Sir David Roxbee Cox (15 July 1924 – 18 January 2022) was a British statistician and educator. His wide-ranging contributions to the field of
statistics
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...
included introducing
logistic regression
In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analy ...
, the
proportional hazards model
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional ha ...
and the
Cox process, a
point process
In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Kallenberg, O. (1986). ''Random Measures'', 4th edition. ...
named after him.
He was a professor of statistics at
Birkbeck College, London
, mottoeng = Advice comes over nightTranslation used by Birkbeck.
, established =
, type = Public research university
, endowment = £4.3 m (2014)
, budget = £109 ...
,
Imperial College London
Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
and the
University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
, and served as
Warden
A warden is a custodian, defender, or guardian. Warden is often used in the sense of a watchman or guardian, as in a prison warden. It can also refer to a chief or head official, as in the Warden of the Mint.
''Warden'' is etymologically identic ...
of
Nuffield College, Oxford
Nuffield College () is one of the constituent colleges of the University of Oxford in England. It is a graduate college and specialises in the social sciences, particularly economics, politics and sociology. Nuffield is one of Oxford's newer c ...
. The first recipient of the
International Prize in Statistics, he also received the
Guy,
George Box
George Edward Pelham Box (18 October 1919 – 28 March 2013) was a British statistician, who worked in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference. He has been called "one of the gre ...
and
Copley medals, as well as a
knighthood.
Early life
Cox was born in
Birmingham
Birmingham ( ) is a City status in the United Kingdom, city and metropolitan borough in the metropolitan county of West Midlands (county), West Midlands in England. It is the second-largest city in the United Kingdom with a population of 1. ...
on 15 July 1924.
His father was a
die sinker and part-owner of a jewellery shop, and they lived near the
Jewellery Quarter
The Jewellery Quarter is an area of central Birmingham, UK, in the north-western area of Birmingham City Centre, with a population of around 19,000 people in a area.
The Jewellery Quarter is Europe's largest concentration of businesses invol ...
.
The aeronautical engineer
Harold Roxbee Cox was a distant cousin. He attended
Handsworth Grammar School, Birmingham.
He received a
Master of Arts
A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. ...
in mathematics at
St John's College, Cambridge
St John's College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge founded by the House of Tudor, Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corpo ...
,
and obtained his
PhD from the
University of Leeds
, mottoeng = And knowledge will be increased
, established = 1831 – Leeds School of Medicine1874 – Yorkshire College of Science1884 - Yorkshire College1887 – affiliated to the federal Victoria University1904 – University of Leeds
, t ...
in 1949, advised by
Henry Daniels and
Bernard Welch. His dissertation was entitled ''Theory of Fibre Motion''.
Career
Cox was employed from 1944 to 1946 at the
Royal Aircraft Establishment
The Royal Aircraft Establishment (RAE) was a British research establishment, known by several different names during its history, that eventually came under the aegis of the UK Ministry of Defence (MoD), before finally losing its identity in me ...
, 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
, mottoeng = Advice comes over nightTranslation used by Birkbeck.
, established =
, type = Public research university
, endowment = £4.3 m (2014)
, budget = £109 ...
. In 1966, he took up the Chair position in Statistics at
Imperial College London
Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
where he later became head of the mathematics department. In 1988 he became Warden of
Nuffield College
Nuffield College () is one of the constituent colleges of the University of Oxford in England. It is a graduate college and specialises in the social sciences, particularly economics, politics and sociology. Nuffield is one of Oxford's newer ...
and a member of the Department of Statistics at
Oxford University
Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...
. He formally retired from these positions in 1994, but continued to work at Oxford.
Cox supervised, collaborated with, and encouraged many notable researchers prominent in statistics. He collaborated with George Box
George Edward Pelham Box (18 October 1919 – 28 March 2013) was a British statistician, who worked in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference. He has been called "one of the gre ...
on a study of transformations such as the Box–Cox transformation
In statistics, a power transform is a family of functions applied to create a monotonic transformation of data using power functions. It is a data transformation technique used to stabilize variance, make the data more normal distribution-like, ...
and they were especially delighted to be credited as Box and Cox. He was the doctoral advisor of David Hinkley, Peter McCullagh
Peter McCullagh (born 8 January 1952) is a Northern Irish-born American statistician and John D. MacArthur Distinguished Service Professor in the Department of Statistics at the University of Chicago.
