Question

1. In the United States, the estimated annual probability that a woman over the age of 35 dies of lung cancer is 0.001304 for current smokers and 0.000121 for non-smokers.   

(a) Calculate and interpret the difference in the proportions and the relative risk. Which is more informative for these data? Why? (b) Calculate and interpret the odds ratio. Explain why the relative risk and the odds ratio take on similar values.

2. For people with a particular type of cancer, the odds ratio for recovery (cancer in remission) between age groups (young versus old) was 4.5.   
(a) Choose one correct interpretation:

i. The probability of recovery for young subjects is 4.5 times the probability of recovery for old subjects. ii. The probability of recovery for old subjects is 4.5 times the probability of recovery for young subjects. iii. The odds of recovery for old subjects is 1/4.5 = 0.22 times the odds of recovery for young subjects. iv. The odds of recovery for old subjects is 4.5 times the odds of recovery for young subjects.


(b) Suppose that the odds of remission for young subjects is 3.1. For each age group, find the proportion of subjects who went into remission.

(c) Find the value of R in the interpretation: “The probability of remission for young subjects is R times that of older subjects.”

Answer 1

1)

Answer)

Given info,

the estimated annual probability that a woman over the age of 35 dies of lung cancer is 0.001304 for current smokers and 0.000121 for non-smokers.

A)

Difference of proportions is equal to 0.001304 - 0.000121 = 0.0012.

The difference between the proportions of female smokers and non smokers over 35 who dies of lung cancer is 0.0012 (0.12%).

Relative risk = 0.001304/0.000121 = 10.78

Female smoker has 10.78 times more chance of dying than non smoker.

Relative risk is more informative.

Since chances of dying due to lung cancer are extremely low.

So difference cannot give any exact conclusion.

B)

Odds ratio = (0.001304/0.998696)/(0.000121/0.99988)

= 10.79

The odds of female smoker over 35 of dying are 10.79 times higher than that of female non smoker.

For unlikely events odds ratio and relative risk are same.

Here we have unlikely event only, since probability of dying is extremely low.