An incidence rate ratio allows us to compare the incident rate between two different groups.
For example, suppose it’s known that people who smoke develop lung cancer at a rate of 7 per 100 person-years.
Conversely, suppose it’s known that people who do not smoke develop lung cancer at a rate of 1.5 per 100 person-years.
We would calculate the incidence rate ratio (often abbreviated IRR) as:
- IRR = Incidence rate among smokers / Incidence rate among non-smokers
- IRR = (7/100) / (1.5/100)
- IRR = 4.67
Here’s how we would interpret this value: The lung cancer rate among smokers is 4.67 times as high as the rate among non-smokers.
How to Interpret Incidence Rate Ratios
Here is how to interpret an incidence rate ratio (IRR):
IRR Less than 1: This indicates that the incident rate is lower in an exposed group compared to an unexposed group.
For example, if smokers developed lung cancer at a rate of 7 per 100 person-years and non-smokers developed lung cancer at a rate of 10 per 100 person-years, then the IRR would be 7/10 = 0.7.
This would mean that smokers experience the incidence (lung cancer) less often than non-smokers.
IRR Equal to 1: This indicates that the incident rate is equal among those in an exposed group and those in an unexposed group.
For example, if smokers developed lung cancer at a rate of 7 per 100 person-years and non-smokers developed lung cancer at a rate of 7 per 100 person-years, then the IRR would be 7/7 = 1.
This would mean that smokers experience the incidence (lung cancer) just as often as non-smokers.
IRR Greater than 1: This indicates that the incident rate is greater in an exposed group compared to an unexposed group.
For example, if smokers developed lung cancer at a rate of 7 per 100 person-years and non-smokers developed lung cancer at a rate of 1.5 per 100 person-years, then the IRR would be 7/1.5 = 4.67.
This would mean that smokers experience the incidence (lung cancer) more often than non-smokers.
Why is Incidence Rate Ratio Useful?
Incidence rate ratio is a useful metric because it’s so easy to interpret and it allows us to immediately understand if exposure to something increases or decreases the rate of some incidence.
For example, just knowing that the IRR of smoking is 4.67 tells us that lung cancer occurs far more often in smokers compared to non-smokers.
We also know that the larger the value for IRR, the greater the ratio of some incident in an exposed group compared to an unexposed group.
Conversely, the closer IRR is to 1 the smaller the difference in the incident rate between an exposed group and an unexposed group.
Example: Calculating Incidence Rate Ratio
Suppose a doctor collects data on how often individuals develop a disease, based on their BMI (body mass index).
The following table summarizes the data:
Using this table, we can calculate the following metrics:
Incidence Rate Ratio of (BMI > 30) vs. (BMI 25-30) = 1.48 / 1.12 = 1.32
- Interpretation: The disease rate among individuals with BMI > 30 is 1.32 times as high as the rate among individuals with BMI between 25 and 30.
Incidence Rate Ratio of (BMI > 30) vs. (BMI < 25) = 1.48 / 0.54 = 2.74
- Interpretation: The disease rate among individuals with BMI > 30 is 2.74 times as high as the rate among individuals with BMI less than 25.
Incidence Rate Ratio of (BMI 25-30) vs. (BMI < 25) = 1.12 / 0.54 = 2.07
- Interpretation: The disease rate among individuals with BMI between 25 and 30 is 2.07 times as high as the rate among individuals with BMI less than 25.
Additional Resources
What is Number Needed to Harm? (Definition & Example)
Number Needed to Harm Calculator
How to calculate the 95%CI confidence interval? Can the method for relative risk ratio calculated by incidence ratio but not the incidence density be used?
Hi Cheng….To calculate the 95% confidence interval (CI) for relative risk (RR), you can use the following method:
### Steps to Calculate 95% Confidence Interval for Relative Risk
1. **Calculate the Relative Risk (RR):**
\[
RR = \frac{a / (a + b)}{c / (c + d)}
\]
Where:
– \( a \) = number of exposed cases
– \( b \) = number of exposed non-cases
– \( c \) = number of unexposed cases
– \( d \) = number of unexposed non-cases
2. **Calculate the Natural Logarithm of RR (ln(RR)):**
\[
\ln(RR) = \ln \left( \frac{a / (a + b)}{c / (c + d)} \right)
\]
3. **Calculate the Standard Error (SE) of ln(RR):**
\[
SE(\ln(RR)) = \sqrt{\frac{1}{a} – \frac{1}{a + b} + \frac{1}{c} – \frac{1}{c + d}}
\]
4. **Calculate the 95% Confidence Interval for ln(RR):**
The 95% CI for the natural logarithm of RR is given by:
\[
\ln(RR) \pm 1.96 \times SE(\ln(RR))
\]
5. **Convert the CI back to the original scale:**
The 95% CI for RR is obtained by exponentiating the lower and upper bounds of the CI for ln(RR):
\[
\text{Lower bound} = \exp\left( \ln(RR) – 1.96 \times SE(\ln(RR)) \right)
\]
\[
\text{Upper bound} = \exp\left( \ln(RR) + 1.96 \times SE(\ln(RR)) \right)
\]
### Example Calculation
Suppose you have the following data:
– \( a = 50 \) (exposed cases)
– \( b = 150 \) (exposed non-cases)
– \( c = 30 \) (unexposed cases)
– \( d = 170 \) (unexposed non-cases)
1. **Calculate the RR:**
\[
RR = \frac{50 / (50 + 150)}{30 / (30 + 170)} = \frac{50 / 200}{30 / 200} = \frac{0.25}{0.15} = 1.67
\]
2. **Calculate the ln(RR):**
\[
\ln(RR) = \ln(1.67) = 0.51
\]
3. **Calculate the SE of ln(RR):**
\[
SE(\ln(RR)) = \sqrt{\frac{1}{50} – \frac{1}{200} + \frac{1}{30} – \frac{1}{200}} = \sqrt{0.02 – 0.005 + 0.0333 – 0.005} = \sqrt{0.0433} = 0.208
\]
4. **Calculate the 95% CI for ln(RR):**
\[
95\% \, CI = 0.51 \pm 1.96 \times 0.208
\]
\[
95\% \, CI = 0.51 \pm 0.408
\]
\[
\text{Lower bound} = 0.51 – 0.408 = 0.102
\]
\[
\text{Upper bound} = 0.51 + 0.408 = 0.918
\]
5. **Convert the CI back to the original scale:**
\[
\text{Lower bound} = \exp(0.102) = 1.107
\]
\[
\text{Upper bound} = \exp(0.918) = 2.505
\]
So, the 95% confidence interval for the RR is approximately (1.107, 2.505).
### Method for Relative Risk Using Incidence Ratio
If you are referring to calculating relative risk using incidence ratios (such as incidence rates in person-time), you can generally use a similar approach but adjusted for the different nature of the data. The principles remain the same, but the calculations for standard error and confidence intervals might vary slightly depending on the exact nature of the data (e.g., if dealing with incidence rates rather than proportions).
In both cases, the key steps are:
– Calculating the RR
– Determining the standard error
– Constructing the confidence interval on the logarithmic scale
– Converting back to the original scale
If you need a specific method for incidence rates, please provide more details on your dataset and calculations.