# “I would like to think of myself as a scientist, who happens largely to specialise in the use of statistics”– An interview with Sir David Cox

## Features

**Author:**Statistics Views**Date:**24 Jan 2014**Copyright:**Image appears courtesy of Sir David Cox

Sir David Cox is arguably one of the world’s leading living statisticians. He has made pioneering and important contributions to numerous areas of statistics and applied probability over the years, of which perhaps the best known is the proportional hazards model, which is widely used in the analysis of survival data. The Cox point process was named after him.

Sir David studied mathematics at St John's College, Cambridge and obtained his PhD from the University of Leeds in 1949. He was employed from 1944 to 1946 at the Royal Aircraft Establishment, from 1946 to 1950 at the Wool Industries Research Association in Leeds, and from 1950 to 1955 worked at the Statistical Laboratory at the University of Cambridge. From 1956 to 1966 he was Reader and then Professor of Statistics at Birkbeck College, London. In 1966, he took up the Chair position in Statistics at Imperial College London where he later became Head of the Department of Mathematics for a period. In 1988 he became Warden of Nuffield College and was a member of the Department of Statistics at Oxford University. He formally retired from these positions in 1994 but continues to work in Oxford.

Sir David has received numerous awards and honours over the years. He has been awarded the Guy Medals in Silver (1961) and Gold (1973) by the Royal Statistical Society. He was elected Fellow of the Royal Society of London in 1973, was knighted in 1985 and became an Honorary Fellow of the British Academy in 2000. He is a Foreign Associate of the US National Academy of Sciences and a foreign member of the Royal Danish Academy of Sciences and Letters. In 1990 he won the Kettering Prize and Gold Medal for Cancer Research for "the development of the Proportional Hazard Regression Model" and 2010 he was awarded the Copley Medal by the Royal Society.

He has supervised and collaborated with many students over the years, many of whom are now successful in statistics in their own right such as David Hinkley and Past President of the Royal Statistical Society, Valerie Isham. Sir David has served as President of the Bernoulli Society, Royal Statistical Society, and the International Statistical Institute.

This year, Sir David is to turn 90. Here Statistics Views talks to Sir David about his prestigious career in statistics, working with the late Professor Lindley, his thoughts on Jeffreys and Fisher, being President of the Royal Statistical Society during the Thatcher Years, Big Data and the best time of day to think of statistical methods.

**1. With an educational background in mathematics at St Johns College, Cambridge and the University of Leeds, when and how did you first become aware of statistics as a discipline?**

I was studying at Cambridge during the Second World War and after two years, one was sent either into the Forces or into some kind of military research establishment. There were very few statisticians then, although it was realised there was a need for statisticians. It was assumed that anybody who was doing reasonably well at mathematics could pick up statistics in a week or so! So, aged 20, I went to the Royal Aircraft Establishment in Farnborough, which is enormous and still there to this day if in a different form, and I worked in the Department of Structural and Mechanical Engineering, doing statistical work. So statistics was forced upon me, so to speak, as was the case for many mathematicians at the time because, aside from UCL, there had been very little teaching of statistics in British universities before the Second World War. Afterwards, it all started to expand.

**2. From 1944 to 1946 you worked at the Royal Aircraft Establishment and then from 1946 to 1950 at the Wool Industries Research Association in Leeds. Did statistics have any role to play in your first roles out of university?**

Totally. In Leeds, it was largely statistics but also to some extent, applied mathematics because there were all sorts of problems connected with the wool and textile industry in terms of the physics, chemistry and biology of the wool and some of these problems were mathematical but the great majority had a statistical component to them. That experience was not totally uncommon at the time and many who became academic statisticians had, in fact, spent several years working in a research institute first.

**3. From 1950 to 1955, you worked at the Statistical Laboratory at Cambridge and would have been there at the same time as Fisher and Jeffreys. The late Professor Dennis Lindley, who was also there at that time, told me that the best people working on statistics were not in the statistics department at that time. What are your memories when you look back on that time and what do you feel were your main achievements?**

Lindley was exactly right about Jeffreys and Fisher. They were two great scientists outside statistics - Jeffreys founded modern geophysics and Fisher was a major figure in genetics. Dennis was a contemporary and very impressive and effective. We were colleagues for five years and our children even played together.