Education
McCullagh is from Plumbridge ...
, Basilio de Bragança Pereira, Wally Smith, Gauss Moutinho Cordeiro, Valerie Isham, Henry Wynn and Jane Hutton. He served as President of the Bernoulli Society from 1979 to 1981, of the Royal Statistical Society
The Royal Statistical Society (RSS) is an established statistical society. It has three main roles: a British learned society for statistics, a professional body for statisticians and a charity which promotes statistics for the public good.
...
from 1980 to 1982, and of the International Statistical Institute
The International Statistical Institute (ISI) is a professional association of statisticians. It was founded in 1885, although there had been international statistical congresses since 1853. The institute has about 4,000 elected members from gov ...
from 1995 to 1997. He was an Honorary Fellow of Nuffield College
Nuffield College () is one of the constituent colleges of the University of Oxford in England. It is a graduate college and specialises in the social sciences, particularly economics, politics and sociology. Nuffield is one of Oxford's newer ...
and St John's College, Cambridge
St John's College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge founded by the House of Tudor, Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corpo ...
, and was a member of the Department of Statistics at the University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
.
Personal life
In 1947, Cox married Joyce Drummond, and they had four children. He died on 18 January 2022, at the age of 97.
Research
Cox made pioneering and important contributions to numerous areas of statistics and applied probability, of which the best known are:
* Logistic regression
In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analy ...
, which is employed when the variable to be predicted is categorical (i.e., can take a limited number of values, e.g., gender, race (in the US census)), binary (a special case of categorical with only two values - e.g., success/failure, disease/no disease), or ordinal, where the categories can be ranked (e.g., pain intensity can be absent, mild, moderate, severe, unbearable). Cox's 1958 paper and further publications in the 1960s addressed the case of binary logistic regression.
* The proportional hazards model
Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional ha ...
, which is widely used in the analysis of survival data, was developed by him in 1972. An example of the use of the proportional hazards model is in survival analysis in medical research. The model can be used in clinical trials to investigate time-based information about cohorts of patients, such as their response to exposure to certain chemical substances.
* The Cox process was named after him.
Awards
Cox received numerous awards and honours for his work. He was awarded the Guy Medal
The Guy Medals are awarded by the Royal Statistical Society in three categories; Gold, Silver and Bronze. The Silver and Bronze medals are awarded annually. The Gold Medal was awarded every three years between 1987 and 2011, but is awarded biennia ...
s in Silver (1961) and Gold (1973) of the Royal Statistical Society
The Royal Statistical Society (RSS) is an established statistical society. It has three main roles: a British learned society for statistics, a professional body for statisticians and a charity which promotes statistics for the public good.
...
. He was elected Fellow of the Royal Society of London
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...
in 1973. The next year, he was elected to the American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, ...
. He was knighted by Queen Elizabeth II
Elizabeth II (Elizabeth Alexandra Mary; 21 April 1926 – 8 September 2022) was Queen of the United Kingdom and other Commonwealth realms from 6 February 1952 until her death in 2022. She was queen regnant of 32 sovereign states during ...
in 1985. He was elected to the American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...
in 1990. Cox became an Honorary Fellow of the British Academy
The British Academy is the United Kingdom's national academy for the humanities and the social sciences.
It was established in 1902 and received its royal charter in the same year. It is now a fellowship of more than 1,000 leading scholars s ...
in 1997 and was a Fellow of the American Statistical Association
The American Statistical Association (ASA) is the main professional organization for statisticians and related professionals in the United States. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest continuous ...
. He was a Foreign Associate of the US National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nat ...
and a foreign member of the Royal Danish Academy of Sciences and Letters
{{Infobox organization
, name = The Royal Danish Academy of Sciences and Letters
, full_name =
, native_name = Det Kongelige Danske Videnskabernes Selskab
, native_name_lang =
, logo = Royal ...
. In 1990, he won the Kettering Prize and Gold Medal for Cancer Research for "the development of the Proportional Hazard Regression Model." In 2010 he was awarded the Copley Medal
The Copley Medal is an award given by the Royal Society, for "outstanding achievements in research in any branch of science". It alternates between the physical sciences or mathematics and the biological sciences. Given every year, the medal is t ...
of the Royal Society "for his seminal contributions to the theory and applications of statistics", the same year in which he was elected a foreign fellow of the Royal Society of Canada. He was also the first ever recipient of the International Prize in Statistics. He received the award in 2016. In 2013 Cox was elected an Honorary Fellow of the Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...
