*** Aging research invites some unique statistical modeling challenges: the natural course of development in the later years of life is generally marked by declines across the board. That’s why many constructs describing such processes contain in their very cores this ‘going down’ direction of changes. Specialized methods have grown out of this ‘data design’, in which all cases (patients, residents, older adults in general) show declines, and there is a sharp end it too[i]. Some specifics:

1. Notational basis and intro

*** In the notation shown in step 1 (^superscript represents ‘up there’, in ‘potential outcomes’ world, while _superscript is ‘down on earth, realized’), common RQs related to aging are comparisons of potential outcome of ‘frailty’

Frailty_i ^{10Years.Later} vs. Frailty_{i Now}

* which asks how much would time normally ‘lead to’ my level of frailty 10 years from now. Notice that this ‘time effect’ is different than the effect of some anti-aging multivitamins, to take an example:

Frailty_i ^{10Years.Later.IF.Multivitamins} vs. Frailty_i ^{10Years.Later. If.RegularBusiness}

* here both are potential/unknownable, because they both will happen in the future. This makes evident the two layers of causal questions (‘nested counter-factuals’), one asking about ‘the effect of time (aging per se)’ vs. the ‘derailing’ effect of some ‘aging prevention’ initiative.

 

[i] This ‘necessary end’ point is evident in the calculations of life expectancy (at birth, e.g.) from mortality tables: from the percentages of deaths within each age group, e.g. how many 60 year olds died this year, tables of such probabilities of death are derived, by age, but this probability does not ‘trail off’ continuously upwardly, even though (very few) older adults can live even beyond 100 years of age, but becomes a sharp 1.0 for the ‘last age group’: everyone in that group will die, with probability 1 or 100% (the calculator has to impose this ‘constraint’, see  [1]. I show an adapted view of a figure from [2], which shows how we need to ‘force’ everyone to die, even though we don’t observe that outcome for them in the ‘time window’ the data covers.

+++ This same view’ is seen when one builds up a ‘survival step graph’, or curve, by hand, which shows the percent still ‘living’  as a function of time (even though survival can be used for any process that has a clear end, like ‘treatment adherence, until dropping out of treatment) – this curve has to come down and in the case of biological death has to touch the bottom, i.e. the horizontal axis, where the percent remaining living is a sharp 0. This illustrates also the peculiarity of age as a variable, which is bounded on left at 0, and on the right at some ‘ceiling’ value: the continuous unending distribution of values assumed in many statistical tests is not applicable to age.