education.SomeCollege**) + 0.4123(**Education.GraduatedCollege**) − 0.5369(**SmokingStatus.Yes**) − 0.1485(**CigarettesPerDay.1to10**) − 0.4599(**CigarettesPerDay.11to20**) − 0.712(**CigarettesPerDay.21to30**) − 1.051(**CigarettesPerDay.30+**) − 1.23(**BloodPressureMedication.Prescribed**) − 1.491(**StrokeHistory.Yes**) − 0.6388(**HighBloodPressure.Yes**) − 0.8538(**Diabetes.Diagnosed**) − 0.000136(**TotalCholesterol**) − 0.0002852(**SystolicBloodPressure**) + 0.0003342∗(**DiastolicBloodPressure**) + 0.0003147(**BMI**)  − 0.00007206(**BPM**) + 0.0002211(**Glucose**) − 0.1139(**PCA1**) + 0.7346(**PCA2**)

- For Categorical Variables: There are multiple cases for each variable. If the patient is in their 50's only use the **Ages.50's** quantifier and ignore **Age.40's** and **Age.60's**
- Model is used for finding the odds of the patient getting diagnosed with Coronary Heart Disease

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# <center>Conclusion and Discussion</center>

- Further analysis can be done with interaction and hierarchical variables
- Model is limited to the sample (both time and location)
- Model might be out of date given the time period of the sample and the medical advances since 1948 and 1971

## <center>Any Questions?</center>