Česky

JOSEF DOLEJŠ

Email: djosef@post.cz

List of publications

Introduction

Decrease of total radioactivity along with time

Decrease of postnatal mortality along with age

Individual development versus population heterogeneity

Model of congenital individual risks

Other examples

Mortality spectrum in 5 countries and all graphs

Mortality levels in 5 countries and all charts

Estimation of congenital defects

Points of time axis

Mortality rate in hours after birth

General trends of postnatal mortality in Europe







TOPlist
MODEL OF CONGENITAL INDIVIDUAL RISKS


   It explains the decline of mortality within a population as the result of the more affected individuals dying off ( Dolejs, 2001 or Dolejs, 2003).
The model starts from two presuppositions:
   1) Every impaired individual possesses an individual risk of mortality, defined by the degree of impairment. A congenital defect may be so slight that the baby survives until high age, or so severe that it dies during the first hours. Some congenital defects remain undiscovered for the whole lifetime. Congenital individual risk of death can assume varied values, being different by several orders. The individual risk of death associated with congenital defect is almost zero in case of a major part of population. Non-zero value of risk is observed in case of more affected individuals and the most impaired ones with an extreme congenital individual risk die during first hours of life.
   2) The changes of congenital individual risk value along with age are small when compared to the total range of congenital individual risks within the population. The model presumes that the congenital individual risk of death is age independent and depends on the severity of the congenital defect.
   According to the model, the type of the mortality decline along with age is determined by the type of statistical distribution of congenital individual risks within the population at the moment of birth. The mortality rate R(t) of congenital defect in year t as calculated against the entire population is the number of deaths D(t) in year t over the number of living people L(t) at the beginning of this year. In the model, it applies to the dependence of the mortality R(t) upon the age, that:



   , where x could be interpreted as the number of deaths per one living per one year inside subpopulation with similar impairment, f(x) is a frequency function of individual risks x (for t = 0), Xmax is a maximum individual risk of a particular population reflecting the condition of the most impaired individuals in the whole population and S(t) is a survival curve (percentage of all living individuals at the age t). The actual size of the entire population does not suffer any substantial change up the age of 10 years and the survival curve of the entire population S(t) is 1 (S(t) is more than 0.98).
    It applies for the lognormal distribution of individual risks f(x), which can be substituted by the formula f(x) = const/x for large x, that:



   , where a parameter R(1) corresponds to the mortality rate at the age t = 1 year (Dolejs, 2001 or Dolejs, 2003). As the most affected individuals die within the first hours of life, the maximum individual mortality risk Xmax can be higher than 10 at the moment of birth (if one year is used as the time unit of mortality rate). The exponential element of Eq. (2) can be ignored for t>1 after the end of the first year (the value of the product t.Xmax is high for t>1). Consequently, since the end of the first year the mortality decreases with the first power of age:



   The decline corresponds to a linear function with a slope equal to -1 within the log-log scale. It applies for the even distribution or normal distribution with a large variance of congenital individual risks f(x) that:







    For t > 1 the second element in brackets can also be ignored and the mortality declines with the second power of age: