A Relational Model of Mortality at Older Ages in Low Mortality Countries

This paper presents a relational model of age-specific death rates at ages 45-99. It is based upon death rates calculated for single years of age and five-year periods from 1950 to 1985 in 16 low-mortality countries. Eighty-two data sets are used in the construction of the model. These data passed a rigorous quality test which involved comparisons of intercensal changes in cohort size with intercensal deaths. Construction of the model is based upon a logit transformation of death rates, which performed slightly better than a logarithmic transformation in statistical tests. A 'standard' mortality pattern is produced as a summary of age-specific death rates in these 82 data sets. Expressed in logits, the standard is highly linear in age for males. For females, systematic curvature of the type first identified by Horiuchi and Coale is observed. The proportionate rate of change in women's age-specific death rates is highest in the age group 70-80. Once this pattern has been embodied in the standard, we are generally more successful in predicting death rates for females than for males in the 82 populations by means of a two-parameter linear transformation of the standard. Thus, the value of using the relational model relative to Gompertz or logistic representations of age patterns is much greater for females than for males. Over time in a particular country, the parameter which represents the level of mortality, α, has generally fallen for both sexes and faster for females. The value of the slope parameter, β, has also typically fallen, reflecting larger gains in logits of age-specific death rates at the very old than at younger old ages. This trend casts doubt on the validity of the 'rectangularizing survival curve' as a representation of old-age mortality trends. We conclude that there is little evidence of regional clustering in values of β, which suggests that regional model life tables are losing utility as a tool for the study of old-age mortality in low-mortality countries. We demonstrate how the relational model can be used graphically to identify national idiosyncracies in old-age mortality. In addition, we show that data that failed our earlier quality check typically begin to exhibit an irregular pattern of deviations from the standard around the ages at which the data deteriorate.