# Elite athletes live longer and age slower – and we have a calculation for it

We know that exercise is good for us, but how does it really benefit our longevity and aging? Are our weekly gym sessions contributing to our longevity and the rate of aging? Our recent paper published in BMJ Open in collaboration with Polish researchers examined the rate of aging and mortality of Olympic athletes.

The study shows that individuals such as athletes whom had participated in regular and/or intense exercise, and had committed sports as their life-time career enjoy a lower mortality risk than their general population. But does this illustrate a slower rate of aging? If so, how slow are these athletes aging?

In short, we found that for every three-fold reduction in mortality risk, the rate of aging among Olympic athletes decelerates by one percent.

How is the rate of aging attained?

As mentioned before by many demographers and gerontologists, when an individual reaches the maximum manifestation of senescence, the individual dies from the population. Aging can hence be illustrated by examining the age-specific mortality trajectory, i.e the mortality rate across ages. If a person dies at age 60, it contributes to the overall mortality trajectory of the population. The rate of aging can hence be deduced from d(log(mu(x)))/dx, given that x is age at death and mu(x) is the mortality rate.

And a bit of basic mathematics with an illustration using the Gompertz mortality function in the human population:

mu(x)= a*exp(bx)

Take the logarithmic of the exponential increase mortality function, a linear equation is observed;

log(mu(x))= log a + bx

For its tangent or rate of change,

d(log(mu(x)))/dx=b

In almost all datasets, particularly human datasets, the Gompertz function is fitted for the hazard shape. There are cases where Gompertz does not fit the human population, and it is only under extreme and very rare disease cases.

For Maximum likelihood estimation, it estimates likelihood of death of an individual at a given age; the deduction is obtained as follows, where sigma represents the parameters of the mortality function:

logL(sigma, delta, x, y) = sum(log((mu(x)^delta) * s(x) *s(y)))

If the individual is dead, delta=1; otherwise delta=0.

By introducing delta, the algorithm permits the entry of survived individuals in the study, i.e delta =0, their contribution to the likelihood will be to their age at last follow-up whereby mu(x) will then equate to 1. (N.B any number that is raised to the power of 0 equates to 1).

Regardless of dead or alive individuals by end study, athletes entering the observational study will enter at their respective recruitment age. S(y) is the survival function of an individual at time of recruitment to the study. As athletes are recruited at different ages, it is an error to not consider left truncation in the algorithm, which is represented as y in the algorithm.

With the basis of the algorithm, data conditioning was then set to adjust for calendar medical improvements. Because… an individual born in 1950 has a different survival probability and hence a different mortality risk to an individual born in 1990. It would also be an error to toss all individuals into the algorithm without considering the potential bias as introduced from improvements made in medicine.

Poland experienced several times extreme isolation, and the country’s identity disappeared on the map not once, but twice. The stringent forces from political transitions and sociodemographic changes that had occurred over the last hundred years played a significant role in Poland’s mortality trends and its age-specific mortality trajectories. The article shows the most appropriate approach to produce reliable risk estimates from valuable data such as contemporary data recorded in the 1500s.

Contemporary data containing variable and survival follow-up came to existence during the early 1950s (e.g here and here). Due to the changes in health interventions and policies, individuals live longer, develop and die from cancer, and are less likely to die from infectious disease. Studies that were recorded prior to that era can now be brought to good use, and medical frontiers can now review the determinants that may alter both the rate of aging and the risk for mortality.

This short illustration originates from Yuhui Lin, lead author of the article  published in BMJ Open. Yuhui Lin currently works as a media intelligence. Her main research interest is in individuals of the population who are living under extreme risks or with extreme behavioral habits. This includes rare genetic disorders. For any feedback or communication, contact: yuhui.linney @ gmail.com.

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