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If a test for a disease has a sensitivity of 90% and a specificity of 95%, what

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Question: 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)

Options:

  1. 0.009
  2. 0.0095
  3. 0.095
  4. 0.1

Correct Answer: 0.009

Exam Year: 2022

Solution: 

True positive rate = Sensitivity × Prevalence = 0.9 × 0.01 = 0.009.

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)
  1. 0.009
  2. 0.0095
  3. 0.095
  4. 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.
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