On Juno and Screening Test Stats
“Well, well” says the convenience store clerk. “Back for another test?”
“I think the first one was defective. The plus sign looks more like a division symbol, so I remain unconvinced,” states Juno the pregnant teenager.
“Third test today, mama-bear,” notes the clerk.
Juno recluses herself and uses a do-it-yourself pregnancy test in the restroom, on film.
“What’s the prognosis … minus or plus?” asks the clerk.
…”There it is. The little pink plus sign is so unholy,” Juno responds.
She’s pregnant, clearly, and she knows she is.
(from Juno the movie*)
Juno\’s pregnancy test
Think of how a statistician might consider Juno’s predicament – when a testing device is useful but sometimes gives an unclear or wrong signal.
Scientists use two terms – sensitivity and specificity – among others, to assess the accuracy of diagnostic tests. In general, these terms work best for tests that provide binary sorts of outcomes – “yes” or “no” type situations. Sensitivity refers to how well a screening tool detects a condition that’s really present (pregnancy, in the teenager’s case). Specificity, by contrast, measures how well a test reports results that are truly negative.**
Juno’s readout is relatively straightforward – a pink plus sign or, not; the possibilities regarding her true condition are few.
Still, even the simplest of diagnostic tests can go wrong. Errors can arise from mistakes in the procedure (a cluttered, dirty store is hardly an ideal lab environment), from flawed reagents (the package might be old, with paper that doesn’t turn vividly pink in case of pregnancy) or from misreading results (perhaps Juno needs glasses).
Why does this matter, now?
Of course, breast cancer is not like pregnancy. Among other distinguishing features, it’s not a binary condition; you can’t be a little bit pregnant. (Both are complicated, I know.)
To get to the bottom of the screening issue, we’ll have to delve deeper, still.
*Thanks Juno, Dwight and everyone else involved in the 2007 film; details listed on IMBD.
**I was surprised to find few accessible on-line resources on stats. For those who’d like to understand more on the matter of sensitivity and specificity, I recommend starting with a 2003 article by Tze-Wey Loong in the British Medical Journal. This journal, with a stated mission to “help doctors to make better decisions” provides open, free access to anyone who registers on-line.
I’ll offer an example here, too:
To measure the accuracy of Juno’s kit, a statistician might visit a community of 100 possibly pregnant women who used the same type of device. If 20 of the women are indeed pregnant (as confirmed by another test, like a sonogram), but only 16 of those see the pink plus sign, the sensitivity of the test would be 16/20, or 80 percent. And if, among the 80 women who aren’t due, 76 get negative results, the specificity would be 76/80, or 95 percent.
False negatives: among the 20 pregnant women 4 find negative results; the false negative rate (FN) is 4/20, or 20 percent.
False positives: among the 80 women who aren’t pregnant 4 see misleading traces of pink; the false positive (FP) rate is 4/80, or 5 percent.