AE 16: Risk of heart disease

Odds ratios

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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 systolic blood pressure and whether someone has family history of hypertension to determine the odds of being 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
• sysBP: systolic blood pressure (mmHg)
• prevalentHyp: No = Hypertension not prevalent in family history; Yes = Hypertension prevalent in family history

Part 1:Odds Ratios

Let’s start by looking at the relationship between a family history of hypertension and being high risk of heart disease.

	0	1
No	2604	319
Yes	992	325

Answer the following questions using this form.

1. Calculate the odds ratio of being high risk of having heart disease for those with a family history of hypertension vs. those without a family history hypertension.

2. Suppose you fit a model using prevalentHyp to predict the odds of being high risk of having heart disease. The model has the following form:

\[\log\big(\frac{\hat{\pi}}{1-\hat{\pi}}\big) = \hat{\beta}_0 + \hat{\beta}_1 \times \text{PrevalentHypYes}\]

What is the value of the estimated coefficient \(\hat{\beta}_1\)?

3. Based on this model, what are the odds of being high risk of heart disease for people with no family history of hypertension?

Part 2: Add systolic blood pressure.

Let’s add systolic blood pressure to the model.

term	estimate	std.error	statistic	p.value
(Intercept)	-4.490	0.317	-14.158	0.000
prevalentHypYes	0.329	0.123	2.677	0.007
sysBP	0.019	0.002	7.754	0.000

Answer the following questions using this form.

1. Interpret the coefficient of sysBP in terms of the log-odds of being high risk of having heart disease.

2. Interpret the coefficient of sysBP in terms of the odds of being high risk of having heart disease.

3. How do you expect the log-odds of being high risk for heart disease to change when going from a person with systolic blood pressure of 120 mm Hg to a person with systolic blood pressure of 125 mm Hg. Assume both people do not have a family history of hypertension.

4. How do you expect the odds of being high risk for heart disease to change when going from a person with systolic blood pressure of 120 mm Hg to a person with systolic blood pressure of 125 mm Hg. Assume both people do not have a family history of hypertension.