Principal Components in Regression Analysis

Abstract

A new technique for deriving exogenous components of mortality risks from national vital statistics has been developed. Each observed death rate D(v) (where i corresponds to calendar time (year or interval of years) and j denotes the number of corresponding age group) was represented as D(v) = A(j) + B(i)C(j), and unknown quantities A(j), B(i), and C(j) were estimated by a special procedure using the least-squares principle. The coefficients of variation do not exceed 10%. It is shown that the term A(j) can be interpreted as the endogenous and the second term B(i)C(j) as the exogenous components of the death rate. The aggregate of endogenous components A(j) can be described by a regression function, corresponding to the Gompertz-Makeham law, A(τ) = γ + β · ε(ατ), where γ, β, and α are constants, τ is age, A(τ)|(τ≡τj) ≡ A(τ(j)) ≡ A(j), and τ(j) is the value of age τ in jth age group. The coefficients of variation for such a representation does not exceed 4%. An analysis of exogenous risk levels in the Moscow and Russian populations during 1980-1995 shows that since 1992 all components of exogenous risk in the Moscow population had been increasing up to 1994. The greatest contribution to the total level of exogenous risk was lethal diseases, and their death rate was 387 deaths per 100,000 persons in 1994, i.e., 61.9% of all deaths. The dynamics of exogenous mortality risk change during 1990-1994 in the Moscow population and in the Russian population without Moscow had been identical: the risk had been increasing, and its value in the Russian population had been higher than that in the Moscow population.