Introduction Odds Ratio
An 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.
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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.
When computing the OR, one would do:
- The numerator is the odds in the intervention arm
- The denominator is the odds in the control or placebo arm= OR
Calculating ODDs Ratios
The ratio of the probability of success and failure is known as the odds. If the probability of an event is $P_1$ then the odds are:
\[OR=\frac{p_1}{1-p_1}\]
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 Odds Ratio is the ratio of two odds that can be used to quantify how much a factor is associated with the response factor in a given model. If the probabilities of occurrences of an event are $P_1$ (for the first group) and $P_2$ (for the 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 $i$th 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 is associated with a one-unit increase in the independent variable.
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