Odds ratio
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The document discusses odds ratios, which are used to measure the association between an exposure and an outcome. An odds ratio is calculated by dividing the odds of an event in one group (e.g. exposed to a drug) by the odds of the event in another unexposed group. Odds ratios can be calculated in both cohort and case-control studies. While relative risk can only be calculated in cohort studies, odds ratios are commonly used to approximate relative risk in case-control studies when the outcome is rare. The document provides examples of how to calculate odds ratios from 2x2 contingency tables and interprets what different values mean.
Odds ratio
- 2. ODDS: Chance of event occurring divided by chance of event not occurring. › For example, in 100 births, the probability of a delivery being a boy is 51% and being a girl is 49% › The odds of a delivery being a boy is 51/49 = 1.04 In simpler term, an odds of an event can be calculated as : Number of events divided by number of non-events
- 3. ODDS RATIO An odds ratio is the odds of the event in one group , for example, those exposed to a drug, divided by the odds of the event in another group not exposed Odd ratio in epidemiology: In case control study since the incidence is not available so relative risk can not be calculated directly. Therefore Odd ratio is obtained which is a measure of strength of association between exposure and outcome
- 4. Case control Exposed a b unexposed c d 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 a/c ad = b/d bc Odd ratio of x indicated the cases are x times more likely to exposed to the risk factor than the control
- 5. 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 a/b Odd ratio= c/d =ad/bc
- 6. 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.
- 7. Outcome Outcome yes no Exposed a b Un exposed c d Incidence of outcome among the exposed= a/ a+b Incidence of outcome among the unexposed= c/c+d Relative risk =a/ a+b a<<<b a+b=b c/c+d c<<<d; c+d=d =a/b c/d =ad/bc Relative risk= Odds ratio
- 8. Odds ratio is a measure of true relative risk when: 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.
- 9. Interpretation of odds ratio (OR) : OR of >1 indicates that the exposure is associated with an increased risk of developing the disease. OR of <1 indicates that the exposure is associated with the reduced risk of (protect against) developing the outcome. Closer the value of OR to 0 greater the protection. The OR will rarely equal to 1 in absence of true risk or protection.
- 10. Paired Matching: In paired matched case- control study each case is matched to a control . The pairing is done independent of the exposure status under study Data are analyzed in terms of case-control pairs rather than for individual subjects. Four types of case-control combinations are possible in regard to exposure history.
- 11. CONTROL Exposed Unexposed Exposed A B CASES C D Unexposed
- 12. Concordant pairs are ignored since they don’t contribute in calculation of OR . Discordant pairs of cases and controls are used to calculate the matched OR. Matched OR = Ratio of discordant pairs pairs in which cases exposed / pairs in which controls were exposed
- 13. Case Control (RC) NO RC Heavy 190 a 115 b >3 cups/day Light 210 a+ 218 b+ <3 cups/day None 100 c 167 d
- 14. Constructing a confidence interval ( 95% or 99%) around the observed OR. If the CI does not contain null value then it indicates significant association. By performing chi square test on 2 by 2 table used to generate OR the statistical significance of OR is automatically assessed. ADJUSTED OR When the observed OR is adjusted against the confounders by multiple regression technique the outcome is adjusted OR
- 15. Uses of OR= 1. OR are appropriate measure of RR in case control studies. 2. OR are commonly used in meta analysis. 3. OR are the output of logistic regression analysis. Disadvantages of OR= 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<1 it is smaller than the true relative risk.