Risk difference, odds ratio, and risk ratio are all statistical measures used to quantify the
relationship between an exposure and an outcome, but they differ in how they express that
relationship. Here's a breakdown of each:
1. Risk Difference:
• Calculation: Risk difference is simply the difference between the probability of the
outcome occurring in the exposed group and the probability of it occurring in the
unexposed group.
• Interpretation: It tells you how much higher the risk of the outcome is in the exposed
group compared to the unexposed group. For example, a risk difference of 0.05 means
that people exposed to the factor are 5% more likely to experience the outcome than
those not exposed.
• Advantage: Easy to understand and interpret for absolute effects.
2. Odds Ratio:
• Calculation: Odds ratio is the ratio of the odds of the outcome occurring in the exposed
group to the odds of it occurring in the unexposed group. Odds are different from
probability; they tell you how likely it is for something to happen compared to how likely
it is not to happen.
• Interpretation: It tells you how much more likely it is for the outcome to occur in the
exposed group compared to the unexposed group. For example, an odds ratio of 2 means
that people exposed to the factor are twice as likely to experience the outcome as those
not exposed.
• Advantage: More helpful for interpreting the effect of an exposure on rare events, as it
focuses on relative differences rather than absolute changes.
3. Risk Ratio:
• Calculation: Risk ratio is the ratio of the probability of the outcome occurring in the
exposed group to the probability of it occurring in the unexposed group. Similar to risk
difference, but expressed as a ratio.
• Interpretation: It tells you how much higher the risk of the outcome is in the exposed
group compared to the unexposed group, expressed as a multiple. For example, a risk
ratio of 1.5 means that people exposed to the factor are 50% more likely to experience
the outcome than those not exposed.
• Advantage: Easier to interpret than odds ratio for relative effects, especially when close to
1.
Examples:
Smoking and lung cancer:
• Risk difference: Imagine a study where 10% of smokers develop lung cancer within 10
years, compared to 5% of non-smokers. The risk difference would be 0.05, meaning
smokers are 5% more likely to develop lung cancer than non-smokers.
• Odds ratio: In the same scenario, the odds ratio could be around 2. This means that
smokers are twice as likely as non-smokers to experience lung cancer within 10 years.
• Risk ratio: The risk ratio would also be 2 in this case, confirming that smokers have a 2fold higher risk of lung cancer compared to non-smokers.
2. Vitamin C and the common cold:
• Risk difference: Suppose research shows that 15% of people who take vitamin C
supplements get a cold within a month, while 20% of those who don't take them do. The
risk difference would be -0.05, suggesting that taking vitamin C might reduce the risk of
getting a cold by 5% (although further research would be needed to confirm this).
• Odds ratio: The odds ratio in this case might be around 0.75, indicating that people taking
vitamin C are 75% less likely to catch a cold than those who don't.
• Risk ratio: The risk ratio would be slightly lower than 1 - likely around 0.95 - which further
emphasizes the potential protective effect of vitamin C against the common cold.
3. Exercise and heart disease:
• Risk difference: A study might find that 5% of physically inactive people develop heart
disease within 10 years, compared to 3% of those who exercise regularly. The risk
difference would be 0.02, showing a smaller absolute benefit of exercise in this case.
• Odds ratio: The odds ratio could be around 0.6, implying that physically active individuals
are 40% less likely to experience heart disease within a decade.
• Risk ratio: Again, the risk ratio would be around 0.6, representing a 40% reduction in heart
disease risk for those who exercise consistently.
This document is prepared by Muhammed Elnaggar. Feel free to get more documents on the
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