. In 2016, he won the BBVA Foundation Frontiers of Knowledge Award
The BBVA Foundation Frontiers of Knowledge Awards () are an international award programme recognizing significant contributions in the areas of scientific research and cultural creation. The categories that make up the Frontiers of Knowledge Awards ...
in the Basic Sciences category jointly with Bradley Efron
Bradley Efron (; born May 24, 1938) is an American statistician. Efron has been president of the American Statistical Association (2004) and of the Institute of Mathematical Statistics (1987–1988).Cochran, J. (1 September 2015), "ASA Lead ...
, for the development of "pioneering and hugely influential" statistical methods that have proved indispensable for obtaining reliable results in a vast spectrum of disciplines from medicine to astrophysics, genomics or particle physics.
Publications
Cox wrote or co-authored over 300 papers and books. From 1966 to 1991 he was the editor of ''Biometrika
''Biometrika'' is a peer-reviewed scientific journal published by Oxford University Press for thBiometrika Trust The editor-in-chief is Paul Fearnhead (Lancaster University). The principal focus of this journal is theoretical statistics. It was es ...
''. His books are as follows:
*''Planning of experiments'' (1958)
*''Queues'' ( Methuen, 1961). With Walter L. Smith
*''Renewal Theory'' ( Methuen, 1962).
*''The theory of stochastic processes'' (1965). With Hilton David Miller
*''Analysis of binary data'' (1969). With Joyce Snell
*''Theoretical statistics'' (1974). With D. V. Hinkley
*''Problems and Solutions in Theoretical Statistics'' (1978). With D. V. Hinkley
*'' Point Processes'' (Chapman & Hall/CRC, 1980). With Valerie Isham
*''Applied statistics, principles and examples'' (Chapman & Hall/CRC, 1981). With Joyce Snell
*''Analysis of survival data'' (Chapman & Hall/CRC, 1984). With David Oakes
*''Asymptotic techniques for use in statistics''. (1989) With Ole E. Barndorff-Nielsen
*''Inference and asymptotics'' (Chapman & Hall/CRC, 1994). With Ole E. Barndorff-Nielsen
*''Multivariate dependencies: models, analysis and interpretation'' (Chapman & Hall, 1995). With Nanny Wermuth
*''The theory of design of experiments''. (Chapman & Hall/CRC, 2000). With Nancy M. Reid
*''Complex stochastic systems'' (Chapman & Hall/CRC, 2000). With Ole E. Barndorff-Nielsen and Claudia Klüppelberg
*''Components of variance'' (Chapman & Hall/CRC, 2003). With P. J. Solomon
*''Principles of Statistical Inference'' (Cambridge University Press, 2006).
Selected Statistical Papers of Sir David Cox 2 Volume Set
Principles of Applied Statistics
(CUP). With Christl A. Donnelly
He was named editor of the following books:
*
*
*
*
The following book was published in his honour:
''Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday''
See also
* Logrank test
References
*
External links
Sir David Cox
– homepage at web-site of University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
.
* The certificate of election to the Royal Society is available a
Cox, David Roxbee
* There are two photographs a
* Cox's time in the Cambridge Statistical Laboratory is recounted i
* Summary of his life and work, page 3 o
ENBIS News, Winter/Spring 2006
* For Cox's PhD students see page.
{{DEFAULTSORT:Cox, David
1924 births
2022 deaths
20th-century British mathematicians
Academics of Birkbeck, University of London
Academics of Imperial College London
Alumni of St John's College, Cambridge
Alumni of the University of Leeds
Elected Members of the International Statistical Institute
English mathematicians
English statisticians
Fellows of Nuffield College, Oxford
Fellows of St John's College, Cambridge
Fellows of the American Statistical Association
Fellows of the Royal Society
Foreign associates of the National Academy of Sciences
Honorary Fellows of the British Academy
Knights Bachelor
Members of Academia Europaea
People educated at Handsworth Grammar School
People from Birmingham, West Midlands
Presidents of the International Statistical Institute
Presidents of the Royal Statistical Society
Queueing theorists
Recipients of the Copley Medal
Wardens of Nuffield College, Oxford
Members of the American Philosophical Society