It was October 2014 when the British newspaper The Guardian published a report on an Italian nurse accused of murder. The nurse in question, Daniela Poggiali, had allegedly dosed elderly patients at the Umberto I hospital with lethal amounts of potassium in order to kill them surreptitiously.

Tabloid newspapers post grainy pictures of Poggiali posing for a selfie with the body of her ‘victim’, and colleagues say she likes to play God. Although she is charged with only two murders, the media suggest that she may be responsible for many more deaths.

The report also reaches Richard Gill, Professor Emeritus of Statistics. The charge disquiets him because it is too reminiscent of an earlier case in which he was involved as an expert: the case of the unjustly convicted Dutch nurse Lucia de B, who was acquitted in 2010.

Together with fellow statistician Julia Mortera of Roma Tre University, Gill decides to contact Poggiali’s lawyer in order to offer their services as statisticians. The lawyer gratefully accepts their offer and sends them all the relevant documents.

A PATTERN AND A MURDER WEAPON

Based on the data in these documents, the statisticians discover that the case against Poggiali rests on two pillars derived from a report by two Italian academics: Professors Tagliaro and Micciolo, a toxicologist and an epidemiologist, respectively.

They started by reviewing the number of deaths over the previous few years in the department where Poggiali worked. From that statistical analysis, a pattern emerges. During Poggiali’s working hours, the mortality rate among patients was significantly higher. The number of deaths that occurred during Poggiali’s shifts also slowly increased over the years. Up until the moment she is arrested, when it suddenly drops.
And so, Tagliaro and Micciolo conclude that Daniela’s presence accounts for 60 deaths.

In addition, the prosecutor also provides a forensic piece of evidence concerning the murder weapon. The ocular fluid of the most recent death showed an unusually high concentration of potassium. This proves that the woman was killed with potassium chloride, which was allegedly administered via an infusion.

A pattern, a murder weapon and – to top it all off – a selfie with the victim: Poggiali has to be guilty.

‘The report was sent to us as a scanned fax’, says Gill. ‘It was extensive and full of statistics, but it was immediately clear to us that these statistics were utterly amateurish. They had done all the maths, but it simply didn’t add up.’

Gill and Mortera request the raw data from the prosecutor and the hospital, which they eventually receive just one week before the trial. The statisticians have to copy data from the barely legible photocopies into spreadsheets in order to be able to analyse them, but after pulling a few all-nighters, they come to very different conclusions from Tagliaro and Micciolo.

TIME OF DEATH

Firstly, they discover that, although there is an increase in the number of deaths during Poggiali’s shifts, this applies to all nurses. Most deaths in the hospital occur in the morning, and it is during the morning shift that the largest number of nurses are scheduled to work. Any given nurse will therefore be working the most hours at the peak of the death rate, simply because there are more nurses scheduled for that time of day.

But even then, the mortality rate was still considerably higher during Poggiali’s shifts. This too can be explained, according to Gill: ‘Many people think that the time stated on a death certificate is the same as the time of death, but that’s not true. It’s the time at which a qualified doctor certifies that the person has died. This often happens at shift change or just after midnight, when a qualified doctor comes in specifically to check whether people have died.’

The data do indeed show that the times of death are not evenly distributed, as you would expect to see if this was truly the moment that someone drew their last breath. Instead, there are clear peaks around midnight and at the change of shifts, when the doctor comes to the ward and records the deaths.

Gill: ‘Daniela was often already there before the start of her scheduled shift and she often stayed around to help after her shift was over. Maybe she was a very conscientious nurse, or maybe she was paid by the hour and she needed the money. But because she worked slightly longer shifts, she was present more often than her colleagues at the times when the deaths were recorded.

‘You work about fifteen minutes longer than the other nurses, but you have double the number of deaths. That adds up quickly; especially on a ward where a few patients die every week. These are people with terminal illnesses and the very elderly.’

The fact that the number of deaths fell sharply shortly after her arrest can also be easily explained, according to Gill. The news of the ‘Angel of Death’ had been widely reported in the Italian press and, as a result, the Umberto I hospital attracted fewer patients. Fewer patients means fewer deaths.

The statisticians’ contra-expertise casts the killing pattern in a completely different light. However, the prosecutor clings to the other piece of evidence: the lethal amount of potassium.

OCULAR FLUID

Gill: ‘The evidence on the potassium contained a huge error which we only discovered in the past six months. We were hired to look into the statistics on the deaths and we only later found out through another expert that the potassium analysis included statistics as well.

‘Tagliaro, the prosecution’s expert, had measured the level of potassium in the ocular fluid of the last deceased person, and based on that, he calculated what the concentration must have been at the time of death. He had developed this method himself. According to him, the concentration had been far too high, which was a sign that potassium chloride had been used to commit murder. It was the only piece of solid evidence in the entire case.

‘However, he failed to take the measurement inaccuracy into account in his calculations. Statistically, he should have done so. If you include the margin of error, the measured value falls within the normal margins. Moreover, he had already published articles proving that this method was too inaccurate to be used as forensic evidence. Tagliaro is quite simply completely incompetent, and yet, it took seven years to convince the Italian legal system of this.’

After being sentenced to life imprisonment, an appeal, two retrials that also ended in acquittals and a total of over two years in prison, Poggiali was set free in October. Whether this freedom will last is yet to be seen. The Italian public prosecutor can still lodge an appeal against the acquittal. Poggiali herself has stated that she would like to work as a nurse again.

HEALTHCARE SERIAL KILLERS

For Gill, this is the second case he has worked on where someone was convicted on the basis of faulty statistics. This prompted him to write a manual for the British Royal Statistical Society on how statistics can be used in court, particularly in cases of so-called healthcare serial killers.

‘In the Western world, cases like these occur about once a year. In some cases, there is solid evidence that it was indeed the work of a murderer, but much more often, there isn’t. Take, for example, this Italian case and the Lucia de B. case. All kinds of suggestions are made using statistics and there might be a selfie that influences public opinion but otherwise has no evidential value. Once the public has formed an opinion and the police have dug their heels in, no more evidence is needed. You don’t stand a chance when you end up in a situation like that.’

In England, the next case involving a nurse charged with murder presents itself. Although Gill is not personally involved this time, he follows the case closely. ‘The English judiciary has been trying to convict Lucy Letby for five years now. It’s yet another case of a failing hospital that has been the subject of major inspection reports. The hospital will be looking for a scapegoat.

‘Statistically, there were fewer deaths when Letby was on holiday. But when more people are on holiday, there might also be fewer patients. There are so many variables and so many odd things that can cause peaks and troughs that it doesn’t really say anything. However, the hospital will be looking for evidence to confirm their suspicions.

‘That’s why the manual that I’m writing is important; it will explain all these issues. Not just for statisticians, but also for lawyers, and defence lawyers in particular. Lawyers don’t know how to work with statistical evidence. In their eyes, there is either a fact or no fact, there are no uncertain facts.’