Calculate the hazard ratio based on the following data: Niacin group (N=1200) had 380 primary endpoint events, and Placebo group (N=1600) had 275 primary endpoint events.

Steps to Solve

1. Calculate the event rate in the Niacin group

To find the event rate, divide the number of patients who reached the primary endpoint by the total number of patients in the Niacin group:

$Event\ Rate_{Niacin} = \frac{380}{1200}$

2. Calculate the event rate in the Placebo group

To find the event rate, divide the number of patients who reached the primary endpoint by the total number of patients in the Placebo group:

$Event\ Rate_{Placebo} = \frac{275}{1600}$

3. Calculate the Hazard Ratio

Divide the event rate in the Niacin group by the event rate in the Placebo group:

$Hazard\ Ratio = \frac{Event\ Rate_{Niacin}}{Event\ Rate_{Placebo}} = \frac{\frac{380}{1200}}{\frac{275}{1600}}$

4. Simplify the Hazard Ratio equation

$Hazard\ Ratio = \frac{380}{1200} \cdot \frac{1600}{275} = \frac{380 \cdot 1600}{1200 \cdot 275} = \frac{608000}{330000}$

5. Calculate the final Hazard Ratio value

$Hazard\ Ratio = \frac{608000}{330000} \approx 1.8424$

6. Choose closest answer

The closest answer to our calculated value is $1.80$.