Falsely Identifying the Enemy

In a recent discussion group at work, we were discussing predictive modeling and the “false positives vs false negatives” trade-off. As I’ve described in previous posts, your predictive algorithm (be it a computer-run statistical model or some fuzzy logic inside your brain) outputs a probability. Your model tells you “There is a 26% chance that this person has cancer.” If sheer prediction on a portfolio of data points is all you want, you’re done. But usually some kind of action is required given the model output. Your model doesn’t neatly cleave the population into “cancerous vs. cancer free”. You have to set a cut-off probability, such that everyone above the threshold is treated as if they have cancer and everyone below is treated as if they don’t. Maybe I want to aggressively treat everyone who might have cancer, so I set the cutoff low at 10%. Or maybe I don’t want to put someone through chemotherapy unless I’m really sure, so I set the cutoff higher at 50%. Or maybe this is just a screening for additional tests, so I want to set the cutoff low, say 5% or even 1% lest I miss an opportunity to treat a cancer early. A higher threshold means you’re more certain you’ve identified most of the cancerous patients, but you’re also wrongly classifying healthy people as cancerous. A lower threshold means you misidentify fewer healthy people as cancerous (saving them the indignities of additional tests and chemo) but you also miss a few cancers that you otherwise could have treated. The threshold depends on the relative costs of the two kinds of errors, and sometimes errors in both directions are costly.

The example I actually used in our discussion group was the following. It's World War II in London. You are reading the output of radar imaging. Those blips could be a flock of birds. Or it could be the Luftwaffe doing another bombing raid on London. Do you scramble the British fleet of Spitfires to go meet them? Or do you save yourself the fuel and effort? It obviously depends on how certain you are about your reading of the radar blips, but it also depends on what you consider a reasonable cutoff. Are you 90% sure these are Nazis? Then you should probably scramble the fighters. Only 10% sure? Well…probably, maybe not. Depends on the cost of fuel and other resources spent scrambling the fighters. 1%? 0.01%? Surely you can’t be sending them up every time a flock of birds looks creates funny-looking blips on your radar, but then again failing to repel a bombing raid is very costly indeed.

I didn’t even think about it during the meeting, but later it struck me that a lot of people these days are misidentifying things as Nazis. The threshold they set is far too low (in addition to their underlying predictive algorithm being inaccurate and extremely biased). When actual Nazis hold a parade, they say, “See! We told you this was a very big deal and now there they are!” And most of us just shrug and say, “Stopped clocks. Yes, we all knew that there was a small segment of self-identified Neo Nazis. You don’t get credit for ‘calling it’ when you’ve been calling everyone you don’t like a Nazi for the last several years.” My example was meant to be completely apolitical and simply illustrate the “relative costs of false positives and false negatives” problem, but it generalizes well. This is another reason to set your threshold high. Too many false positives, and people start questioning your credibility. They may stop believing you when you most need them to.