STUMP » Articles » Mortality with Meep: Death Distributions and Survival Probability » 9 January 2019, 09:39

Where Stu & MP spout off about everything.

Mortality with Meep: Death Distributions and Survival Probability  

by

9 January 2019, 09:39

I am not talking about table selection yet, but I do want to talk about survival probabilities, because of one of the dumbest mortality-related tweets I’ve seen [mainly because I do not collect or search out mortality tweets. Yet. I’m sure far dumber exist.]


Twitchy uses this tweet to call RBG-ism a cult, but that’s not my point. I understand wanting somebody to live longer — I would give up some days of my life to have Stu live longer — but I CAN’T DO THAT.

Nobody can do a damn thing about extending RBG’s life, other than her doctors, and even then there are limits.

So I’m going to talk about death distributions and survival probabilities, using a standard calendar year mortality table, and just assuming it stays constant through the mortality projection [this is not how the world works, but that’s for a later time.]

CONSTRUCTING THE SURVIVAL CURVE

People talk life expectancy all the time (and I will at another time), but let’s do something easier to understand: survival probability, S(x).

We’re going to start at age 0 [birth], and S(x) is the probability you’re still alive at age x. By definition, S(0) = 1 — you’re born at age 0, with probability 1.

Remember those q_x’s? [Reminder about the q_x’s) We can use the q_x’s to build up the survival curve, by noting that the probability of surviving is the same as the probability of not having died.

That may seem elementary to you, and i’s an elementary concept:

Probability that something happened = 1 – probability that that something did not happen

I use this basic probability rule all the time.

So if I want S(1) = 1 – probability died between age 0 and 1 = 1 – q_0

Likewise, S(n) = probability one survived to age (n-1) * probability didn’t die between age (n-1) and n = S(n-1) * (q_{n-1})

So I can build up a whole curve this way.

SURVIVAL CURVES FOR MALES AND FEMALES

Using the most recent calendar year Social Security mortality table (2015), here are the male and female survival curves.

FINDING SURVIVAL PROBABILITY FROM CURRENT AGE

So here’s the beauty — if I develop the whole S(x) curve (and yes, there are special interpolation choices one can make for fractional ages), I can determine the survival curve starting at any age.

I simply have to divide S(x) by S(current age).

So, say you’re a man currently 60 years old. You are obviously alive, so survival at age 60 = 1 now. In my original function S(60) = 86% (I’m removing decimals for simplicity).

If I want to know my probability of surviving to age 100, say, I calculate S(100)/S(60) = 1.1% (nope, chances aren’t good).

So let me show you survival curves starting at age 60:

Starting at age 80:

AGE AT DEATH PERCENTILES

Finally, we can look at percentiles, given current age. I’m using whole number ages for simplicity (and I may be off by one year, depending).

If you are just born, the 10th percentile for death is at age 55 for men and age 63 for women.

The median age at death is 81 for men and 85 for women.

The 90th percentile is 93 for men and 96 for women.

That’s at birth. Using these mortality rates, 80% of men would die between age 55 and 93, and 80% of women would die between age 63 and 96 (note the big disparities for “dying young”).

What if you’re currently 80 years old? Let’s ignore the extremes right now, and just look at the medians.

Median age at death for males currently age 80 would be 88, and for women, it’s 92.

Here are two graphs showing these percentiles for men:

And for women:

By the way, looking at these percentiles is far more useful for retirement planning purposes than looking at life expectancy. Note that, even from birth, the 90th percentiles for survival is in the 90s. If you’re planning for retirement, you need to consider the possibility of living to 100.

No, I don’t care that your parents died when they were 70 — there have been amazing increases in survivorship for a variety of reasons.

Spreadsheet with work here.

SOME NOT QUITE AS STUPID TWEETS

Let’s go back to what inspired me to do these calculations:


[I think that tweep is referring to Rahm Emanuel’s brother re: living past age 75]




And from the original idiot:


You used an idiotic subjunctive, dude. There are counterfactuals (such as “What if RBG had retired in 2014”) and there are not-in-any-universe questions.


I wouldn’t make fun of Rob. His subjunctive is a better one.


Seriously…. has any Supreme Court Justice become less liberal in the past 100 years? (I can’t find the piece right now, but I think the answer is either 1 or 2, depending on how you consider the question.)


Sure, if you were actually God.

Look, if you’re going to try to spur discussion, why not ask “What if we were living in the Matrix?” or some such stoner crap.

via GIPHY


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