Introduction Odds Ratio

Medical students, students from clinical and psychological sciences, professionals allied to medicine enhancing their understanding and learning of medical literature and researchers from different fields of life usually encounter Odds Ratio (OR) throughout their careers.

Odds ratio is a relative measure of effect, allowing the comparison of the intervention group of a study relative to the comparison or placebo group. When computing Odds Ratio, one would do:

• The numerator is the odds in the intervention arm
• The denominator is the odds in the control or placebo arm= OR

If the outcome is the same in both groups, the ratio will be 1, implying that there is no difference between the two arms of the study. However, if the OR>1, the control group is better than the intervention group while, if the OR<1, the intervention group is better than the control group.

The ratio of the probability of success and failure is known as odds. If the probability of an event is $P_1$ then the odds is:
\[OR=\frac{p_1}{1-p_1}\]

The Odds Ratio is the ratio of two odds can be used to quantify how much a factor is associated to the response factor in a given model. If the probabilities of occurrences an event are $P_1$ (for first group) and $P_2$ (for second group), then the OR is:
\[OR=\frac{\frac{p_1}{1-p_1}}{\frac{p_2}{1-p_2}}\]

If predictors are binary then the OR for ith factor, is defined as
\[OR_i=e^{\beta}_i\]

The regression coefficient $b_1$ from logistic regression is the estimated increase in the log odds of the dependent variable per unit increase in the value of the independent variable. In other words, the exponential function of the regression coefficients $(e^{b_1})$ in the OR associated with a one unit increase in the independent variable.