What is the probability of a person being diagnosed with a disease if the preval
Practice Questions
Q1
What is the probability of a person being diagnosed with a disease if the prevalence of the disease in a population is 2% and the test for the disease has a sensitivity of 90% and a specificity of 95%? (2021)
0.018
0.020
0.090
0.095
Questions & Step-by-Step Solutions
What is the probability of a person being diagnosed with a disease if the prevalence of the disease in a population is 2% and the test for the disease has a sensitivity of 90% and a specificity of 95%? (2021)
Step 1: Identify the given information. The prevalence of the disease (P(Disease)) is 2%, which is 0.02. The sensitivity of the test (P(Positive|Disease)) is 90%, which is 0.90. The specificity of the test is 95%, which means the probability of testing positive when not having the disease (P(Positive|No Disease)) is 5%, or 0.05.
Step 2: Calculate the probability of not having the disease (P(No Disease)). Since the prevalence is 2%, P(No Disease) = 1 - P(Disease) = 1 - 0.02 = 0.98.
Step 3: Calculate P(Positive). This is the total probability of testing positive, which includes true positives and false positives. Use the formula: P(Positive) = P(Positive|Disease) * P(Disease) + P(Positive|No Disease) * P(No Disease).
Step 4: Substitute the values into the formula: P(Positive) = (0.90 * 0.02) + (0.05 * 0.98). Calculate this to get P(Positive).
Step 5: Calculate P(Disease|Positive) using Bayes' theorem: P(Disease|Positive) = (P(Positive|Disease) * P(Disease)) / P(Positive). Substitute the values you have calculated.
Step 6: Perform the calculations to find the final probability of being diagnosed with the disease given a positive test result.
