When To Research Medical Symptoms And Diagnoses

Answer to the example:
Rihanna is correct. @Sparkle, you had the right instincts. You got the numerator right, you understood what goes into the denominator (when you said "overall"), but considered only one aspect and neglected the other. This is quite common, although most people don't even get that far. Dealing with probabilities is tricky. Let's clarify using natural frequencies.

 

Consider 1000 FB users.
If the rate of Brain-Rot is 1%, then 10 people have BR. 990 people do not.
If the test is 90% sensitive: it will correctly pick up 9 out of those 10 cases. It will miss one (this is the false-negative).
If the test has a 5% false-positive rate (as given), then out of the 990 people who do not have disease, 50 will still test positive (i.e. false-positive) and 940 will be true negative (i.e no disease, test negative).

So probability that a positive test means you have disease is: 9/(9+50) = ~15% (with some rounding).

 

Now why did we go through all that stuff? The take-home lesson is this:

You will rarely if ever have all this information. You might be told by enthusiastic medical personnel (especially ones that paid vast amounts in shady transactions to go to med school, plus own testing labs on the side) that this or that test is "90% accurate" - "Oh-oh very good test Saar, very good!". Now you know that even with that level of accuracy, there is some (hidden) false positive rate and some "base rate" of the condition in the population (that 1% rate of BR among FB users in our example). And, a "90%" accuracy could still mean only a 15% chance of disease! So don't freak out right away!

This is particularly true of routine tests under asymptomatic conditions undertaken as part of some screening effort or your yearly physical.

 

Most people have a poor grasp of risk. A better understanding may help make better decisions in all aspects of life.

For a useful resource, see: Harding Center for Risk Literacy.
For some health related information, see here.
One useful book from one of the founders is: Risk Savvy. The example above is used very often to introduce students to such calculations. Good explanations along with a plea for natural frequencies (as opposed to probabilities or Bayesian calculations) can be found in this book. It is a light read (with a fair amount of fluff ), but since you can zip through it in an evening, not bad.

For a quickie TEDx talk, see here.

 

The goal of all this harangue was not to drag you, dear reader, through detail. It is not intended to be a "Be Your Own Surgeon: Sunday Surgery for Fun & Profit" exercise. The idea is to encourage you to be educated and vigilant, to point you to questions you might ask:

(1) When faced with relative frequencies always ask "compared to what"? This is the nonsense you see in the Daily Mail as alluded to by Cimorene in an earlier post.

(2) Better yet, ask for absolute frequencies. In one study, a frequency of 1 in 7000 for clots due to a 2nd gen. birth control pill went up to 2 in 7000 with the 3rd gen. pill. Using relative frequencies, this was reported as "double the risk" in the press! Ugh, ugh, ugh, Grrrrrrrrrrr.

See the TEDx talk. Now you know to immediately ask -"oh, double the risk? From what to what? Give me the absolute numbers".

(3) Be aware that a good test does not automatically mean that you are in trouble. 90% 'accuracy' could still mean only 15% probability of ... well, whatever. You need a lot more information about the test, about the prevalence of the condition etc. before you can take appropriate action.

Be risk savvy. Avoid freak-outs.

 

These probability issues have great impact. Not just in medical matters, but for example, in law as well. For a discussion on the sorts of things we have discussed, but from a different vantage point, see:

The Prosecutor's Fallacy.
The Sally Clark Case.
The Aftermath for Sally Clark.
The Lessons from People v. Collins.

Prepare to be horrified. Cultivate a healthy skepticism for expert pronouncements. This is manageable only if you have some statistical savvy and confidence!

 

If we are still doing anecdotes...
A while ago, I tested positive for an STD and knew it to be impossible. I asked what the chances of the test results being wrong were and was talked down by the (religious) nurse.
So I went home and looked up the % (of false positives) and scheduled a retest and got a negative.
((The retest costed me about the same as the medicines prescribed, so I suppose I got even?..Grrr ))

 

Of course! They are often illuminating!

Oooh, great story, couldn't ask for a better example!

 

On top of this are the absolute, flat out fraudsters. My favourite example du jour is Elizabeth Holmes of Theranos. This woman is amazing in the most horrifying way. Such chutzpah!! Holy Smokes!
Jeez, get on with the miniseries and Hollywood movie already! Jennifer Lawrence in the lead role perhaps? Where's my script?