David Cox (statistician)

Sir David Cox FRS FBA FRSE FRSC
Cox in 1980
Born	(1924-07-15)15 July 1924 Birmingham, England
Died	18 January 2022(2022-01-18) (aged 97)
Alma mater	St John's College, Cambridge (MA) University of Leeds (PhD)
Known for	Cox proportional hazards model Cox process Box-Cox transform Matrix-exponential distribution Method of supplementary variables Stochastic processes Design of experiments Analysis of binary data
Spouse	Joyce Drummond ​ (m. 1947)​
Children	4
Awards	Knight Bachelor Fellow of the Royal Society Guy Medal (Silver, 1961) (Gold, 1973) George Box Medal (2005) Copley Medal (2010) International Prize in Statistics (2016) BBVA Foundation Frontiers of Knowledge Award (2016)
Scientific career
Fields	Statistics
Institutions	Royal Aircraft Establishment Wool Industries Research Association University of Cambridge Birkbeck College, London Imperial College London Nuffield College, Oxford
Thesis	Theory of Fibre Motion  (1949)
Doctoral advisor	Henry Daniels Bernard Lewis Welch
Doctoral students	David Hinkley Peter McCullagh Basilio de Bragança Pereira Walter L. Smith Gauss Moutinho Cordeiro Adelchi Azzalini Valerie Isham Henry Wynn Claudio Di Veroli Jane Hutton
Other notable students	Nancy Reid (postdoc)

Sir David Roxbee Cox FRS FBA FRSE FRSC (15 July 1924 – 18 January 2022) was a British statistician and educator. His wide-ranging contributions to the field of statistics included introducing logistic regression, the proportional hazards model and the Cox process, a point process named after him.

He was a professor of statistics at Birkbeck College, London, Imperial College London and the University of Oxford, and served as Warden of Nuffield College, Oxford. The first recipient of the International Prize in Statistics, he also received the Guy, George Box and Copley medals, as well as a knighthood.

Early life

Cox was born in Birmingham on 15 July 1924.^[1][2] His father was a die sinker and part-owner of a jewellery shop, and they lived near the Jewellery Quarter.^[3] The aeronautical engineer Harold Roxbee Cox was a distant cousin.^[4] He attended Handsworth Grammar School, Birmingham.^[3][5] He received a Master of Arts in mathematics at St John's College, Cambridge,^[1][3][6] and obtained his PhD from the University of Leeds in 1949, advised by Henry Daniels and Bernard Welch. His dissertation was entitled Theory of Fibre Motion.^[7]

Career

Cox was employed from 1944 to 1946 at the Royal Aircraft Establishment, from 1946 to 1950 at the Wool Industries Research Association in Leeds,^[8] 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 mathematics department. In 1988 he became Warden of Nuffield College and a member of the Department of Statistics at Oxford University. He formally retired from these positions in 1994, but continued to work at Oxford.^[8][9]

Cox supervised, collaborated with, and encouraged many notable researchers prominent in statistics. He collaborated with George Box on a study of transformations such as the Box–Cox transformation and they were especially delighted to be credited as Box and Cox.^[10][11] He was the doctoral advisor of David Hinkley, Peter McCullagh, Basilio de Bragança Pereira, Wally Smith, Gauss Moutinho Cordeiro, Valerie Isham, Henry Wynn, Claudio Di Veroli and Jane Hutton.^[7] He served as president of the Bernoulli Society from 1979 to 1981,^[12] of the Royal Statistical Society from 1980 to 1982,^[13] and of the International Statistical Institute from 1995 to 1997.^[14] He was an Honorary Fellow of Nuffield College and St John's College, Cambridge, and was a member of the Department of Statistics at the University of Oxford.^[1]

Personal life

In 1947, Cox married Joyce Drummond, and they had four children.^[15] He died on 18 January 2022, at the age of 97.^[16][17]

Research

Cox made pioneering and important contributions to numerous areas of statistics and applied probability, of which the best known are:

• Logistic regression, 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^[18] and further publications in the 1960s addressed the case of binary logistic regression.^[19]
• The proportional hazards model, which is widely used in the analysis of survival data, was developed by him in 1972.^[20][21] 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.^[22]
• The Cox process was named after him.^[23]

