Variance in death and its implications for modeling and forecasting mortality

Abstract

The slope and curvature of the survivorship function reflect the considerable amount of variance in length of life found in any human population. Part is due to the well-known variation in life expectancy between groups: large differences according to race, sex, socioeconomic status, or other covariates. But within-group variance is large even in narrowly defined groups, and changes substantially and inversely with the group average length of life. We show that variance in length of life is inversely related to the Gompertz slope of log mortality through age, and we reveal its relationship to variance in a multiplicative frailty index. Our findings bear a variety of implications for modeling and forecasting mortality. In particular, we examine how the assumption of proportional hazards fails to account adequately for differences in subgroup variance, and we discuss how several common forecasting models treat the variance along the temporal dimension.

Why Lifespans Are More Variable Among Blacks Than Among Whites in the United States

“…Edwards (2011), Edwards and Tuljapurkar (2005), Engelman et al (2010), Nau and Firebaugh (2012), Tuljapurkar (2010), Tuljapurkar and Edwards (2011), and van Raalte and Caswell (2013) used age 10. Gillespie et al (2013) and Smits and Monden (2009) used age 15, but Wilmoth and Horiuchi (1999) used both age 15 and age 30.…”

“…Although we know from prior studies that lifespans are more variable for blacks than for whites (Edwards and Tuljapurkar 2005; Lynch et al 2003; Tuljapurkar and Edwards 2011), the sources of this difference remain unexplored. Studies of the black-white disparity in mortality have focused instead on life expectancy.…”

“… 1 Following Tuljapurkar and Edwards (2011), we use age 10 to separate adult mortality from infant and child mortality. We reach the same conclusions whether we use age 10 or age 20 as the cutoff point.…”

Life Expectancy in Developed Countries is Higher Than Conventionally Estimated. Implications from Improved Measurement of Human Longevity

“…Apart from its consequences for measuring longevity and assessing its prospects, the effect of an artificially accelerated worsening of mortality implied by the conventional period life table has consequences for the discussion of the rectangularisation of the survival curve (Fries 1980;Wilmoth and Horiuchi 1999;Kannisto 2000;CanudasRomo 2008;Thatcher et al 2010;Engelman et al 2010;Tuljapurkar and Edwards 2011). The above 'paradoxes' show that the usual way of studying that process based on period life tables may be misleading, because the period life table-by its very design-compresses the life experience of individuals when mortality tends to decline.…”

Does selection of mortality model make a difference in projecting population ageing?

“…Similarly, compared to the baseline standard, the Brass model tends not to change the death rates at the oldest ages (Ediev 2014). The Bongaarts model, on the other hand, assumes pure (age) shift of old-age mortality and does not account for the compression of period mortality (Cheung et al 2005;Cheung and Robine 2007;Ediev 2013aEdiev , 2013bFries 1980;Kannisto 2000;Tuljapurkar and Edwards 2011;Wilmoth and Horiuchi 1999), which results in possibly exaggerating mortality decline at the oldest-old ages.…”