Time to die
- Why! Do you look depressed!
- I have every reason to.
- I have only seen you once like this. When the doctor at the hospital said ‘You are going home today’ and you misheard it as ‘You are going home to die.’
- The doctor called me again today.
- Are you sure it was today?
- Morbidly funny!
- What did he say?
- That I have tested positive for a deadly disease.
- Did he say which one?
- Does it matter?
- What more did he say?
- The test is 99% reliable.
- What does that mean?
- That if you have the disease the test will reveal it in 99% of the cases.
- And if you don’t?
- Then the test will say you have the disease in 1% of the cases.
- All these talk about percentages has made me thirsty. Let’s go and find a bar.
- I am dying and all you can think of is booze!?
- When we are both drunk maybe we’ll see the world in a brighter light.
Problem source: http://thinkzone.wlonk.com/ by Keith Enevoldsen.
February 10th, 2010 at 2:25 am
- Perhaps we should stop at the library on the way to the bar, and find out the prevalence of the disease. Knowing only the sensitivity and specificity of the test tells the patient nothing about his posterior probability of infection, given a positive test result.
FOR EXAMPLE:
If the disease is rare, infecting one person in 1000, then there will be 1000 persons infected in every million. If all were tested, there would be 990 “true positives” (infected AND positive) and 9990 “false positives” (uninfected AND positive), for 10,980 positive results in all. Therefore, the probability that my friend is actually infected is 990/10,980 ~ 9%. I’ll drink to that!
However, if the disease is endemic, infecting one person in 10, there will be 100,000 persons infected in every million. If, as before, all were tested, there would be 99,000 “true positives” and 9000 “false positives,” for 108,000 positive results in all. Now the probability that my friend is infected is 99,000/108,000 ~ 91.7%. No bar for us, I’m taking him back to the hospital!