Extended longevity. Observation and methods

This paper examines and demonstrates importance of the adult modal age at death (M) in longevity research. Unlike the life expectancy at birth (e0) and median age at death, M is determined solely by old-age mortality as far as mortality follows a bathtub curve. It represents the location of “old-age death heap” in the age distribution of deaths, and captures mortality shifts more accurately than conditional life expectancies such as e65. Although M may not be directly determined from erratic mortality data, a recently developed method for deriving M from the P-spline-smoothed mortality curve based on penalized Poisson likelihood is highly effective in estimating M. Patterns of trends and differentials in M can be noticeably different from those in other lifespan measures, as indicated in some examples. In addition, major mathematical models of adult mortality such as the Gompertz, logistic and Weibull models can be reformulated using M, which plays critical roles as the mortality level parameter in those models.

Data from a longitudinal follow up of 14,000 elderly Costa Ricans 1990-2011 show that the death rate ratio (DRR) among males of the Nicoya region is 0.72 (95% CI: 0.62 – 0.82) compared to the rest of Costa Rican males. The DRR for Nicoyan women is not significantly different from one. Accordingly, life expectancy at age 55 for Nicoyan men would be 31.1 years compared to the 26.0 years in Japan, the country with the highest life expectancy. We further explore genetic versus environmental determinants by examining differential effects by migration status: DRR of men born and living in Nicoya (relative to other Costa Ricans) is 0.56 (CI: 0.45 – 0.69), compared to the DRR of 0.87 of immigrants and of 1.10 of out-migrants. The Nicoyan advantage is concentrated in cardio-vascular mortality, with a DRR of 0.50 for non-migrant Nicoya men. Nicoyans do not show significant advantages in most traditional risk factors such as blood pressure or lipids, but do show advantages in three potential markers of stress: overnight urinary cortisol, serum Dehydroepiandrosterone sulfate (DHEAS), and Leukocyte Telomere Length. They also have significantly lower body weight, waist circumference, fasting glucose and disability (physical and cognitive) levels.

At adult ages x, the force of mortality increases more or less exponentially with age, and the parameter associated with age, Beta, can be used to gauge the rate of senescence (ageing) of a generation. The hypothesis has recently been advanced that, with rare exceptions, the rate of senescence at the individual level is constant through space and time, and not far from 0.1.
We contribute to this discussion in two ways: first, we propose a new and simpler method to estimate the rate of senescence Beta when frailty and period effects operate, and, secondly, we offer a few empirical estimates for Beta, for various cohorts, in different countries (all data taken from the Human Mortality Database). The transformation that we suggest leads to a linear estimation, which is considerably simpler than all the others we are aware of, characterized by non-linear equations, numerical recursive likelihood maximization, etc.
Our estimates of the rate of senescence Beta are all very close to 0.1, but most of the differences that we detect (e.g. by country) are statistically significant, and there appears to be a decreasing trend of Beta over time.