Critical Thinking

Sir International Prize in Statistics. The inaugural prize

Sir David Cox,  whose full name Sir David Roxbee Cox, was born on July 15, 1924, in Birmingham Warwickshire England. In 1947, Cox married Joyce Drummond. Their marriage produced four children and two grandchildren. Sir David is best known for his proportional hazards model as a British statistician. Cox is known as one of the world’s leading living statisticians. He developed and made important contributions to numerous areas of statistics and applied probability over the years, of which 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.”

Cox studied at St. John’s College,  in Cambridge from 1944 to 1946. He did numerous jobs in his college years first job was at the Royal Aircraft Establishment at Farnborough. While studying at Cambridge during the Second World War he was sent to work in a military research establishment Royal Aircraft Establishment at the age of 20.  At the time there were very few statisticians,  Even though the realization was that statisticians are need in the military. Back then the assumption was that anyone who was did reasonably well at mathematics could understand statistics in a short period of time.

Cox worked in the Department of Structural and Mechanical Engineering, performing statistical analysis. Cox claimed statistics was forced upon him at the age of 20, as at the time he studied mathematics., His only other experience was at UCL, where he had been very little teaching of statistics in British universities before the second world war.            He later worked at the Wool Industries Research Association of Science and Technology in Leeds from 1946 to 1950. Statistics played a role in cox job at the Wool industry  In Leeds, They utilized statistics to some extent, and also applied mathematics due to the fact that there were all sorts of problems connected with the wool and textile industry. Because of the physics, chemistry and biology of the wool with most of these problems caused by mathematical and also had a statistical component to them.  While working at the Wool industries he received his doctorate in  Statistics from the University of Leeds in 1949.

Cox worked as an assistant lecturer in mathematics at Cambridge from 1950 to 1955. While continuing his studies he became a reader in statistics at Birkbeck College, London in 1956, and later on a professor in 1961. Cox has received numerous awards over the years. In 1961 he was awarded the Guy Medals in Silver and in 1973 Gold by the Royal Statistical Society.  Cox became a professor of Statistics and taught statistics from 1966 to 1968 at the Imperial College in London.  

In 1972  Cox received the inaugural prize for the development of his proportional hazards model that today bears his name. He is the first-ever recipient of such an award  International Prize in Statistics. The inaugural prize recognized Sir David’s seminal 1972 paper in which he developed today Sir Davids Cox Model is still being applied in many fields of science and engineering, from disease risk assessment and treatment evaluation to product liability, school dropout, re-incarceration and AIDS surveillance systems. 

Cox statistical Model “hazard function” is used to analyze the field of survival and concerned with the interval of time that passes until a particular event, such as a mechanical failure or the death of a patient, takes place. It also analyzes the rate at which the failure happens or the patient dies.

In 1972 when Cox introduced the “Cox proportional hazards model”, which he proposed as a hazard function which would separated into time-dependent and time-independent parts.  The Proportional hazards models are a class of survival models in statistics. The Survival models relates to time that passes before some event occurs to one or more covariates that may be associated with that quantity of time.

“In a proportional hazards model, the effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. For example, taking a drug may halve one’s hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure”. Wikipedia

There are other types of survival models such as accelerated failure time models that do not exhibit proportional hazards. The accelerated failure time model describes the situation where the biological or mechanical life history of an event is accelerated. Today Cox Model is used in extensive medical research for analyzing of medical data with the separation of inputs that depends on time from those that do not.

Cox’s marks on research  was so great that in 1972 one of Cox papers was one of the three most cited papers in statistics which ranked “16th in Nature’s list of the top 100 most cited papers of all time for all fields.” the paper was presented at an “RSS Ordinary Meeting and published in our Series B Journal.” This prize is a thoroughly well-deserved recognition of Sir David Cox’s seminal 1972 paper.

Sir David Cox who is a  Prominent British statistician has been named the inaugural recipient of the International Prize in Statistics. Like the many Medals, Abel Prize, Turing Award and Nobel Prize, the International Prize in Statistics is considered the highest honor in its field.

Sir Cox Model has led some  life-changing breakthroughs with far-reaching impacts,  which includes:

Demonstrating that a major reduction in smoking-related cardiac deaths could be seen within just one year of smoking cessation, not 10 or more years as previously thought
Showing the mortality effects of particulate air pollution, a finding that has changed both industry practices and air quality regulations worldwide
Identifying risk factors of coronary artery disease and analyzing treatments for lung cancer, cystic fibrosis, obesity, sleep apnea and septic shock.

