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WHY DO HUMAN CANCER DEATH RATES INCREASE WITH AGE? A NEW METHOD OF ANALYSIS OF THE BIOLOGY OF CANCER ALAN C. BURTON" Introduction Pathologists naturally are impressed by the difference between different types and sites of cancer. Physiologists and biophysicists should be more interested in the common feature of all cancers, which is of course that tumour cells escape from the "contact inhibition" that regulates normal growth of tissues, and in the factors that have been shown to affect the incidence of cancer in general, at all sites in the body. Two such factors are known: the recently discovered very significant reduction in cancer incidence and deaths in populations living at altitudes above 2,000 feet, particularly for ages above 55 years [1, 2]; and the long-known remarkable increase in age-specific rates, per 100,000 population of that age, at ages above 25 years. A possible third case ofgeneral reduction ofcancer ofall or many sites may be Mormons versus non-Mormons [3]. This is thought to be something to do with the Mormon life-style or religious rules, but could be a combination of moderately high altitude and alkaline water supply. Doll and his colleagues [4, 5] have attempted to describe the increase with age by mathematical equations, and to interpret the result in terms of a sequence of up to five "critical" events required to establish a lethal tumour. The equations, based on a power law, however, do not fit the data very well. The power of the age that fitted for different sites of cancer "varied from 1 for some cancers to 6 for others," and a long "effective exposure time" (up to 32 years) had to be subtracted from the age to obtain straight lines on log-log plots. In this paper a very different mathematical approach is used and the results seem to give a new perspective on the biology of human tumours. The analysis is based on very simple logic.»Department of Biophysics, University of Western Ontario, London, Ontario N6A 5Cl, Canada. Perspectives in Biology andMedicine · Spring 1977 j 327 Source of the Data Publications ofthe World Health Organization [6] give absolute numbers ofdeaths per year from cancer, in 5-year age groups, from birth to greater than 85 years, for male and female. The latest figures in the data, for 1965, were used. The totals for "all sites" and for up to 50 specific sites (e.g., stomach, kidney) are given for 37 different countries. Separate tables give the age distribution of populations of these countries ; thus the age-specific rates could be calculated. Plan and Methods of the Investigation Establhhing "standard curves" of rate versus age.—Twenty-five of the countries listed were chosen to calculate the mean rate and the standard deviation (SD) in each age group. The countries excluded were Spain and the Republic of Ireland, for which age distributions of population are not given, and countries of mean, population-weighted altitude above 2,000 feet (Chile, Colombia, Mauritius, Mexico, Switzerland, Venezuela , and Yugoslavia). This was because the altitude effect above 2,000 feet is firmly established [1, 2] and if the "standard" data are to be used to detect unexpectedly large deviations from standard values, the known factors, such as altitude, should be eliminated. Two other countries were excluded—Ceylon and the United Arab Republic—because their reported rates were only about one-tenth of the expected rates for their (low) altitudes. This is application of a "criterion of rejection," not considered quite respectable by some. It was verified that ifthey were added to the other 25 countries the mean values would be only slightly altered, but the standard deviation would be more seriously increased. Pooling the data for the standard countries gave total populations of over 3 X 108 for each sex, and total cancer deaths of over half a million. Even for the smallest age groups (above 80 years) the total population was in the millions. With these large numbers, fortuitous fluctuations ofcalculated rates are very improbable. Similar standard curves for individual sites were computed. Even for the sites that contribute only 1 percent of all cancers, the numbers were sufficiently high in all age categories...

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