AE 15: Risk of heart disease

Odds + probabilities

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Questions from the video?

High risk of heart disease

This dataset is from an ongoing cardiovascular study on residents of the town of Framingham, Massachusetts. We want to use the total cholesterol to predict if a randomly selected adult has a high risk of having coronary heart disease in the next 10 years.

• high_risk:
  • 1: High risk of having heart disease in next 10 years
  • 0: Not high risk of having heart disease in next 10 years
• totChol: total cholesterol (mg/dL)

heart <- read_csv("data/framingham.csv") %>%
  select(totChol, TenYearCHD) %>%
  filter(!is.na(totChol)) %>% #remove observations with missing cholesterol
  mutate(high_risk = as.factor(TenYearCHD))

Calculating probability and odds

1. What is the probability a randomly selected person in the study does not have a high risk of heart disease?

2. What are the odds a randomly selected person in the study does not have a high risk of heart disease?

Logistic regression model

1. Fit the appropriate model to predict whether a person has a high risk of heart disease given their total cholesterol.

2. Based on the model, if a randomly selected person has a total cholesterol of 225,

   • what are the log-odds they have a high risk of heart disease?
   • what are the odds they have a high risk of heart disease?
     
   • what is the probability they have a high risk of heart disease? Calculate the answer “manually” using the odds or log-odds.

3. Based on the model, if a randomly selected person has a total cholesterol of 226,

   • what are the log-odds they have a high risk of heart disease?
   • what are the odds they have a high risk of heart disease?
   • what is the probability they have a high risk of heart disease?

Comparing log-odds and odds

1. Based on your answers in the previous section, how do the log-odds change when going from a person with total cholesterol of 225 mg/dL to a person with total cholesterol of 226 mg/dL?

2. How would you interpret the coefficient of totlChol in terms of the log-odds?

3. What would be the interpretation of totChol in terms of the odds?