 

 

Cox became a member of the Royal Society in 1973 and was knighted in 1985. In 1988 Cox became a warden at Nuffield College,  in Oxford. In 1990 Cox received an award from The General Motors Cancer Research Foundation’s Kettering Prize, an Honour for outstanding contributions to the treatment of cancer. Cox was an Honorary of the “Fellow of the British Academy in 2000”. Cox became a  Foreign Associate of the US National Academy of Sciences and a foreign member of the Royal Danish Academy of Sciences and Letters.

 He later received a Copley Medal in 2010. Cox wrote books on so many aspects of statistics which included  “The Theory of Stochastic Processes with H.D. Miller, in 1965, Theoretical Statistics with D.V. Hinkley, 1974, Analysis of Survival Data with David Oakes, in 1984, and Principles of Statistical Inference in 2006.

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

Cox who is an expert in the field of statistics, created the proportional hazards model “The Cox Model” which is widely used to analyze the survival data and allows researchers to more easily identify the risks of specific factors for mortality or other survival outcomes among groups of patients with “disparate characteristics”.  The Cox Model has been used to identify the disease risk assessment and treatment evaluation to product liability, school dropout, re-incarceration and AIDS surveillance systems, essentially in all fields of science, as well as in engineering.     

Professor Cox changed the way people analyze and understand the effect of natural or human-induced risk factors on survival outcomes,  he paved the way for powerful scientific inquiry and discoveries that made a huge impact on human health worldwide. “Susan Ellenberg, chair of the International Prize in Statistics Foundation”.   The Use of the ‘Cox Model’ in the physical, medical, life, earth, social and other sciences, as well as engineering fields, has yielded more benefits and detailed information that has assisted researchers and policymakers address some of society’s most pressing challenges.”

During Cox’s 50-year career which included technical and research positions in both private and nonprofit organizations, as well as numerous academic organizations as professor or department chair at which includes  Birkbeck College, Imperial College of London, Nuffield College and Oxford University. He considers himself to be a scientist who happens to specialize in the use of statistics, which he defined as the science of learning from data. Statistics is a critical component in the development of public policy and has played fundamental roles in vast areas of human development and scientific exploration. Cox formally retired from these positions in 1994, but remained and is still active in the profession in Oxford, England.

 

 

 

 

Basics of the Cox proportional hazards model

The Cox model is expressed by the hazard function denoted by h(t). Briefly, the hazard function can be interpreted as the risk of dying at time t. It can be estimated as follow:

h(t)=h0(t)×exp(b1x1+b2x2+…+bpxp)h(t)=h0(t)×exp(b1x1+b2x2+…+bpxp)

where,

?      t represents the survival time

?      h(t)h(t) is the hazard function determined by a set of p covariates (x1,x2,…,xpx1,x2,…,xp)

?      the coefficients (b1,b2,…,bpb1,b2,…,bp) measure the impact (i.e., the effect size) of covariates.

?      the term h0h0 is called the baseline hazard. It corresponds to the value of the hazard if all the xixi are equal to zero (the quantity exp(0) equals 1). The ‘t’ in h(t) reminds us that the hazard may vary over time.

The Cox model can be written as a multiple linear regression of the logarithm of the hazard on the variables xixi, with the baseline hazard being an ‘intercept’ term that varies with time.

The quantities exp(bi)exp(bi) are called hazard ratios (HR). A value of bibi greater than zero, or equivalently a hazard ratio greater than one, indicates that as the value of the ithith covariate increases, the event hazard increases and thus the length of survival decreases.

Put another way, a hazard ratio above 1 indicates a covariate that is positively associated with the event probability, and thus negatively associated with the length of survival.

In summary,

?      HR = 1: No effect

?      HR < 1: Reduction in the hazard ?      HR > 1: Increase in Hazard

 

 

 

 

 

 

References:

https://www.statslife.org.uk/news/3052-sir-david-cox-honoured-with-first-international-prize-in-statistics

 

https://www.britannica.com/biography/David-Cox-British-statistician

 

 

http://www.statisticsviews.com/details/feature/5770651/I-would-like-to-think-of-myself-as-a-scientist-who-happens-largely-to-specialise.html

 

https://www.prnewswire.com/news-releases/international-prize-in-statistics-awarded-to-sir-david-cox-for-survival-analysis-model-applied-in-medicine-science-and-engineering-300347100.html

 

https://en.wikipedia.org/wiki/David_Cox_(statistician)

 

http://www.sthda.com/english/wiki/cox-proportional-hazards-model