Revisiting Construction of Period Life Tables

A classic problem in life table construction is the calculation of the probability of death in an age interval (x,x+n) from the observed age-specific death rate _n M_x. For period life tables one typically makes the assumption that _n M_x= _n m_x and proceeds to apply conversion formula _n q_x=(n* _n m_x)/(1+n*(1- _n a_x )* _n m_x ). However, the application of this formula derived from a cohort perspective to estimation for life tables calculated from period data can be problematic. Cohort measure are different from their period counterparts in that cohort measures are concerned with all events that occurred to the cohort members while period measures are only concerned with the events that occurred to individuals within a given period and age interval. Three issues might preclude the direct application of the formula above to period life table construction: the ambiguity in the definition of _n a_x; the definition of _n M_x; the conversion formula between _n m_x and _n q_x. In this paper, we give clear definition for _n a_x and _n M_x from period perspectives, and derive the conversion formula between _n m_x and _n q_x for the construction of period life tables. We use simulated data to illustrate the problems with traditional indicators and asses the performance of our revised definitions.