Question

1) Researchers in a city are studying bloodstream infection in two different hospitals. There are 50 patients with bloodstream infections in hospital A with a patient population of 500. And 10 patients with bloodstream infection in hospital B with a patient population of 450. In each city half of the population was exposed to chemical substance that is being studied to evaluate its effect on bloodstream infections and 10% of the diseased population was exposed to a chemical substances.

a) What is the relative risk of bloodstream infection in hospital A?

b) What is the relative risk of bloodstream infection in hospital B?

Answer 1

a) The relative risk of bloodstream infection in hospital A can be calculated as follows:

First, we need to calculate the number of patients who were exposed to the chemical substance in each hospital:

Hospital A: 500/2 = 250 patients exposed
Hospital B: 450/2 = 225 patients exposed

Next, we calculate the number of patients who had bloodstream infection and were exposed to the chemical substance:

Hospital A: 50 x 0.1 = 5 patients with bloodstream infection and exposed to chemical substance

The relative risk of bloodstream infection in hospital A is the ratio of the number of exposed cases to the number of unexposed cases:

Relative risk in Hospital A = (5 / (50 - 5)) / (250 - 5) / (500 - 250) = 5 / 45 / 250 / 250 = 0.0036

b) The relative risk of bloodstream infection in hospital B can be calculated similarly:

Hospital B: 10 x 0.1 = 1 patient with bloodstream infection and exposed to chemical substance

Relative risk in Hospital B = (1 / (10 - 1)) / (225 - 1) / (450 - 225) = 1 / 9 / 224 / 225 = 0.0004

So the relative risk of bloodstream infection in hospital B is 0.0004