# Odds ratio

The **odds ratio (OR)** is the *ratio* of the *odds* of D (Disease) in the presence of V (Variant Allele) and the odds of D (Disease) in the absence of V (Variant Allele). Recall that odds and probability are slightly different in that...

Ratio: N(D|V) / ( N(D|v) + N(D|~V) )

Prob: N(D|V) / ( N(D|v) + N(D|~V) )

This statistic attempts to quantify the strength of the association between A and B.

If the OR is greater than 1, then A is considered to be associated with B in the sense that, compared to the absence of B, the presence of B raises the odds of A.

Often the odds ratio is used to compare the occurrence of some outcome (A) in the presence of some exposure (B), with the occurrence of the outcome (A) in the absence of a particular exposure (absence of B).

Two similar statistics that are often used to quantify associations are the **risk ratio (RR)** and the **absolute risk reduction (ARR)**.

Often, the parameter of greatest interest is actually the RR,

RR is the ratio of the probabilities analogous to the odds used in the OR. However, available data frequently do not allow for the computation of the RR or the ARR but do allow for the computation of the OR, as in case-control studies

The OR plays an important role in logistic regression (in the logistic function model, aka logit model; see also probit model, and sigmoid function)