The estimation of the share of deaths caused by a congenital defect
The assumptions:
1) empirical mortality from dominant causes decreases with the first power of age
It is valid already from the first day of life up the age of 10 years in the category "All diseases").
2) mortality in a hypothetical homogenous population without congenital defects is equal to R(1)/(365x10) in all ages,
where R(1)/(365x10) is the value of real mortality at the age of 10 and R(1) is the mortality rate during the first day.
3) fragile subpopulation with congenital individual risks of death could died off during the first 10 years
consequently, it is valid up the age of 10 years
R(t)=[-dS(t)/dt]/S(t)=-dS(t)/dt (S(t) > 0.98 for age less then 10 years),
where S(t) is a survival curve. Consequently, the number of death in time t per time unit is
d(t) = Lo[-dS(t)/dt] = LoR(t)
where Lo is the sum of individuals born within a particular period.
The total number of deaths D(0-10) within the age interval 1day-10 years is
D(0-10) = Lo.R(1).ln(365x10)
where the product R(1)ln(365x10) is the definite integral from the function R(1day) / t
within the age interval 1day-10 years. The number of deaths Dh(0-10) in the hypothetical homogenous population
without congenital defects within the age interval 1day-10 years is
Dh(0-10) = Lo.3650.R(1)/3650 = Lo.R(1)
Consequently, the share in the total number of deaths is
Dh(0-10)/D(0-10) = 1/[1+ln(3650)] = 0.10
Thus minimally 90% of deaths are from the fragile subpopulation within the age interval 1sd day-10 years.
These estimation of the size of fragile subpopulation is conservative
because the rest population at the age of 10 could be also heterogeneous....
Česky