Subsections
• Mathematics and statistics play a critical rôle in epidemiology
• Data does not equal information
• Statisticians, as the leaders in epidemiology and population-based medical research projects
• Computers and statistics

  
Mathematicians and Statisticians in Medical Research

Epidemiology is the science of understanding what really makes a difference to our health and well-being, as a population. It is one thing for medical researchers to show that exposure to substance $A$ causes disease $B$ in rats. It is quite another thing to show that, for human beings, there is any evidence that their usual levels of exposure to substance $A$ contribute to their risk of disease $B$; and if so, by how much. Without this, the public health significance of the putative disease-causing exposure cannot be determined.

Epidemiology differs from most other areas of science in that it necessarily must rely on observation, rather than experiments. It is almost impossible to conduct long-term controlled, randomised experiments on humans. Epidemiologists must rely on `quasi-experiments of opportunity', such as:

case-control studies

comparing the past life-experiences of people who have, or have had, a particular disease (cases) with that of comparable people of the same age and sex who do not have the disease (controls);

cohort studies

comparing the health status of workers who are known to have been exposed to potential carcinogens (e.g. through working in certain industries), with that of comparable people of the same age and sex who were not exposed;

migrant family studies

comparing immigrants with their non-migrating relatives, in order to study the effects of any environmental differences between the original and emigrating country, while controlling for genetic factors;

twin studies

studying the different life experiences of twins, in those pairs for which one twin has a certain disease while the other does not, or studying the health status of pairs in which one twin was exposed to some particular factor, such as smoking, while the other was not. Twin studies naturally control for age, sex and genetic factors. They also allow inference to be made about the possible rôle of genetic factors on disease, and on disease-causing processes, by comparisons between identical and non-identical pairs.

Two well-known examples of the insights given by these approaches are:

• smoking is responsible for a large proportion of the major causes of death (such as cancer and heart disease), making tobacco companies contributors to more deaths during the 20$^{\mathrm{th}}$ century than wars and mass-murderers; and
• modern western lifestyle makes living easier and more comfortable, but increases the risk of major chronic diseases, including heart disease and some cancers.

In some instances these findings have revolutionised the life-style of at least part of the Australian community. Smoking rates have plummeted since the mid-century. Food consumption has changed towards less meat, lower fat content, and greater emphasis on Southern European and other cultural cuisines, which are associated with better health outcomes. We even look at the sun in a different way!

  
Mathematics and statistics play a critical rôle in epidemiology

Studies are useless unless they are designed properly. A study cannot be designed unless one knows what the question is, and how the data is to be analysed. Furthermore, the data should be of the highest possible quality. Therefore, by simple logic, the following theorem is proved: epidemiological studies cannot succeed without mathematics and statistics.

  
Data does not equal information

This is the only equation that I will present in this talk.

Ad hoc collections of data cannot necessarily be used to gain information. On the other hand, data collected with a clear underlying purpose, so as to address a well-defined question, using a well-designed process for collection, can be incredibly informative--provided it is analysed properly.

Rag-bag collections of data, no matter how large, more often than not are virtually useless. They constitute a waste of time, both of the collectors and the givers of the data. They therefore constitute a waste of money. Worst of all, they have the real potential of being misleading. For example, people telephoning-in their opinions to e.g. television stations or police switchboards, offering opinions about public issues and the like, is a very dangerous practice for society.

`Findings' are flawed, in that they cannot be assured to represent the opinions or views of the population. The viewpoints of small groups with extreme, unrepresentative attitudes can be mis-represented as `public opinion'. The same concerns apply to poorly sampled scientific data.

  
Statisticians, as the leaders in epidemiology and population-based medical research projects

A natural consequence of the above is that many mathematically and statistically trained scientists are now leaders in public health research. In fact, statisticians have always played a major rôle in these areas. John Snow, who stopped a cholera outbreak in London by removing a water pump, owes much to William Farr, who provided invaluable statistical information to support his theory that cholera was a water-borne epidemic.

• Richard Peto (Head of Epidemiology at Oxford University)
• Nick Day (Head of Medical Research Council Unit at University of Cambridge)
• Malcolm Pike (Head of Department of Preventive Medicine at the University of Southern California in Los Angeles, and former Head of Epidemiology at Oxford University)
• and our own John Kaldor (Head of the Epidemiology Unit and Deputy Director of the National Centre in HIV Epidemiology and Clinical Research, in Sydney)

were all outstanding mathematicians in their undergraduate and graduate careers.

  
Computers and statistics

The analysis of data has been revolutionised in recent years by the advent of high-speed personal computers. Unfortunately, computerised statistical packages for analysing data are nothing if downright dangerous to the public, in the hands of people who do not understand the mathematical and design principles behind statistical methods: ``Rubbish in -- rubbish out''.

Package-users need to be aware of just what statistical analysis is really about, of how it aims to seek out and quantify the signal from amongst the noise and not to arbitrate on the `truth'. Users need to be aware of what a `$p$-value' means; and more especially, what it does not mean.

Most of the brightest and quantitatively-adept students are being attracted towards computer science. If only they could also be encouraged to study properly the methods of applied statistics, then these individuals would have enormous power in their finger-tips to help society, through contributions to medical and health research.