Cardiovascular Disease Sudden death is an important, lethal cardiovascular endpoint. Most previous studies of risk factors for sudden death have focused on men. Looking at this issue for women is important as well. For this purpose, data were used from the Framingham Heart Study. Several potential risk factors, such as age, blood pressure and cigarette smoking are of interest and need to be controlled for simultaneously, along with other factors. Therefore a multiple logistic regression (logistic regression with multiple predictors) was fitted to these data as shown below. The response is 2-year incidence of sudden death in females (yes or no) without prior coronary heart disease.

Let Y=Incidence of sudden death in females (1=yes, 0=no). Model fit to data is:

Logit[P(Y=1)]=B ₀ +B ₁ BP + B ₂ WEIGHT + B ₃ CHOL + B ₄ GLUCOSE + B ₅ SMOK + B ₆ HEMATOCRIT

+ B ₇ VITAL + B ₈ AGE



1. State the fitted logistic regression model using the parameter estimates given above.
2. Compute the odds ratios relating the additional risk of sudden death associated with smoking adjusted for all other factors in the model.
3. Compute the odds ratio relating the additional risk sudden death associated with a 10 year increase in age adjusted for all other factors in the model.
4. Provide 95% confidence intervals for each of the odds ratios calculated above.
5. From this model, is it possible to assess if the OR associated with smoking changes with age? Why or why not?

Bonus:

Calculate the predicted the probability of sudden death for a 50 year old woman with systolic blood pressure of 120 mmHg, a relative weight of 100% a cholesterol level of 250 mg/100mL, a glucose level of 100 mg/100mL, a hematocrit of 40%, and a vital capacity of 450 centiliters who smokes 10 cigarettes per day. (Note that these numbers are near average for a healthy woman except for the cholesterol level which is high, and of course the number of cigarettes smoked.)

(hint, the Framingham study was a prospective study from which we can estimate the probability of disease given exposure. Use the definition of the logit --- and that logit (P) is modeled as a linear function of predictors.

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