mercoledì 26 dicembre 2018

Health-adjusted life expectancy calculator

Per la versione in Italiano clicca per il calcolatore online.

As one ages, the chance of dying increases, but it is not constant for everyone. This online calculator gives a probability of reaching a given age taking into account current age and fitness level.

Background

Paradoxically, an elderly has a larger life expectancy than a newborn. This is because if one reaches a given age, the probability of dying before that age is zero as it has already happened.
Additionally, the fitter one is the better one fends off disease, thus lives longer. After all, an infection results in an elevated heart-rate that equivalent to exerting oneself doing exercise.

To do the calculations you need to know your age and MET.
Your age can be determined by looking at section 3 of your driving licence.
Your maximal MET (metabolic equivalent of task) can be found on certain medical check-up reports. It can be found by doing one of various exercise tests, such as Margaria–Kalamen test. Alternatively, if you doing some excercise to find out —doesn't bode well—you can guestimate it: if can walk slowly it is more than 2, if you can walk briskly 4, if you can run 7, if you can run a half-marathon or a full marathon 12 or above, if you can an ultra-marathon 18.

The probabilities are based on an advanced distribution discussed below that better fits centagenerians. It does not account for death by external causes ("violent deaths"). These have a probability that is so low that it would not show due to rounding (cf. data from ISTAT gives an annual 0.7% chance of a fatal traffic accident, 0.6% fatal fall, 0.08% poisoning, 0.08% homicide and so forth).

Calculator

Age, n0
MET

Distribution parameters

Leave these as they are, unless you know what you want to change. These two parameters depend on the population (genetics, climate, healthcare system), currently set to Italy.

δ (aging rate)
Nk_0(pivot age)

75% change to get to NaN.

50% change to get to NaN.

25% change to get to NaN.

Equations

The equation is: $$\large{F(N)=1 - e^{\displaystyle -k \cdot \int_{n_0}^{N} \Big(1 - e^{-e^{\frac{n-N_k}{\delta}}}\Big) dn}}$$ The N_k is obtained thusly: $$\large{N_k = N_{K_0} + 8 [1 - e^{(- \frac{met - 6}{3})}]}$$