Coronary Heart Disease in British Male Physicians A Probability Assessment

Probability Assessment of Coronary Heart Disease in British Male Physicians

In 1985, Breslow performed research investigating the mortality rates due to coronary heart disease among British male doctors, categorizing them by their smoking behavior (as cited in Hand et al., 1994). The gathered data is shown in the following table.

Age, smoking, and heart disease in a sample of male physicians

Age (in years)

Nonsmokers

Smokers

35-44

45-54

55-64

65-74

75-84

Using the data, we can answer the following questions:

Question 1: How many doctors were surveyed?

To calculate the entire number of doctors examined, we add the number of nonsmokers and smokers for every age category:

Total = (2 + 32) + (12 + 104) + (28 + 206) + (28 + 186) + (31 + 102)

Total = 34 + 116 + 234 + 214 + 133

Total = 731

A total of 731 doctors were examined.

Question 2: How many of these doctors reported that they smoked? How many reported that they did not smoke?

To determine the number of doctors who smoked and those who did not, we combine the figures in the corresponding columns:

Nonsmokers = 2 + 12 + 28 + 28 + 31 = 101

Smokers = 32 + 104 + 206 + 186 + 102 = 630

Among the examined doctors, there were 101 nonsmokers and 630 smokers.

Question 3: What is the probability that a person who died of coronary heart disease was between the ages of 35 and 44? Within this age group (i.e., 34 to 44), what is the probability that the person was a smoker?

To compute the probability, we divide the number of individuals in the age category by the overall quantity of examined doctors:

P(35-44) = (2 + 32) / 731 = 34 / 731 ? 0.0465

The probability that an individual who died from coronary heart disease was aged between 35 and 44 is roughly 0.0465.

Within the 35-44 age group:

P(Smoker) = 32 / 34 ? 0.9412

The probability that an individual who died from coronary heart disease aged between 35 and 44 was a smoker is roughly 0.9412.

Question 4: What is the probability that someone who died of coronary heart disease between the ages of 75 and 84 was a smoker?

P(Smoker | 75-84) = 102 / (31 + 102) = 102 / 133 ? 0.7669

The probability that an individual who died from coronary heart disease aged between 75 and 84 was a smoker is roughly 0.7669.