Estimation of Adult Survival Probabilities at Various Five-Year Ages beyond Age 5 from the Cumulative Life Table Survival Ratios - T(x+5)/T(x) in Life Table Terminology: A Methodological Investigation

Subrata Lahiri, International Institute for Population Sciences (IIPS)

This study focuses in identifying the appropriate set of age-specific survival probabilities (p-values) based on a given set of 5-year cumulative life table survival ratios (5-cum-LSRs), defined by the ratios of the form T(x+5)/T(x) in life table terminology. These p-values not only satisfy the usual properties of a life table p-values but also depict the true picture corresponding to those of the true life table. This paper proposes two approaches for estimating p-values at various ages for a given set of 5-cum-LSRs -- one makes use of a chain relationship between two successive p-values for a given set of 5-cum-LSRs, and the other one is based on an iterative procedure (with an analytical proof of covergence) under various approximations for L(x,x+5) values. Empirical investigations of the approaches based on model life tables shows that the estimated p-values so obtained beyond age 5 are almost identical to the true ones.