Question

Suppose we are interested in studying whether exposure to a pesticide increases the risk of prostate cancer. Assume that 20% of controls are exposed to the pesticide and we wish to detect an odds ratio of 2.7 from the exposure. Note that p2 = 0.2 and we need to calculate p1. How many cases and how many controls are needed in your case-control study?

Answer 1

The formula to calculate the odds ratio is:

Here, p2 = 0.2 and p1 we need to calculate:

(1-p1)/p1 = 10.8

Therefore, p1 = 0.084

Let's use the following formula to calculate the number of cases required in our study:

You could use any other formula too, but as here it isn't mentioned in your question, I will be using the above formula:

So, for 95% confidence level,

We will assume p = 0.1 as 1 in 10 have the risk of generating prostate cancer

q = 1-p = 0.9

d = 0.05 (Assume)

Therefore, n = 138

Hence, 138 cases are required to perform the case-control study and out of these, 20% (28 people) are the controls.