Demographic Factors and Cancer Mortality. A Mathematical Model for Cancer Mortality in Denmark 1943–78

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Abstract
Deaths from cancer in Denmark from 1943–1978 were extracted from the Danish National Death Register at the Danish Institute for Clinical Epidemiology. This paper illustrates the relationship between demographic factors and mortality from a large group of cancers, which increases progressively from young adult life into old age. One-year age-specific mortality rates between 30 and 79 years of age were computed for 14 different cancer sites among both males and females, in five ten-year birth cohorts and for the capital and provinces. The number of deaths at a particular age were found to follow a Poisson distribution and the mortality rate could be expressed by the function lx=bxk where lx is the mortality rate at age x, and b and k are parameters to be estimated. With this model a straight line is obtained, when mortality and age are plotted on a double logarithmic scale. The maximum likelihood estimates of b and k were found iteratively for each of the 280 combinations of sex—cancer site—residence—cohort. For fixed sex and cancer site the relationship between age, residence and cohort was examined. It appeared that k was independent of residence. For 10 of the male cancers and 12 of the female cancers, k was found to be in dependent of cohort and in the last 6 cases k was found to be a linear function of cohort. For 12 out of 14 cancer sites among males the ratio of mortality in the capital to mortality in the provinces was significantly greater than one. Among females this was only the case for 4 out of 14 cancers. For comparable sites this ratio for females never exceeded that for males. Briefly the trend in the cohort mortality was increasing for cancers of the respiratory system, the respiratory system, the mouth and pharynx, pancreas and skin. The trend by cohort was decreasing for cancers of the digestive organs (except pancreas) and the genital organs.

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