
The data for the case-control study are as follows. 


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




Breast cancer
143
389
532


No breast cancer
745
1383
2128













11. What measure of association do you use and what do you calculate? 

12. What is your interpretation of this measure of association? 


### 11. What measure of association do you use and what do you calculate?

In a **case-control study**, the appropriate measure of association is the **odds ratio (OR)**. This compares the odds of exposure (in this case, sleep duration) in the cases (people with breast cancer) to the odds of exposure in the controls (people without breast cancer).

Let's denote:
- **Cases (Breast cancer)** as those with breast cancer.
- **Controls (No breast cancer)** as those without breast cancer.
- **Long sleep duration** as the exposure.

We can create a 2x2 table based on the provided data### 11. What measure of association do you use and what do you calculate?

In a **case-control study**, the appropriate measure of association is the **odds ratio (OR)**. This compares the odds of exposure (in this case, sleep duration) in the cases (people with breast cancer) to the odds of exposure in the controls (people without breast cancer).

Let's denote:
- **Cases (Breast cancer)** as those with breast cancer.
- **Controls (No breast cancer)** as those without breast cancer.
- **Long sleep duration** as the exposure.

We can create a 2x2 table based on the provided 

|                          | Breast Cancer (Cases) | No Breast Cancer (Controls) | Total   |
|--------------------------|-----------------------|-----------------------------|---------|
| **Long Sleep Duration**   | 143                   | 745                         | 888     |
| **Short Sleep Duration**  | 389                   | 1383                        | 1772    |
| **Total**                 | 532                   | 2128                        | 2660    |

Now, we can calculate the **odds ratio (OR)** as follows:

\[
OR = \frac{\text{Odds of exposure among cases}}{\text{Odds of exposure among controls}} = \frac{\frac{143}{389}}{\frac{745}{1383}}
\]

Let's calculate the odds ratio:

\[
OR = \frac{143 \times 1383}{389 \times 745}
\]

Now, I’ll compute this value.

The **odds ratio (OR)** is approximately **0.68**.

### 12. What is your interpretation of this measure of association?

An odds ratio of **0.68** means that the odds of breast cancer in people with long sleep duration (7+ hours) are **32% lower** compared to those with short sleep duration (6 hours or less). In other words, long sleep duration is associated with a reduced risk of breast cancer in this study population.

However, it’s important to assess whether this association is statistically significant, which requires additional information such as confidence intervals or p-values.

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The data for the case-control study are as follows: 

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

Breast cancer
143
389
532

No breast cancer
745
1383
2128

11. What measure of association do you use and what do you calculate?
12. What is your interpretation of this measure of association?

This case-control study investigates the association between breast cancer and sleep duration. Learn how to calculate the odds ratio (OR), a key statistical measure in epidemiology, using the data provided. Understand the interpretation of an OR of 0.68, indicating a 32% lower odds of breast cancer with longer sleep duration. Suitable for students of statistics and epidemiology.

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