If a test for a disease has a sensitivity of 90% and a specificity of 95%, what
Practice Questions
Q1
If a test for a disease has a sensitivity of 90% and a specificity of 95%, what is the probability of a true positive result if the prevalence of the disease is 1%? (2022)
0.009
0.0095
0.095
0.1
Questions & Step-by-Step Solutions
If a test for a disease has a sensitivity of 90% and a specificity of 95%, what is the probability of a true positive result if the prevalence of the disease is 1%? (2022)
Step 1: Understand the terms. Sensitivity is the probability that the test correctly identifies a person with the disease (true positive rate). Prevalence is the proportion of the population that has the disease.
Step 2: Identify the values given in the question. Sensitivity = 90% (or 0.9), Prevalence = 1% (or 0.01).
Step 3: Calculate the true positive rate using the formula: True Positive Rate = Sensitivity × Prevalence.
Step 4: Substitute the values into the formula: True Positive Rate = 0.9 × 0.01.
Step 5: Perform the multiplication: 0.9 × 0.01 = 0.009.
Step 6: Interpret the result. The probability of a true positive result is 0.009, which means there is a 0.9% chance of a true positive result given the prevalence of the disease.
Sensitivity – The probability that the test correctly identifies a true positive case of the disease.
Specificity – The probability that the test correctly identifies a true negative case (not having the disease).
Prevalence – The proportion of the population that has the disease.
True Positive Rate – The actual probability of a true positive result, which is influenced by both sensitivity and prevalence.
