# Mathematics, medicine and teaching

Mathematician Stéphanie van der Pas, winner of the C.J. Kok Jury Award for her PhD thesis in 2017, divides her time between research and education, and between pure mathematics and practical application.

In her thesis Van der Pas describes new statistical techniques that support researchers in the field and ensure that common mistakes occur less frequently. From Bayesian statistics to p-hacking, from artificial hips to hereditary diseases, they all come up in Van der Pas’s thesis, in which pure mathematics is applied in a way that takes human error and unexpected situations into account.

### Winding road

Van der Pas didn’t choose to study mathematics straight away. ‘After high school I went to study medicine. I did that for a year, but I learned that it did not suit me, and that I need the certainty that mathematics offers. In mathematics you prove something, which can be true or not. I think that’s a nice environment.’

After medicine, Van der Pas moved on to study mathematics and classical languages. ‘I also liked classics in high school - it’s a bit of a hobby that got out of hand.’

### Mathematical Greek texts

She learned a lot about writing during classical languages, she tells. ‘When I started to write my math thesis, I noticed that my writing experience was of great use, and in classical languages I graduated on a linguistic phenomenon in mathematical Greek texts. So some things have passed over from my mathematics study to my study of classical languages, and vice versa.’

Perhaps it was the winding road to her current field that gave Van der Pas a unique view on the application of her work. She also received the C.J. Kok Jury Award for her thesis, in which she worked on pure mathematics, in the form of statistical methods, but adapted to the vagaries of practical research and the mistakes that occur there.

### Bayesian statistics

The core of the statistical research that Van der Pas performs is the search for important data in huge datasets full of noise. She likes to use an example to explain: ‘Think of congenital diseases - genetic disorders. If we suspect that there are genetic causes to a certain disease, the search begins.’ Finding the genetic basis of a given disease is to look for a needle in a haystack. ‘There are ten thousand genes, but the disease may be caused by just ten genes. If there are only a handful of patients with the given disease, it can take years to find what you are looking for.’ This is the type of data that Van der Pas’s research is all about: how to find those few genes?

A lot of statistics is done using computers, that can give goods answer in the form of p-values or confidence intervals. But the reliability of these answers is not always beyond doubt. ‘We have developed a method that not only provides an estimate, but also an uncertainty margin - and we have even investigated how reliable this uncertainty margin is.’

### No clear yes or no

For this Van der Pas used so-called Bayesian statistics - not the most common form of statistics. Bayesian statistics do not give a clear ‘yes’ or ‘no’, but an estimate. ‘In order to make the estimate more accurate, prior knowledge can be incorporated into the method in Bayesian statistics.’

If a researcher knows in advance that a dataset will consist mainly of noise plus a few informative measuring points, this can be processed using Bayesian statistics. ‘It is a very intuitive way of constructing estimates, which involves the characteristics of the problem itself. We have built a function that uses and reflects the presumptions.’

### Artificial hips

Van der Pas’s research is quickly labeled as ‘interdisciplinary’, but she watches it differently. ‘My research is purely mathematical, but it is certainly designed to be applied, in this case in the hospital.’ In the final chapter of her thesis, Van der Pas discusses how she applied her research to a study on artificial hips, which are given to almost 30,000 people a year. ‘Those things do not last forever, so you want to know how long they last exactly. That information is useful in operations, maintenance and production of artificial hips.’

‘From a statistical point of view it’s not very convenient that people have two hips,’ Van der Pas explains. Therefore, you have to work with dependent observations. ‘That makes many methods useless.’

### Do the wrong thing

‘Many researchers ignore that there are people with two artificial hips; they pretend that they are dealing with two different patients. That is not true of course, but it turns out to be less of a problem than not to do that and afterwards remove all patients with two artificial hips from a dataset.’ The instinct of a researcher is to remove the outliers from a dataset, but that produces seriously misleading results. ‘So it’s better to do the wrong thing straight away,’ says Van der Pas. ‘We did not think that it would be so useless that it would be better to do the research wrong, than to correct the results with the wrong statistical methods.’

This shows that we can not only look at statistics in a mathematical sense - the practical aspect must be involved also. ‘In mathematical terms it is not correct to see one patient as two patients, but the practical effect is small. Precisely because of a wrong correction, which seems mathematically obvious, you send the data in the wrong direction.’ For example, it is easy to cheat with a p-value, an estimate of the significance of a research conclusion - even with the best intentions. ‘We are looking for alternatives, tests that deliver values that are not so susceptible to unintentional abuse.’

### Education and research

Since finishing her PhD, Van der Pas has been dividing her time between education and research. ‘I have a great job that is a good fit after my doctoral research. Half the time I work in the Snellius Building on the theoretical side of statistics.’ The other half of the time she works at the medical statistics group at the LUMC as an assistant professor, developing the ideas she used in her dissertation and putting them into practice. This combination of pure mathematics developed by a researcher who has a deep and broad understanding of the field in which the developed techniques will be used, is strong. It was Van der Pas’s hope that the balance between theory and practice would provide a good interaction, and that the two sides would inform and inspire each other. ‘And that has absolutely been the case.’

*Photo: Stéphanie van der Pas is handed the C.J. Kok Jury Award by rector magnificus Carel Stolker.*