Odds Ratio

Odds Ratio (OR) measures the association between an outcome and a treatment/exposure.  Or in other words, a comparison of an outcome given two different groups (exposure vs. absence of exposure).

OR compares the odds of an outcome with and without treatment.

Odds represent the probability of an event occurring divided by the probability of an event not occurring.

Although related, probability and odds are not the same. Probability values can only range from 0 to 1 (0% to 100%), whereas odds can take on any value.

An OR value of 1 shows no effect, while OR < 1 indicates lower odds and OR > 1 indicates higher odds due to exposure.

OR assesses whether a treatment is a risk factor for an outcome.

Calculating OR requires the frequencies of two dichotomous variables.

For example: a study consist 263 participants, where the aim of the study is to assess the OR of having the flu virus given the presence of a diet pill.

•    The two dichotomous variables are flu virus (yes/no) and diet pill consumption (regular use/no regular use).
•    Among 100 participants, 45 have the flu and take diet pills regularly. While 86 have the flu but don’t take pills regularly.
• Meanwhile, 32 don’t have the flu but take pills regularly. And 100 don’t have the flu or take pills regularly.
• To calculate the OR, we make sure the numerator and denominator are in the correct location:
  • The numerator is 45/32, flu cases among regular diet pill users; and
  • the denominator of the ratio is the number of participants who have the flu and do not take diet pills regularly (86) divided by the number of participants who do not have the flu and do not take diet pills regularly (100).
  • OR = (45/32) / (86/100) = 1.63
• Thus, regular diet pill users have 1.63 times higher odds of having the flu than non-users.