The first lectures on statistics I attended as a student consisted of a short course by Harold Jeffreys who had at the time a massive reputation as virtually the inventor of modern geophysics. His *Theory of Probability*, published first as a monograph in physics was and remains of great importance but, amongst other things, his nervousness limited the appeal of his lectures, to put it gently. I met him personally a couple of times – he was friendly but uncommunicative. When I was later at the Statistical Laboratory in Cambridge, relations between the Director, Dr Wishart and R.A. Fisher had been at a very low ebb for 20 years and contact between the Lab and Fisher was minimal. I heard him speak on three of four occasions, interesting if often rambunctious occasions. To some, Fisher showed great generosity but not to the Statistics Lab, which was sad in view of the towering importance of his work.

To some, Fisher showed great generosity but not to the Statistics Lab, which was sad in view of the towering importance of his work.

**4. You have also taught at many institutions over the years including Princeton, Berkeley, Cambridge, Birkbeck College and Imperial College London before joining Nuffield College here at Oxford. Over the years, how did the teaching of statistics evolve and adapt to meet the changing needs of students?**

As I said, when I was a student, there was very little teaching of statistics in British universities. It has evolved over the years and was first primarily a postgraduate subject, taken after reading mathematics if you wished to be a scientific statistician, rather than an economic statistician. You took at least a diploma, or a one-year MA or a doctorate. Then statistics came into mathematics degrees, partly to make them more appealing to a wider audience and that has changed, so nowadays, most statisticians start fairly intensively in an undergraduate course, which has some advantages and some disadvantages.

**5. How did your teaching and research motivate and influence each other? Did you get research ideas from statistics and incorporate them into your teaching?**

Much of my research has come from talking to scientists. Sometimes ideas come from lecturing because the way to really understand a subject is to give a course of lectures on the subject and sometimes that throws up more theoretical issues that you might not otherwise have been thought of. The overwhelming majority of my work comes either directly or indirectly from some physical biological or medical problem, but in many different ways – casual conversation sometimes.

**6. You have taught many who have gone onto make their own important contributions towards statistics such as David Hinkley whom is now renowned for his work on bootstrap methods and Valerie Isham who recently served as the President of the Royal Statistical Society. The late Professor Dennis Lindley told me that “One of the joys of life is teaching a really good graduate.” Would you be in agreement?**

I would say that one of the joys of life is learning from a good graduate. The first duty of a doctoral student is clearly to educate their supervisor which my own doctoral students have down. Hopefully, they’ve learnt a bit from me occasionally! I am absolutely certain that I learnt a lot from Valerie, for instance, as we’ve worked together on and off for around forty years. Having such students is fantastic. I have been fortunate and happy as at Birkbeck - I had largely evening students. They were highly motivated and very able. Many of the graduate students at Imperial came from other places, or were international students of high standard. Also rather importantly, my students have been very nice people!

**7. You are best known for your innovative work on the proportional hazards model, which is now widely used in the analysis of survival data. What research led to this discovery? What set you on the right path? **

Two different things – first of all, I had been interested in reliability in an industrial context since I worked in the textile industry and to some extent, when I was at the Royal Aircraft Establishment, when strength of materials was important. I had a long interest in testing the strength and reliability which is also related to looking at the duration of life. Then the more specific thing was that at least four or five people from different areas in the US and the UK said that they had a certain kind of data with people’s survival times under various treatments and all sorts of further aspects with regards to the patient but they did not know how to analyse this data. The work led to one paper but the reason it is so popular is totally accidental. Other people wrote easily useful software in which to implement the method which is not my speciality at all. I had software to implement it but it was not suitable for general use. In a sense, it became almost too easy and so people just started to use the method because it was painless! The proportion of my life that I spent working on the proportional hazards model is, in fact, very small. I had an idea of how to solve it but I could not complete the argument and so it took me about four years on and off, often thinking about it during the night.

