Question

To study the relationship between coffee consumption and incidence of cancer in a country, researcher Ben randomly sampled 300 people from all cancer patients in the population, and randomly sampled another 700 people from all other residents. Based on interviews with the 1000 subjects in the combined sample, Ben gathered information to split them into two categories of coffee consumption: high and low.
It is found that within the sample,
•   exactly 90 subjects are cancer patients with high level of coffee consumption, and
•   30% of the subjects have high level of coffee consumption.

a) What is a good estimate of the risk of cancer among people with high level of coffee consumption in the country

b) What is a good estimate of the odds ratio of cancer between people with high level of coffee consumption, and people with low level of coffee consumption, in the country (to 2 decimal places)?

c) What is a good estimate of the odds of cancer among people with high level of coffee consumption in the country (to 2 decimal places)?

d) What is a good estimate of the risk ratio of cancer between people with high level of coffee consumption, and people with low level of coffee consumption, in the country (to 2 decimal places)?

e) What is the rate of cancer among people with high level of coffee consumption in the sample (to 2 decimal places)?

Answer 1

Coffee Consumption Suffering from Cancer Total

Yes NO

High 90 210 300

Low 210 490 700

Total 300 700 1000

Part A

Risk of cancer among people wit high level of coffee consumption = People with high level of coffee consumption and cancer/Total number of people with high level of coffee consumption

= 90/300

= 0.30

Part B

Odds Ratio of cancer between people between high level of coffee consumption and low level of coffee consumption = Odds of high level of cancer and consumption/Odds of low level of consumption and cancer

= (90/210)/(210/490)

= 0.4286/0.4286

= 1

Part C

Odds of cancer among people with high level of coffee consumption = 90/210

= 0.43

Part D

The risk ratio of cancer between people with high consumption coffee and low consumption of coffee would be:

= (90/300)/210/300)

= 90/210

= 0.43

Part E

Rate of cancer among people with high level of coffee consumption = Total number of cancer with high consumption of coffee/Total number of people with high consumption of coffee

= 90/300

= 0.3

The rate of cancer among people with high coffee consumption is 0.3*100 or 30%.

Total Coffee Consumption Yes High Suffering from Cancer NO 90 210 3001 Low 210 490 700 300 700 1000 Total