Awards

Cox received numerous awards and honours for his work. He was awarded the Guy Medals in Silver (1961) and Gold (1973) of the Royal Statistical Society.^[1][24] He was elected Fellow of the Royal Society of London in 1973.^[25] The next year, he was elected to the American Academy of Arts and Sciences.^[26] He was knighted by Queen Elizabeth II in 1985.^[6][27] He was elected to the American Philosophical Society in 1990.^[28] Cox became an Honorary Fellow of the British Academy in 1997 and was a Fellow of the American Statistical Association.^[29] He was a Foreign Associate of the US National Academy of Sciences and a foreign member of the Royal Danish Academy of Sciences and Letters.^[6][24] 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 of the Royal Society "for his seminal contributions to the theory and applications of statistics",^[30] the same year in which he was elected a foreign fellow of the Royal Society of Canada.^[31] He was also the first ever recipient of the International Prize in Statistics. He received the award in 2016.^[32] In 2013 Cox was elected an Honorary Fellow of the Royal Society of Edinburgh.^[33] In 2016, he won the BBVA Foundation Frontiers of Knowledge Award in the Basic Sciences category jointly with Bradley Efron, 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.^[9]

Publications

Cox wrote or co-authored over 300 papers and books.^[34] From 1966 to 1991 he was the editor of Biometrika.^[30] 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). ISBN 978-0-521-68567-2
• 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:

• D. R. Cox; D. M. Titterington, eds. (1991). Complex Stochastic Systems. Royal Society. ISBN 978-0-85403-453-6.
• D. R. Cox, ed. (1992). The Collected Works of John W. Tukey: Factorial and ANOVA. Vol. VII. Taylor & Francis. ISBN 978-0-412-06321-3.
• D. R. Cox; D. V. Hinkley; Ole E. Barndorff-Nielsen, eds. (1996). Time series models in econometrics, finance and others. Taylor & Francis. ISBN 978-0-412-72930-0.
• D. M. Titterington; D. R. Cox, eds. (2001). Biometrika: One Hundred Years. Oxford University Press. ISBN 978-0-19-850993-6.

The following book was published in his honour:

• Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday ISBN 978-0-19-856654-0

See also

• Logrank test

References

1. "'Genius' statistician and Honorary Fellow dies aged 97 | StJohns". www.joh.cam.ac.uk. Retrieved 21 January 2022.
2. "Today's Birthdays". The Daily Telegraph. 15 July 2010. p. 28. Retrieved 21 January 2022 – via Newspapers.com.
3. "David Cox". ukdataservice.ac.uk. Archived from the original on 12 October 2016.
4. Cox, Harold Roxbee (April 1999). "Myself, when young" (PDF). Aeronautical Journal. 103 (1022): 178–180. doi:10.1017/S0001924000096433. S2CID 113908453.
5. "Famous Alumni". Handsworth Grammar School. Retrieved 21 January 2022.
6. "Sir David Cox". American Academy of Political and Social Science. 8 August 2016. Retrieved 21 January 2022.
7. David Cox at the Mathematics Genealogy Project
8. Gregersen, Erik (13 February 2015). "Sir David Cox, British statistician". Encyclopædia Britannica. Retrieved 11 October 2016.
9. "The BBVA Foundation distinguishes David Cox and Bradley Efron for revolutionizing statistics and making it an indispensable tool for other sciences". BBVA Foundation Frontiers of Knowledge Awards (Press release). 24 January 2017. Retrieved 20 January 2022.
10. "Professor Sir David Cox", The Times, no. 73693, p. 79, 29 January 2022
11. Box, George E. P.; Cox, D. R. (1964). "An analysis of transformations". Journal of the Royal Statistical Society, Series B. 26 (2): 211–252. doi:10.1111/j.2517-6161.1964.tb00553.x. JSTOR 2984418. MR 0192611.
12. "History". www.bernoulli-society.org. Archived from the original on 28 September 2021. Retrieved 20 January 2022.
13. "Sir David Cox, 1924-2022". RSS. Retrieved 20 January 2022.
14. "History of the International Statistical Institute | ISI". www.isi-web.org. Archived from the original on 16 December 2022. Retrieved 20 January 2022.
15. Nancy Reid (August 1994). "A Conversation with Sir David Cox". Statistical Science. 9 (3): 439–455. doi:10.1214/ss/1177010394. JSTOR 2246357.
16. "Sir David Cox, 1924-2022". Nuffield College Oxford University. Retrieved 20 January 2022.
17. "'Genius' statistician and Honorary Fellow dies aged 97 | StJohns".
18. Cox, DR (1958). "The regression analysis of binary sequences (with discussion)". J R Stat Soc B. 20 (2): 215–242. doi:10.1111/j.2517-6161.1958.tb00292.x. JSTOR 2983890.
19. Cramer, J. S. (August 2003). "The origins and development of the logit model" (PDF). Logit Models from Economics and Other Fields. Cambridge University Press. pp. 149–157. doi:10.1017/cbo9780511615412.010. ISBN 978-0-521-81588-8.
20. Kalbfleisch, John D.; Schaubel, Douglas E. (10 March 2023). "Fifty Years of the Cox Model". Annual Review of Statistics and Its Application. 10 (1): 1–23. Bibcode:2023AnRSA..10....1K. doi:10.1146/annurev-statistics-033021-014043. ISSN 2326-8298. S2CID 253787572.
21. Cox, David R (1972). "Regression Models and Life-Tables". Journal of the Royal Statistical Society, Series B. 34 (2): 187–220. doi:10.1111/j.2517-6161.1972.tb00899.x. JSTOR 2985181. MR 0341758.
22. Spruance, Spotswood L.; Reid, Julia E.; Grace, Michael; Samore, Matthew (2004). "Hazard Ratio in Clinical Trials". Antimicrobial Agents and Chemotherapy. 48 (8): 2787–2792. doi:10.1128/AAC.48.8.2787-2792.2004. PMC 478551. PMID 15273082.
23. Singpurwalla, Nozer D. (14 August 2006). Reliability and Risk: A Bayesian Perspective. John Wiley & Sons. p. 134. ISBN 978-0-470-06033-9.
24. "Penn State Holds 2015 Rao Prize Conference to Honor Winners". AMSTATNEWS. American Statistical Association. 1 August 2015. Retrieved 21 January 2022.
25. Reid, Nancy (2024). "Sir David R. Cox. 15 July 1924 — 18 January 2022". Biographical Memoirs of Fellows of the Royal Society. 77: 69–91. doi:10.1098/rsbm.2023.0052.
26. "David Roxbee Cox". American Academy of Arts & Sciences. Retrieved 14 April 2022.
27. "No. 50221". The London Gazette. 6 August 1985. p. 10815.
28. "APS Member History". search.amphilsoc.org. Retrieved 14 April 2022.
29. "Sir David Cox Hon FBA". British Academy. Retrieved 21 January 2022.
30. "David Cox". The Royal Society. Retrieved 11 October 2016.
31. "NEW FELLOWS 2010" (PDF). Royal Society of Canada. Retrieved 29 September 2022.
32. Talley, Jill (19 October 2016). "International Prize in Statistics Awarded to Sir David Cox for Survival Analysis Model Applied in Medicine, Science, and Engineering" (PDF) (Press release). American Statistical Association. Retrieved 20 October 2016.
33. "Sir David Cox FRS, HonFBA, HonFRSE - The Royal Society of Edinburgh". The Royal Society of Edinburgh. Archived from the original on 2 February 2018. Retrieved 1 February 2018.
34. "Publications of Sir David Cox". Nuffield College. Retrieved 21 January 2022.

• "'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". Statistics Views. John Wiley & Sons. 24 January 2014. Archived from the original on 12 October 2016. Retrieved 11 October 2016.

External links

• Sir David Cox – homepage at web-site of University of Oxford.
• The certificate of election to the Royal Society is available at Cox, David Roxbee
• There are two photographs at Portraits of Statisticians
• Cox's time in the Cambridge Statistical Laboratory is recounted in The History of the Cambridge Statistical Laboratory Archived 19 December 2013 at the Wayback Machine
• David Roxbee Cox at the Mathematics Genealogy Project

Academic offices
Preceded by Michael Brock	Warden of Nuffield College, Oxford 1988–1994	Succeeded by Sir Anthony Atkinson