A LIFE TABLE FOR DEATHS FROM TUBERCULOSIS IN 1947

Abstract

Symbols: x: Age
P_x: Population of age x
t_x: Number of deaths at age x due to tuberculosis
L_x: Number of survivals at age x, tuberculous deaths only being considered.
For the construction of an ordinary life table two principal data, viz. statistics of deaths and population classified by age are necessary. But if we at temp to construct a life table for a specified deaths, e. g. deaths due to tuberculosis, although death statistics classified by age is available, the corresponding population which might die eventually from tuberculosis is unknown. However, if we assume that the total number of deaths from tuberculosis (∑t_x) in a calendar year were born simultaneously (∑t_x=L₀) and that from this starting population (L₀) the tuberculous deaths occurred annually in succession (t₀, t₁, t₂, ………t_ω), then the number of survivals at succeeding age may be obtained by in general
Then the sum total of the survivors (∑L_x) may be regarded as the whole population which might eventually die from tuberculosis. But number of deaths by age due to tuberculosis in any calendar year is dependent on the age composition of the actual population, and the age composition is the product of changing numbers of births and deaths during about 100 years in the past. Hence, in attempting to construct a specified life table for a certain calendar year, the influence of the changing age composition must be eliminated. For that purpose the age composition bf actual population should be assumed to be equal to l_x of the life table for the corresponding calendar year.
In my case the age distribution of tuberculous deaths in 1947 was corrected by multiplying each of tz with the corresponding factor (C_x) respectively,
C_x being B_x /A_x
where B_x =proportion of each 12 (l_x +/l_x+1) in 100, 000.
A_x = proportion of each P_x in 100, 000.
Then C_x t_x =D_x is the standardized age distribution of tuberculous deaths, the standard population being l_x in the life table for 1947. As mentioned above, ∑D_x is to be regarded as a starting population born simultaneously, namely, ∑D_x =L₀.
L_x. t_x =L_x+1 is the population of age x+1, and ∑L_x is a whole population which might eventually die of tuberculosis.
The data adjusted on this assumption are shown in Table Iand II. Using these A 12 Abstracts of Papers Published in Japanese data an abridged life table was constructed by King's formulae.
The result is shown in Table III and Fig. I-III.
Mortality Rate, q_x. q₀ is very low, . 00361 for male and. 00420 for female. q₁ is about twice as high as q₀. Then male q_x-curve falls gradually, reaching the minimum at about x=12. Then it rises rapidly till x=22. Between x=22 and x=47 the curve rises very slowly, and above x=47, it ascends straightly.
The femal q_0-32 are higher than those of male. From the minimum between x=7 and 12, the curve rises first slowly and then rapidly. From q₂₂ to q₃₂ the curve runs alrn2st horizontally. After dropping a little at x=37, it rises straightly as the age advances.