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__Odd's Ratio__

**DEFINITION:**

- ODDS:The probability that an event will occur divided by the probability that the event will not occur
- Odds = Probability/(1-probability)
- RATIO:Is the number (a) of observations in a given group with a given characteristic ( such as having an MI) divided by the number (b) of observations without the given characteristic (such as not having MI). v ODDS RATIO: Is the ODDS that a patient is exposed to the risk factor divided by the ODDS that a control is exposed

**Odd ratio in case control study:**

- Odd of exposure among the cases : a/c
- Odd of exposure among the control: b/d
- Therefore Exposure odd ratio is: a/c ⁄b/d

Case | control | |
---|---|---|

Exposed | a | b |

unexposed | c | d |

b/d bc

- In a case control study, the most characteristic feature is odd's ratio

**Odds ratio in cohort study:**

Outcome YES | Outcome No | |
---|---|---|

Exposed | a | b |

unexposed | c | d |

- Odd of outcome among exposed=a/b
- Odd of outcome among unexposed=c/d

c/d

- Odds ratio can be calculated in a cohort study and in a case-control study.
- The exposure odds ratio is equal to the disease odds ratio.
- Relative risk can only be calculated in a cohort study.
- Odds ratio can be a measure of relative risk in case control study.

- The outcome is relatively rare. ( prevalence is 10% or less in general population)
- The cases must be representative of the cases in the population.
- The controls must be representative of the controls in the population

**Interpretation of odds ratio (OR) :**

- OR of >1 indicates that the exposure is associated with an increased risk of developing the disease.
- OR of Closer the value of OR to 0 greater the protection.
- The OR will rarely equal to 1 in absence of true risk or protection

**Uses of OR**

- OR are appropriate measure of RR in case control studies.
- OR are commonly used in meta analysis.
- Odds ratio is the measure of the strength of the association between risk factor and outcome.
- OR are the output of logistic regression analysis.

**Disadvantage:**

- OR exaggerate RR in common outcomes(prevalence>10).
- In those cases if OR >1 it is larger than the true RR and conversely if OR

**Exam Question**

**In a study done to establish Smoking as a risk factor for a disease, 30 out of 50 smokers developed the disease while 10 out of 50 non-smokers developed the disease. Odd's ratio is 6****Odds ratio is related to Relative risk****Odds = Probability/(1-probability)****Using case control study only odds ratio can be calculated.****Association can be measured by odds ratio****In a case control study, the most characteristic feature is odd's ratio****Odds ration is designated as ad/bc**

**Don't Forget to Solve all the previous Year Question asked on Odd's Ratio**