Suppose we completed the cohort study that we proposed above.  The data for the cohort study are as follows:  
(To keep it simple, we are going to use cumulative incidence; however, if we had data on person time, then we could calculate incidence density using the person time as the denominator. )


Long sleep duration 
(7+ hours)
Short sleep duration
 (6 hours or less)




Breast cancer
389
143




No breast cancer
19057
4406






19446
4549




calculate the relative risk

To calculate the **relative risk** (RR) from a cohort study, we use the formula:

\[
RR = \frac{\text{Incidence in Exposed Group}}{\text{Incidence in Unexposed Group}}
\]

Here, we assume "Long sleep duration" is the **exposed** group and "Short sleep duration" is the **unexposed** group. The cumulative incidence for each group is calculated as:

\[
\text{Cumulative Incidence} = \frac{\text{Number of cases of breast cancer}}{\text{Total number of people in that group}}
\]

### Step 1: Calculate the cumulative incidence for the exposed (long sleep duration) group.
- Number of breast cancer cases (long sleep duration) = 389
- Total number of people with long sleep duration = 19,446

\[
\text{Incidence in Long Sleep Duration Group} = \frac{389}{19446} = 0.020
\]

### Step 2: Calculate the cumulative incidence for the unexposed (short sleep duration) group.
- Number of breast cancer cases (short sleep duration) = 143
- Total number of people with short sleep duration = 4,549

\[
\text{Incidence in Short Sleep Duration Group} = \frac{143}{4549} = 0.0314
\]

### Step 3: Calculate the relative risk.
\[
RR = \frac{0.020}{0.0314} = 0.637
\]

Thus, the relative risk is approximately **0.637**, meaning that those with long sleep duration (7+ hours) have a lower risk of breast cancer compared to those with short sleep duration (6 hours or less).

Would you like further details or clarification? Here are some related questions to deepen understanding:

1. How is relative risk interpreted in terms of public health?
2. How would the relative risk change if we had person-time data for incidence density?
3. What is the difference between relative risk and odds ratio?
4. How could confounding factors affect the relative risk calculation?
5. How would we perform a hypothesis test to check if this relative risk is statistically significant?

**Tip:** Relative risk below 1 suggests a protective factor, while above 1 suggests a risk factor.

Suppose we completed the cohort study that we proposed above. The data for the cohort study are as follows: Long sleep duration (7+ hours) and short sleep duration (6 hours or less) with breast cancer and no breast cancer cases. Calculate the relative risk.

Learn how to calculate relative risk from cohort study data on sleep duration and breast cancer. This problem involves concepts such as cumulative incidence and the relative risk formula. Suitable for college students or advanced high school students interested in epidemiology.

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