Odds Ratio

Start is the Contingency Table of 2 * 2. "Use" means "Use of medicine".
Ratio

Table of Ratio

In risk analysis a table of ratio (probability) is made from contingency (frequency) table.
Ratio Ratio

After that, we compare the ratio.

By the way, in the discussion of ratio, we often forget the effect of volume of sample.

Difference of ratio is popular index.
Difference ot Ratio

Hypothesis Testing for Difference of Ratio is used to consider the effect of volume of sample.

Ratio of ratio is called "Risk ratio" or "Relative risk".

Odds is the ratio of probability of occur and not occur.
Odds

Logarithm of Odds is called " Logit ".

Odds ratio is the ratio of 2 odds.

Odds and Odds ratio are also calculated without p and q.

Logarithm of odds ratio has the meaning "Difference of Logit" And this meaning is useful to consider the use case of logarithm of odds ratio.

I made Heat Map to compare indexes.

ratio ratio ratio ratio