*(Editor's note: I tell Sir David that I now had a picture in my head of him pacing the house in his pyjamas at four o’clock in the morning with a hot chocolate in one hand, thinking statistical thoughts and he laughs).*

Not quite! It was right before going to bed. There is a well-established literature in mathematics that people who thought about a problem and do not know how to solve it, go to bed thinking about it and wake up the next morning with a solution. It’s not easily explicable but if you’re wide awake, you perhaps argue down the conventional lines of argument but what you need to do is something a bit crazy which you’re more likely to do if you’re half-awake or asleep. Presumably that’s the explanation!

The proportion of my life that I spent working on the proportional hazards model is, in fact, very small. I had an idea of how to solve it but I could not complete the argument and so it took me about four years on and off...

**8. The getstats campaign by the Royal Statistical Society focuses on improving the public’s understanding of statistics in every-day life. Would you have any advice for them and what areas should they focus on that you feel there should be more awareness of in statistics?**

Of course, to some extent, the notion that some very simple and non-technical ideas about collecting data and analysing it are taught to children is very good but then at the other end, there are people who are highly educated but have no sense of statistical arguments, such as many lawyers and senior civil servants. The RSS has done an excellent job in trying to interest MPs in statistical ideas. Both these extremes are important. Sending a very general message to people as far as possible helps, but also sending very focussed messages to key groups of people is more important in the short term. You do see on TV, for instance, that basic principles are being ignored in collecting and analysing evidence. Of course, it’s easy for me to stand on the sidelines and criticise.

**9. You have served as the President for several societies over the years including the Royal Statistical Society, the Bernoulli Society and the International Statistical Institute. What are your memories of your time at the RSS for instance and how you helped the society adapt to the changing needs of the statistical community?**

It was a bit different in my time. I was the President of the RSS at the time when Margaret Thatcher was PM and massacring the civil service and in particular, the government’s statistical service and there was a lot of activity going on about that. But it was done more by going to see people, talking to them and trying to influence them than writing them formal letters. While, of course, openness is a good thing, it is not always the best way to get results. People can take up inflexible attitudes but if you talk to them quietly in private, they are perhaps then more open to new ideas.

**10. You have received numerous awards from the Guy Medal both in Silver and Gold to the Marvin Zelen Leadership Award. Is there a particular award that you were most proud of being awarded? **

It would be the Copley Medal from the Royal Society as it was for general science. It is very nice to receive these awards, of course, perhaps particularly because they represent the fact that your friends have put in efforts on your behalf. Therefore, what I really value is not the award but the appreciation of friends and colleagues. That is what is important but the award and degrees are certainly an honour. If you overvalue an award, that can be dangerous.

**11. You have written many papers and books. What are the ones that you are most proud of?**

The one I’m going to write next, of course! I have flitted about all sorts of different topics, different fields of application, different parts of the subject, and so on. Really, I don’t look back very much.

At the moment, I have just finished a book with a colleague called *Case Control Studies* which is mainly about epidemiological investigation.

...what I really value is not the award but the appreciation of friends and colleagues.

**12. What has been the best book on statistics that you have ever read?**

I honestly don’t know. The position of books is interesting as when I first started in my career, there were hardly any books at all that were treating statistics in a modern way. Then they very slowly began to appear and now there is a flood of them. The standard on the whole that are published now is very high but there is too much to keep up with!

**13. What has been the most exciting development that you have worked on in statistics during your career?**

I’m not sure about exciting (!) but one of the most demanding was being involved in the issues about Bovine TB in badgers, which went on for about ten years. It involved a great deal of work, which was very interesting and instructive in all sorts of ways, and not just in statistics.

I’ve been involved in other government-based topics, such as the group which made the first predictions for the AIDS epidemic, which was also very interesting.

**14. At the recent Future of Statistical Sciences workshop, there was much talk about Big Data and a concern that many ‘hot areas’ such as big data/data analytics, which have close connections with statistics and the statistical sciences, are being monopolised by computer scientists and/or engineers. What do statisticians need to do to ensure their work and their profession gets noticed?**

Do better quality work, which I don’t mean as a criticism as to what is done at the moment but rather, do high quality work that is important in some sense, either intellectually or practically in particular fields. Part of the problem is that relatively speaking, there are not that many statisticians who are trained to the level needed.

