Consider the data on a medical test for SUPERBUG:

1. Out of every 10 000 people with a record of possible symptoms, more or less 100 people were diagnosed with SUPERBUG. These are confirmed cases, based on a combination of doctors' diagnoses, CT-scans, several different tests, and post mortem analyses.

2. It is known that for this test, 10 out of 100 positive test results are incorrect. This is the inverse sensitivity of the test.

3. It is known that for this test, 10 out of 50 negative test results are incorrect. This is the inverse specificity of the test.

You have just been tested for SUPERBUG, but are still waiting for your results. Obviously you will want to know what a positive or negative result will tell you about the likelihood that you have been infected with SUPERBUG, so that you can decide how to deal with the result.

Given the data above:

1. Define the variables you will use in your calculations.

2. Calculate the prevalence of SUPERBUG.

3. Calculate the sensitivity and specificity of the test.

4. Calculate the inverse sensitivity and inverse specificity of the test.

5. Calculate the false positive and false negative rate for the test.

6. Calculate the four prior probabilities, using your variable definitions.

7. Use Bayes' theorem to calculate the PPV.

8. Use Bayes' theorem to calculate the NPV.

9. Explain why the probabilities come out this way.

10. Explain what would cause these probabilities to change.

11. What do these results mean in practice.