Death-Rates in Great Britain and Sweden: Expression of Specific Mortality Rates as Products of Two Factors, and some Consequences thereof

Abstract

1. The specific mortality rates for males, females and the total population for England and Wales, for Scotland and for Sweden, have been fitted to a formula ƒ (t, θ) = α. (t—θ) βθ where ƒ (t, θ) is the specific mortality rate at a time t for age θ, β0 is a function depending solely on the age θ, and α (t —θ)depends only on the time of birth (t — θ). The results are in substantial agreement with those obtained by less refined methods in the previous paper. The probable errors of the values found for à and for β have been calculated. 2. It is shown that the β0 curves for the Scottish and the English males are approximately represented by the Makeham-Gompertz formula A+Becθ, where A, B and c have suitable values. The other β0 curves do not appear to conform exactly to a formula of this type. 3. With the help of the representation of β0 by the Makeham-Gompertz expression the effect of variation of α on the survival curves, the death curves, and the expectation of life has been determined. It is shown that with the range of values of α experienced in Britain during the last 50 years, the most marked effect is most likely to be experienced in the future between the ages of 65 and 85, a very considerable increase of people of these ages being likely provided that the relationship exhibited by the statistics up to the present date is maintained in the future. Though the Makeham-Gompertz formula does not hold in the case of the English and Scottish females, nor for the Swedish statistics, these approximate sufficiently closely to the values for the English and Scottish males, to allow of the conclusion deduced in the latter case being extended to the former. 4. It is strongly emphasised that the validity of all the predictions depends upon a hypothesis of extrapolation which, however attractive in the light of the figures so far available, might not be fulfilled under certain contingencies.

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