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

Abstract

The specific mortality rates for [male][male], [female][female] and total population for England and Wales, for Scotland and for Sweden, have been fitted to a formula j(t, [theta]) =[alpha](t [long dash] [theta])[beta][theta], where f(t, [theta]) is the specific mortality rate at a time t for age [theta], [beta][theta] is a function depending solely on the age [theta], and [alpha](t [long dash] [theta]) depends only on the time of birth (t [long dash] [theta]). The results are in substantial agreement with those previously obtained by less refined methods. The probable errors of the values found for [alpha] and for [beta] have been calculated. It is shown that the [beta][theta] curves for the Scottish and the English [male][male] are ca. represented by the Makeham-Gompertz formula A + Be c[theta], where A, B and c have suitable values. The other [beta][theta] curves do not appear to conform exactly to a formula of this type. With the help of the representation of [beta][theta] by the Makeham-Gompertz expression the effect of variation of [alpha] on the survival curves, the death curves, and the expectation of life has been detd. With the range of values of [alpha] experienced in Britain during the last 50 yrs., 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 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 English and Scottish [female][female], or for the Swedish statistics, these approximate sufficiently closely to the values for the English and Scottish [male][male], to allow of the conclusion deduced in the latter case being extended to the former. It is strongly emphasized 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.