Friday, 12 September 2014

Not driven by statistics

It's Richard D Gill's birthday today.   I've never met him; never heard of him before Tuesday this week; but I like his style; and I love his hat. Anyone with an academic address in The West, gets regular e-mails from the Subcontinent starting "Dear Professor, I am an elite student at the University of Nevaheardapur and have been interested for a solid time in the cutting-edge research of your esteemed laboratory . . ." and asking for employment. Dr Gill's response combines irony and a certain kindness which may help to protect his inbox from overload.  Unless you speak Dutch or read De Telegraaf on a regular basis, you probably won't have heard of Lucia de Berk.  She was found guilty of multiple infanticide in March 2003 and Gill's crap-detector thought the whole case had the ring of nonsense. This was because he was numerate (he is a Professor of Statistical Mathematics at Leiden) and the principals in the witch-hunt against de Berk were woefully, willfully, weak about numbers.  And then he did something about it, pursuing, with siblings Metta de Noo and Ton Derksen, a retrial and exoneration of de Berk. He tells his story at TEDx, and if his delivery is a little all-over-the-place, he's put the slides up in the public domain. I've touched on a comparable English case (with a link to another more coherent TED talk) in which a mother having had her very heart wrenched out by the death of her two children was then convicted of their murder.  The two cases are comparable because a key part of each prosecution case was an estimate of the probability of two or more similar but independent events occurring. In Sally Clark's case, the prosecution decided to call a consultant paediatrician to do the stats, in Lucia de Berk they called a legal psychologist.  In Sally Clark's case it was bonkers to treat the two events (same parents, same locations, half their genes in common) as independent.

To begin near the beginning, in 2001 Lucia de Berk was a paediatric nurse in the Juliana Kinderziekenhuis (JKZ) a children's hospital in Den Haag.  Children are admitted to such a place because they are sick, sometimes very sick indeed and, despite the best efforts of the medical staff and state of the art facilities, sometimes the poor weans don't make it.  After the death of one child, de Berk's manager became convinced that a) the death was unexpected and b) that de Berk was somehow responsible. Nobody denied that she was on the ward when the child pegged out. I said witch-hunt earlier because this man fanned his suspicions into a flaming certainty in the same way that the puritans of Salem found evidence of their convictions wherever they looked.
You can follow the whole de Berk story written with gusto and irony by Richard Gill's statistical colleague Piet Groeneboom [R] in a blog about Amateur Statisticans.  If you're competent in stats and want the details of the appropriate tests and sight of the actual data, albeit not so readable as Groeneboom's account, you should check out Thomas Colignatus's paper in Arxiv.  As the case worked its way up to the Netherlands Supreme Court, nobody thought to ask one of a handful of extremely competent statisticians, including Gill and Groeneboom, employed by the Dutch government to work in their Universities.  At one stage, a judge maintained that the case had not been driven by mere statistics, with the implication that stats was just the icing on a cake of other evidence.  Groeneboom is happy to agree with this statement because as far as he's concerned no sensible or valid statistics had been used.  And the other evidence,was, on any sort of critical scrutiny, a tissue of wet tissues which should never have been asked to, and could not, stand up in court.

But for The Blob, I'll just point out that the amateur statisticians came up with a figure of 1 chance in 342 million that the deaths would occur during or near a shift on which de Berk had served.  This came from multiplying a set of statistically unexciting probabilities to arrive at this monstrously unlikely (and so spuriously convincing when splashed across the news) total. There is an element of ascertainment bias in this, in that the manager pursued evidence of guilt rather than just data.  Anyone with any feeling for numbers would have been suspicious about such an enormously unlikely probability.  But the real issue is that there is no case. From the original suspicious death, the suspicious manager tracked back and identified 6 deaths over the previous three years and then sniffed off like a data-bloodhound to other hospitals where de Berk had previously worked, accumulating more damning evidence along the way.  But if he had just tracked back through his own hospital's records he would have discovered seven deaths in the previous 3 years. So de Berk's arrival was associated with a drop, albeit not significant, in the death rate.  That would surely get her struck off the rolls of the Serial Killers Guild (SKG).

Here's the Hattie Carroll now is the time for your tears insult.  In turning Lucia de Berk's life upside down, the police turned her home over and found a couple of overdue books from the hospital library.  After ten years in court or in jail, de Berk was cleared and compensated by the Dutch government.  But the hospital was still looking for the library fines, partly because they are still convinced that she was guilty. It's like Lindbergh's multiple families yesterday - if you look hard enough at anybody's life, you'll find something murky especially if you look in the dark corners. Richard Gill's most important statement is the fact that there are 2,000 preventable deaths every year in the Dutch health system.  Someone makes a mistake and someone else dies.  But these deaths are, to a close approximation never prosecuted and rarely even investigated.  You may be sure those statistics are true of Ireland, of Ukraine and wherever else readers of The Blob hang out.  We've spent millions of money and person-years of time to halve the number road traffic deaths in Ireland over the last decade.  Should we not now turn our lights on the hospitals to see if we can make similar reductions?
Birthday cake for Professor Gill! to share with Groeneboom, Derksen, de Noo and the other unbelievers.

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