Fraud detection and statistics


Elizabeth Holmes, founder of Theranos, has now been formally indicted for criminal fraud. I’ve commented on the company before, and on the journalistic conventions around intellectuals that fostered her rise. But now that the Theranos story is coming to an end, I feel a need to comment on how utterly unnecessary this all was.

At its peak, Theranos was valued at $9 billion and employed 800 people. Yet according to John Carreyrou, the Wall Street Journal reporter whose investigations exposed Theranos’s fraud, the company is down to just 20 employees who are trying to close up shop.

All credit to Carreyrou, who by all accounts has done an excellent job investigating and reporting on this fiasco, but literally any statistician — anyone who has been through and understood a first-year statistics course — could have said from the start that this was sheer nonsense. That’s presumably why the board was made up mainly of politicians and generals.

The promise of Theranos was that they were going to revolutionise medicine by performing a hundred random medical tests on a drop of blood, and give patients a complete readout of their state of health, independent of medical recommendation of specific tests. But any statistician knows — and every medical practitioner should know — that the reason we don’t do lots of random tests without any specific indication isn’t that they’re too expensive — many aren’t — or that they require too much blood, but that the more tests you do, the more false positives you’re going to accumulate.

If you do a hundred tests on an average person, you’re going to find at least a few questionable results — either from measurement error, or because most tests aren’t all that specific — requiring followups and expensive investigations, and possibly unnecessary treatments.

Of course, if I had to evaluate the proposal for such a company I would keep an open mind about the possibility of a conceptual breakthrough that would allow them to control the false positives. But I would have demanded very clear evidence and explanations. The fact that the fawning news reports back in 2013-15 raved about the genius new biomedical technology, and failed to even claim to have produced (or found) any innovative statistical methodology, made me pretty sure that they had no idea what they were doing. In the end, it turned out that the biomedical innovations were also fake, which I probably should have guessed. But if the greedhead generals — among them the current secretary of defense, who definitely should be questioned about this, and probably ought to resign — had asked a statistician, they could have saved a lot of people a lot of unpleasantness, and maybe helped save Elizabeth Holmes from herself.

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