# How to estimate relative risk for a small group which has 0 members with the outcome?

I have a contingency table that looks like this:

                Disease          Not Disease
Exposed           372              870
Not Exposed         0               23


What methods would I use to estimate if there is a statistically significant difference between the exposed and not exposed?

• Fisher's exact test may work. – Penguin_Knight Apr 26 '15 at 18:38
• @Tim let's say that the outcome is having any allergy and the exposure is having ever lived in a house with a microwave. – Skylar Saveland Apr 27 '15 at 5:18
• @Tim There can be--and often is--baseline risk. For instance, about a third of US adults will eventually die of cancer. Exposure to a carcinogen, then, potentially will increase the risk, but lack of that particular exposure is not going to eliminate all risk of dying from cancer! In many experiments, things happen to the control subjects: that's why we have controls in the first place. This particular table is extraordinary in not exhibiting any occurrences of the disease among the 23 unexposed individuals. – whuber Apr 29 '15 at 16:21

Expected:-

                Disease          Not Disease
Exposed           365.24           876.76
Not Exposed         6.76            16.24


as expected cell values is big enough you can test by Chi-square contingency test.

• (-1) What are those numbers? How were they calculated? Sorry, but your answer does not provide enough information to understand what do you mean. – Tim May 3 '15 at 21:02
• these are expected outcomes $\frac{(sum~of~data~in~that~row)(sum~of~data~in~that~column)}{sum~of~total~data}$ – Hemant Rupani May 4 '15 at 4:34
• stats.stackexchange.com/questions/149219/… – Hemant Rupani May 4 '15 at 4:54
• But this should be a part of your answer if you refer to $\chi^2$. – Tim May 4 '15 at 6:04