Question

4.3 Heart attack is one of the leading causes of death in many countries and cigarette smoking is the most preventable risk factor for heart attack. In a particular population, 20% of people suffered a heart attack, 16% ofpeople are current smokers, and 12% of people had a heart attack while they were smokers. Let event A be a person who is a current smoker and event B be a person who had heart attack. a) Construct a Venn diagram to show the relationship between having a heart attack and current smoking. b) Calculate P(A), PCB), P(AB), and P(AB). c) If a person is randomly selected from current smokers, what is the probability that this person would suffer a heart attack? d) If a person is randomly selected from current non-smokers, what is the probability that this person would suffer a heart attack? e) What is the risk of having a heart attack for current smokers? What is the risk of having a heart attack for current non-smokers? f) What is the relative risk of suffering a heart attack for current smokers compared to current non-smokers? What is the relative risk comparing current non-smokers to current smokers? g) What are the odds of having a heart attack among those who are current smokers? What are the odds of having a heart attack among current non-smokers? h) What is the odds ratio of having a heart attack for current smokers compared to current non- smokers? What would be the odds ratio comparing current non-smokers to current smokers?

Answer 1

a)

b)

P(A) = 0.16

P(B) = 0.2

P(AB) = 0.12

P($\bar{A}$B) = P(B) - P(AB) = 0.2 - 0.12 = 0.08

c)

Given that the person is smoker, probability that person suffer from heart attack = P(B | A) = P(AB) / P(A)

= 0.12 / 0.16 = 0.75

d)

Given that the person is non-smoker, probability that person suffer from heart attack = P(B | $\bar{A}$) = P($\bar{A}$B) / P($\bar{A}$)

= P($\bar{A}$B) / (1 - P(A))

= 0.08 / (1 - 0.16) = 0.095

e)

Risk of having heart attack for current smoker = P(B | A) = 0.75

Risk of having heart attack for current non-smoker = P(B | $\bar{A}$) = 0.095

f)

Relative risk for current smokers compared to current non-smokers = Risk of having heart attack for current smoker / Risk of having heart attack for current non-smoker

= 0.75 / 0.095 = 7.89

Relative risk for current non-smokers compared to current smokers = Risk of having heart attack for current smoker / Risk of having heart attack for current non-smoker

= 0.095 / 0.75 = 0.1267

g)

Odds of having heart attack among current smokers = 0.75 / (1 - 0.75) = 3

Odds of having heart attack among non-current smokers = 0.095 / (1 - 0.095) = 0.105

h)

Odds ratio of having a heart attack for current smokers compared with non-smokers = Odds of having heart attack among current smokers / Odds of having heart attack among non-current smokers = 3 / 0.105 = 28.57

Odds ratio of having a heart attack for non-current smokers compared with smokers = Odds of having heart attack among current non-smokers / Odds of having heart attack among current smokers = 0.105 / 3 = 0.035