# Introduction Odds Ratio

**Introduction Odds Ratio**

**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*.