**15. What do you think the most important recent developments in the field have been? What do you think will be the most exciting and productive areas of research in statistics during the next few years?**

The most immediately important is as you said – Big Data, which will bring forward new ideas but it does not mean that old ideas from the more traditional part of the subject is useless. It is the most obvious and biggest challenge.

Ideally, we should be looking at very important practical problems in a different number of fields and see some sort of common element and build the ideas that are necessary in order to tackle any issues that arise. You should not tackle just one issue successfully but tackle a collection of issues – the Big Data aspect is one common theme undoubtedly. It goes beyond statistics – to what extent Big Data can replace small, carefully planned investigations which are much more sharply focussed on a very specific issue.

My intrinsic feeling is that more fundamental progress is more likely to be made by very focused, relatively small scale, intensive investigations than collecting millions of bits of information on millions of people, for example. It’s possible to collect such large data now, but it depends on the quality, which may be very high or not, and if it is not, what do you do about it?

**16. Do you think over the years too much research has focussed on less important areas of statistics? Should the gap between research and applications get reduced? How so and by whom?**

In British statistics at the moment, the gap between theory and applications is difficult. Theory has almost disappeared. Almost everyone is working on applications. The issue is whether this has gone a bit too far. Everyone has to find their best way of working in principle but if you are a theoretician, then to have really serious contact with applications is for most people, extremely fruitful and indeed almost essential. Some individuals will think that is not true and that it may be better that they sit at their desk and think great thoughts, so to speak! That is another way of working but the danger then is that the great thoughts may have no bearing on the real world. But for most people, it is the interplay which is crucial. Maybe I am not imaginative enough to just sit there and think to myself of abstract problems which are really important enough to spend time on! Others are undoubtedly much better at that which may be their better way of thinking.

My intrinsic feeling is that more fundamental progress is more likely to be made by very focused, relatively small scale, intensive investigations than collecting millions of bits of information on millions of people, for example. It’s possible to collect such large data now, but it depends on the quality, which may be very high or not, and if it is not, what do you do about it?

**17. What do you see as the greatest challenges facing the profession of statisticians in the coming years? **

I know the term ‘the profession of statistics’ is widely used but I am not that keen on it. I would like to think of myself as a scientist, who happens largely to specialise in the use of statistics. That is a question of words to some extent. One answer would be to that the challenge, preferably for an academic statistician, is to be involved in several fields of application in a non-trivial sense and combine the stimulus and the contribution you can make that way with theoretical contributions that those contacts will suggest. As I said before, I don’t think you can lay down a rule as to how what is most productive for everyone.

**18. Are there people or events that have been influential in your career? Also, given that you are one of the most well respected statisticians of your generation and many statisticians look up to you, whose work do you admire (it can be someone working now, or someone whose work you admired greatly earlier on in your career?). **

The person who influenced me by far the greatest was Henry Daniels. I went to work with him at the Wool Research Association and then he went to Cambridge and from there, Birmingham. He was both a very clever mathematician and a very good statistician. He was also actually a very skilful experimental physicist, which is interesting. At the Wool Research Association, he was a statistician but he also ran a measurement lab (what they called a fibre-measurement lab where he developed all sorts of clever measurement techniques).

Maurice Bartlett, who was at Manchester, UCL and then here in Oxford was another major influence and then in the background were people like R.A. Fisher and Jeffreys. I met Jeffreys a few times and went to his lectures – although he wrote beautifully, his lectures were really rather impossible, which was sad.

Otherwise, I have learnt from almost everybody that I’ve had contact with and I certainly include students amongst them.

**19. If you had not got involved in the field of statistics, what do you think you would have done? (Is there another field that you could have seen yourself making an impact on?)**

I thought I would go into either theoretical physics or pure mathematics but I’m very glad I didn’t. I’m not clever enough for either of those fields. They are both fascinating subjects but statistics is a much more easily satisfying life because there are so many different directions in which to go. Whereas in pure mathematics, you are possibly doing things that only two other people in the world may understand and that requires a certain austerity of spirit in order to do that, which I do not possess! I also find quantum mechanics absolutely fascinating but I am not original enough to do striking things in that field.

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