Smoothing of probabilities of death for older people in life expectancy table

Gustaf Strandell, Statistics Sweden
Tomas Johansson, Statistics Sweden

In 2012, Statistics Sweden conducted a review of the calculations for the Swedish life tables. The project had two main objectives: 1. A quality assured production system, and 2. Review of the handling of mortality risks for very old persons at the national and regional levels. This paper focuses on the changes that were made in the handling of mortality risks for persons in the highest ages, where the population is small and mortality risks are high. It also shows how the changed method has affected the estimated average life expectancies at the national and regional levels. Over the years, Statistics Sweden has used various methods to handle the weak relationship between mortality risks and age at the highest ages. Up to 1986, Wittstein's equalisation was used. which overestimated the mortality risks for the oldest persons. Therefore, Statistics Sweden created a method which basically used a "universal" smoothed curve that adjusted the level at the age of 91; thereafter an smoothing took place. Over time, did that method result in a systematic underestimation of mortality risks and thus an overestimation of the life expectancy for newborns, e0. The revised smoothing method involves a procedure in SAS that adjusts the smoothing function to the observed mortality risks. The procedure uses a least-squares method to adjust the specified function to the specified data material. By also taking into account the number of deaths by sex and age, the procedure assigns varying significance for the different age groups for the adjustment. Mortality risks for the oldest persons were previously based on the national mortality risk regardless of the regional level. The disadvantage of this approach was that regional differences for people in the highest ages were thus ignored. Nowadays the regional life tables are based on observations at the regional level.