Question

A cohort of 3000 individuals was chosen to be part of a study on the potential relationship between being infected with hepatitis C virus (HCV) and liver disease. 800 of the cohort members acquire an HCV infection and out of those infected persons 640 develop liver disease. 200 of the remaining cohort members also develop liver disease

A. What is the relative risk of developing liver disease based on exposure to HCV?
B. What is the odds ratio for developing liver disease based on exposure to HCV?

Answer 1

a) 12.0

b) 56.0

Explanation:

a) Relative Risk, also known as risk ratio, is expressed as the probability of an outcome (developing liver disease) in an exposed group divided by the probability of that outcome (developing liver disease) in an unexposed group.

Mathematically,

Relative risk = (probability of disease after exposure)/(probability of disease without exposure)

Probability of liver disease after exposure to HCV = (640/800) = 0.80

Probability of liver disease without exposure to HCV = (200/3000) = 0.06667

Relative Risk = (0.80/0.0667) = 12.0

Meaning that according to the study, one is 12 times more likely to get liver disease after getting exposed to HCV than without exposure to HCV.

b) Odds ratio estimates the how related two events (developing Liver disease and developing HCV) are. It is expressed mathematically as being equal to the odds of one event (developing liver disease) in the presence of the other event (developing HCV) divided by the odds of that one event (developing liver disease) in the absence of the other event (developing HCV).

Odds is defined as the ratio of the probability that an event will occur divided by the probability that the event will not occur, or (probability)/(1-probability)

Odds ratio = (odds of liver disease after exposure to HCV)/(odds of liver disease without exposure to HCV)

odds of liver disease after exposure to HCV = (probability of getting liver disease after exposure to HCV)/(Probability of not getting liver disease after exposure to HCV)

probability of getting liver disease after exposure to HCV = (640/800) = 0.80

probability of not getting liver disease after exposure to HCV = (800-640)/800 = 0.20

odds of liver disease after exposure to HCV = (0.80/0.20) = 4.0

odds of liver disease without exposure to HCV = (probability of getting liver disease without exposure to HCV)/(Probability of not getting liver disease without exposure to HCV)

probability of getting liver disease without exposure to HCV = (200/3000) = 0.06667

probability of not getting liver disease without exposure to HCV = (3000-200)/3000 = 0.9333

odds of liver disease without exposure to HCV = (0.06667/0.9333) = 0.07143

Odds ratio = (4/0.07143) = 56

Hope this Helps!!!