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Researchers trace the risk of harmful effects from an exposure in a variety of ways.
They will often -but not always - talk about a group of people exposed to a risk (e.g. smoking) and a group that does not and separate those groups into those people who present the outcome and those who do not. For example, if we wanted to study the relationship between smoking and lung cancer, we would set up the following table.
The Risk of an outcome is the number of times the outcome occurred as a percentage of all possible occurrences. In the case above, the risk of a patient who smokes developing lung cancer is 150/(150+850) or 15%. In other words, a patient who smokes has a 15% chance of developing lung cancer. Risk is often reported in descriptive articles where there is no control group.
The Relative Risk of an outcome occurring is the risk of the outcome occurring in the group exposed to the risk as a percentage of the risk of the outcome occurring in the group that was not exposed to the risk. In the example above, the risk of a patient who smokes developing lung cancer is 15% (150/1000). The risk of a patient who does not smoke developing lung cancer is 3% (30/1000). The Relative Risk is 15%/3% or 5. In other words, patients who smoke are 5 times more likely to have lung cancer than patients who do not. Relative Risk is also reported as Relative Risk Ratio or Risk Ratio.
The odds of an outcome occurring is the number of times the outcome occurred in patients exposed to the risk as a percentage of the times the outcome occurred in patients who were not exposed to the risk. In the example above, the odds of a patient who smokes developing lung cancer would be 150/30 or 5. In other words the odds are 5:1 that a patient who snokes will develop lung cancer.
The Odds Ratio of an outcome occurring is the odds that the outcome occurs in the group exposed to the risk as a percentage of the odds of the outcome not occurring in the group that is exposed to the risk. In the example above the odds of a patient who smokes developing lung cancer was calculated as 5. The odds of a patient who smokes not developing lung cancer is .87 (850/970). The Odds Ratio would be 5/.87 or 5.7. In other words, a smoker is 5.7 times more likely to develop lung cancer than not.
Relative Risk vs. Odds Ratio
Whether researchers report Relative Risk or Odds Ratio depends on whether they do a cohort study or a case control study. Because of the way subjects are chosen in a case control study, the percentages may be skewed. The Odds Ratio overcomes this problem by having both factors in the denominator.
Until now, the discussion of a harm study has been similar to the discussion of a prognosis study. However, it happens occassionally that researchers come upon a risk accidentally, most often when they are studying a therapy. In those cases they have been able to do a randomized double-blinded placebo-controlled clinical trial to (accidentally) assess harm and the results are presented in a similar way as with a therapy study.
Absolute Risk Increase
The Absolute Risk Increase (ARI) is the difference in risk between the two arms of the study. If the risk of breast cancer in a patient receiving hormone replacement therapy is 1.25% and the risk of breast cancer in a patient receiving a placebo is 1.1%, then the Absolute Risk Increase is 0.15%.
Number Needed to Harm
The Number Needed to Harm is the reciprocal of the Absolute Risk Increase. NNT=1/ARI (where the ARI is reported as a decimal) or 100/ARI (where the ARI is reported as a percentage. In the above example, the Number Needed to Harm would be 667. You would have to treat 667 patients with hormone replacement therapy to increase the risk of breast cancer in one additional patient.