Causality challenges in aging research

*** 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, like ‘sarcopenia’ (i.e. ‘loss of sarcomeres’, and hence of muscle mass/strength). 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 topics:

1. Some notational basics specific to causality in the context of ‘changes’:

*** 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’ (in an old person i )

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 (what time is, is not a simple question btw[ii]). Notice that this ‘time effect’ is different than the effect of some anti-aging multivitamins, to take an example:

Frailtyi 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.

2. How (much) time and causality overlap[iii] ; the graphical window into causality appears to include time in the very definition of the directional edges in the graph[iv]; time ‘precedence’ is often listed as a condition of causality[v] (it may be the distinguishing attribute between ‘cause’ and ‘effect’ when the cause is a necessary and sufficient condition of the effect[vi]).

2.i. The definitions of ‘time’ and ‘causality’ overlap dangerously; and time itself is a difficult construct to spell out[vii], so much so that some scientists argue it may not exist at all (Russell Barbour, e.g.[viii]).

2.ii. An added challenge is “differentiating between true within-individual change and measurement error” (see Lauren Gaydosh’s blog)

*** The conundrum is ‘simple’: if we measure A1c now, say 5.6, and tomorrow, say 5.9, is the 0.3 difference the ‘true change’? A 2% measurement uncertainty makes this difference anywhere between a minimum of [(5.9+2%) -(5.6-2%)] = 0.07 &  and a maximum of [(5.9=-2%) (5.6+2%)] =  0.53, which is 7+ times larger. [ix]

2.iii. On an other hand, reliability and repeated measurement overlap conceptually too[x].

Some further topics to consider:

+1. Continuous time vs. discrete observation timepoints

+2. Causal implications of time precision and the discrete vs. continuous time modeling

+3. Differential missingness implications for causal conclusions

– Recover causal effects from ‘apparent’ effects, paradoxical at times, e.g. apparent ‘benefit’ of Hispanic residents in the US in Covid mortality: age of the living mediates in fact the effect of ethnicity on Covid mortality: the ‘true effect’ is not the ethnicity effect controlled for age (‘age adjusted Covid mortality’), but the ‘total’ effect, both through ‘age’ and directly.

5. How to disentangle ‘normal aging’ changes from ‘accelerated/beyond-normal’ aging, hence distinguishing aging disparities

*** The last part, # 6, will briefly go over some remaining challenges and opportunities for both advancing this field, and for better explaining it, like the ‘equivalence of potential outcomes (‘Rubin’, more properly Cochran’s… see note viii below and image insert) and causal calculus (Pearl) approaches to causality’.

FOOTnotes

[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.

[ii] Some famous phrasing put time in the center of metal controversies, e.g.: 1. “Time is what prevents everything from happening at once”; “time flows at a speed of 1 second per second”. A more interesting inquiry looks into how come time is one-dimensional, but space is more than 1 dimensional; Van Fraassen touches upon this “the temporal relations give rise to a temporal order and the spatial relations to a spatial order. Of the two orders, the latter is by far more complex. Let us assume for a moment that between is indeed a basic relation for both time and space. Then we find nevertheless that the order to which temporal betweenness gives rise is much simpler than the order determined by the spatial betweenness relation. To mention the most obvious case: if X, Y, and Z are in time, but not simultaneous, then one of the three is between the other two; it is not true, however, that if X, Y, and Z are in space, though not in the same place, then one of them is between the other two. The reader may recognize this point in the form of the statement “Space is three-­dimensional, but time is only one-­‐dimensional.”, [3] p. 11 & “In the Theodicy, Leibniz says that in geometry we can prove that there are only three straight lines perpendicular to one another that can intersect at one and the same point and that this shows that space has necessarily exactly three dimensions”, p. 149, but more detailed ‘how come’ can be extracted from AIs, e.g. Claude.ai: “The key is that with four points in 3D space, you have exactly the right number of constraints. Each point has 3 coordinates, giving 12 parameters total. But you can eliminate rigid motions (3 translations + 3 rotations), leaving 6 degrees of freedom. The 6 distances between 4 points provide exactly these 6 constraints.”, but more detailed insights (‘break down…’) can then be asked for.

[iii] “It is yet unclear how the perception of simultaneity and successiveness relates to the present moment and event causality. Desantis and Buehner discuss the relation between time perception and causality.  Traditionally, it has been considered that causality is partly inferred from temporal relations between events with people being more likely to report two events as causally linked if they follow each other closely in time rather than if they are separated by a long delay. Desantis and Buehner review and discuss a complementary literature proposing that time perception is in turn guided by people’s assumptions about the causal  connection between events. This implies that time perception is shaped by the combination of sensory and internal information such as our prior causal expectations.

Finally, a discussion is devoted to how Bayesian models of uncertainty reduction may offer an exploratory hypothesis to understand how causality structures time perception.” [4] p. xxvii

*** Note that some constructs contain in themselves change/dynamic conceptual attributes, beginning with the very ‘aging’ one (which requires >1 age!, and can go 1 step higher too: ‘accelerated aging’), but going then to: longevity, dysregulation, resilience, sarcopenia, increased risk, accumulation of cellular damage, impaired function, loss of physiological integrity, and more. Also of note that language tends to trick us, like using ‘preventing aging’.

