International trends in the rate of logistic mortality increase

Abstract

BACKGROUND: Thatcher et al. (2010) used the simple logistic model with two parameters, which is known to fit data on old-age mortality well (Thatcher 1999), to investigate the old-age mortality compression and estimated the rate of logistic mortality increase, denoted by b, for ages 70-90. They concluded that if logit m(x) tends to fall faster at younger ages, then the slope b of the logit line will become steeper and mortality compression will occur. In this paper, we aim to estimate the rate of logistic mortality increase, denoted by b, for ages 70-90 in 23 countries with good and acceptable quality of data from Human Mortality Database and examine whether there is a universal trend in b. METHODS: We adopt a special case of the logistic model of mortality, which has only two parameters as does the Lexis model, and it is usually written in the form of model (1) μ(x) = a ebx / (1 + a ebx) (1) RESULTS: Our results show that the rate of logistic increase has steadily risen for females and males from about 0.10 in the 1950s to about 0.13 in recent years for most established market-economy countries in Europe as shown in group A (19 European countries). Among males, the value of parameter b is about 0.02 smaller than that for females and the rate of logistic mortality increase always lags behind females about 20 years. However, for Japanese females, although the increase was similar to the common pattern from 0.10 in 1947 to 0.13 in 1984, then the value of parameter b reached the highest 0.14 and became levelling off in the decade 1984-1995. Afterwards, it reverted to the level of 1984. In Canada, b increased at a relatively slower pace from 0.10 in 1950 to 0.12 in 2006 among females, whereas in the US the value of b tended to stay at 0.10-0.11 throughout the whole period 1921-2006. In Australia, b for females fluctuated around 0.10-0.11 before 1980, then a noticeable increase was observed from 0.12 in 1980 to 0.14 in 2007. CONCLUSIONS: The results show that the rate of logistic increase has steadily risen for females and males from about 0.10 in the 1950s to about 0.13 in recent years for most established market-economy countries. Deviant patterns such as slow increase, plateau and decrease are observed for some periods in Australia, Canada, Denmark, Japan and the USA. Possible reasons for those dominant and deviant trends are discussed.