## Natural frequencies “keeping it real”

8 Sep, 10 | by Bob Phillips

So, on hearing Matthew Thompson open up a mini-session with natural frequencies my mind turned to the healing power of crystals, and I become acutely concerned that the open-minds approach of the Teaching EBM Conference had gone too far.

But this was quashed quickly by his description: ‘Natural frequencies’ means ‘real numbers’ … like 30 of 100 patients, not 30% or 0.3 … and this is easier for most people to deal with.

He went on to show that a single box can crack the nut of turning diagnostic test information from meaningless prattle into something highly understandable:

Using this approach means you can loose the faff of nomgrams, converting into odds or pocket calculating and work out, really quickly, what a test result means.

It works like this: take a problem where 30% of the walk-ins will have it. The test you run has 50% sensitivity and 90% specificity. Of 100 people, 30 have the condition.  50% sensitivity means half of the diseased have a +ve test (= 15). 90% specificity means 9/10th of the undiseased will have a -ve test … so one-tenth (=7) will be test +ve.

The result – 70% of the positive tests (15/22) really do have the condition.

Re-run it with a test prevalence of 60% :

60 >>>>>  30
/                     .
/disease               .
100                                .
\not disease         .
\                    .
40 >>>>>    4

Now 30/34 ~ 90% of +ve test results are in folk who really have the disease.

Try it yourself with a prevalence of only 10% and see what the positive test really means …

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• Bob, that's a thing of beautiful simplicity.
One minor point; would it make sense to shift the prev/sens/spec details around on the box so that they sit next to the number they're being used to create? So, prevalence would sit above – in the example – the 30, and then sens would sit above the 15, spec below the 7?

Personally I've taken, every few months with a change of house – and sometimes halfway through – to getting junior docs (and others) to get a pencil and paper and sit through a presentation I've made (meaning grossly ripped off) using the stats from a Ben Goldacre Column which sums it up beautifully. http://www.badscience.net/2006/12/crystal-balls-and-positive-predictive-values/ Most of them refuse to believe the numbers they calculate, and it's rare to run a short session where there aren't genuine gasps of amazement. More recently I've added in the stats from the “MRI can diagnose autism” paper, to prove to them that they can do stats better than the MRC…

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