Ben Goldacre, The Guardian, Saturday 10 April 2010

Lucia de Berk is a Dutch nurse who has spent 6 years in jail on a life sentence for murdering 7 people, in a killing spree that never happened. She will hear about her appeal on Wednesday, and there is now little doubt that she will be let off. The statistical errors in the evidence against her were so crass that they can be explained in one newspaper column. So will the people who jailed her apologise?

The case against Lucia was built on a suspicious pattern: there were 9 incidents on a ward where she worked, and Lucia was present for all of them. This could be suspicious, but it could be a random cluster, best illustrated by the “Texas Sharp Shooter” phenomenon: imagine I am stood in front of a wooden barn with a machine gun in each hand, maniacally firing off a thousand bullets into the wall. I remove my blindfold, walk up to the barn, find 3 bullets which are very close together, and carefully paint a target around them. Then I announce that I am an olympic standard rifleman.

This is plainly foolish. All across the world, nurses are working on wards, where patients die, and it is inevitable that on one ward, in one hospital, in one town, in one country, somewhere in the world, you will find one nurse who seems to be on a lot when patients die. It’s very unlikely that one particular prespecified person will win the lottery, but it’s inevitable that someone will win: we don’t suspect the winner of rigging the balls.

And did the idea that there was a killer on the loose make any sense, statistically, for the hospital as a whole? There were 6 deaths over 3 years on one key ward where Lucia supposedly did her murdering. In the 3 preceeding years, before Lucia arrived, there were 7 deaths. So the death rate on this ward went down at the precise moment that a serial killer – on a killing spree – moved in.

Even more bizarre was the staggering foolishness by some of the statistical experts used in the court. One, Henk Elffers, a professor of law, combined individual statistical tests by taking p-values – a mathematical expression of statistical significance – and multiplying them together. This bit is for the nerds: you do not just multiply p-values together, you weave them with a clever tool, like maybe ‘Fisher’s method for combination of independent p-values’. If you multiply p-values together, then chance incidents will rapidly appear to be vanishingly unlikely. Let’s say you worked in twenty hospitals, each with a pattern of incidents that is purely random noise: let’s say p=0.5. If you multiply those harmless p-values, of entirely chance findings, you end up with a final p-value of p < 0.000001, falsely implying that the outcome is extremely highly statistically significant. With this mathematical error, by this reasoning, if you change hospitals a lot, you automatically become a suspect.

One statistician – Richard Gill – has held the Dutch courts’ feet to the fire, writing endless papers on these laughable statistical flaws (qurl.com/gill ). Alongside the illusory patterns he has identified, there was one firm piece of forensic evidence. Some traces of the drug digoxin were found in one baby who died. The baby had previously been prescribed digoxin, months previously. Three court toxicologists now say the digoxin was not the cause of death.

In fact, even the Dutch state proseution now accepts that Lucia should be acquitted, and that there was no evidence for an unnatural death in any of the patients, though her convictions for stealing two library books from the hospital library – shamefully and bizarrely – will be upheld. Lucia denies stealing these two library books. Now living with her partner while she awaits the final judgement, Lucia is penniless, denied unemployment benefits because of her unusual status, and paralysed down one side following a stroke which she had, in 2006, aged 44, in the week she was told that her conviction would be upheld. Watch what the Dutch legal system does next, because they owe this woman a great deal.