[iv] “The most familiar connection between causality and conditional independence is reflected in the scientific notion of a state, which was devised to nullify the influence that the past exerts on the future by providing a  sufficiently detailed description of the present. In probabilistic terms this came to be known as a Markov property: Future events are conditionally independent of past events, given the current state of affairs. This is precisely the role played by the set of parents ПX in the construction of Bayesian networks (Section 3.3); they screen each variable X from the influence of all other predecessors of X.” [5] P. 385 ‘8. Learning Structure from Data\ 8.1. Causality, Modularity, and Tree Structures’;

“Our probabilistic treatment of causation is influenced by that of Simon [[6]1954, [7]1980], and it stresses non-temporal causal ordering. Suppes [[8]1970] provides a probabilistic account of causation which is based on temporal ordering. A logic-based account of causation and temporal reasoning is  given in Shoham [[9]1988]. A contrast between two conceptions of causal ordering, in the context of representing device behavior in AI systems, is described by Iwasaki and Simon ([10]1986) and de Kleer and Brown ([11]1986 [see [12]] too).” P. 408

[v] “If, then, it be contended, in accordance with Mill’s first position, that by a cause we mean a necessary and sufficient condition (more particularly, a necessary and sufficient precedent condition), it will appear that a hypothesis of causality really involves two universal propositions, and, it may be said, requires a double verification.

This is what is implied in Mill’s account of the simplest use of the direct Method of Difference, where we first observe the absence of the factor in question as well as of the phenomenon it is :supposed to cause, this verifying the supposition that the factor is necessary, and then observe the phenomenon ensuing upon the introduction of the factor, this verifying the supposition that it is sufficient.” [13] p. 132 [Mill (System of Logic, Bk. III, ch. X, § 3)]& “In logical form, if A is something specific ( and, if it is not, no assertion is being made), the assertion “All B are A” is equivalent to the assertion “All non-A are non-B”, each being the contrapositive of the other. What is brought out by the consideration that there may not be “negative instances” is that we are concerned not with relations between A and B in general but with their relations within certain limits or in a certain “field”; and it is the consideration of the “field” that enables us to make the theory of causality precise and to clear up the difficulties in which Mill and others are involved.” p. 133 “We can now see what is meant by speaking of a necessary and sufficient condition of a certain type of occurrence within a certain field; and, assuming it to be a precedent condition, then it is what we call a “cause”. In other words, if there is any force in the line of argument so far pursued, a cause is always a cause within a field.” [13] p. 134

[vi] “when a cause is taken as a necessary and sufficient precedent condition of the occurrence of a

phenomenon (its “effect”) in a certain field, then it follows that the effect is a necessary and sufficient subsequent condition of the occurrence ( or operation) of the cause in the field. So that, granting the temporal priority of the cause, there is no question of any logical priority; and while, if our causal beliefs are true, we can with certainty, given the cause, infer that the effect will occur, we can with equal force infer, given

the effect, that the cause has occurred.” [13] (p.135-6)

[vii] On some of time’s properties, see Shoham [14], e.g.: “Presumably, we will always want to assume that time is acyclic ( that is, that it is a partial order), although some would dispute even this assumption (for treatment of cyclic time see, e.g., [79,98]).” & “In most of the literature in theoretical computer science one finds discrete time(the only exception of which I am aware is [5]).” p. 35

[viii] “There are two parts to my claim that time does not exist. I start from the philosophical conviction that the only true things are complete possible configurations of the universe, unchanging Nows. Unchanging things do not travel in time from Now to Now. Material things, we included, are simply parts of Nows.”  [15] p. 49; “the important thing is to get away from the idea that time is something. Time does not exist. All that exists are things that change. What we call time is- in classical physics at least- simply a complex of rules that govern the change.” p. 137;

[ix] Taylor says: “To estimate the uncertainty in the sum or difference, we had only to decide on their highest and lowest probable values. The highest and lowest probable values of x are x best ± δx, and those of y

are y best ± δy.” [16] p. 45 For products and ratios however, a different rule emerges: “when quantities are multiplied or divided, the fractional uncertainties add” p.  53, where of a quantity x the fractional uncertainty is δx / |x best|, where the absolute value is used to yield a positive value.

[x] “Reactivity is when the process of measurement induces change in the phenomenon. Such occurrences are most likely with attitude and value measures.” [17] p. 211

[xi] A good intuition for the ‘cohort effect’ is the phenomenon of ‘same age groups experiencing that age differently (or not); Garrison Keillor gives some clues: “What is it like to be twenty-one or even thirty? And death — what’s that like? What would you do if communists made you choose between renouncing God and drinking a pitcher of warm spit? What would it be like to put your arms around a girl? I’d seen it done by older kids but never tried it myself. What would it feel like? Would we talk? Would I kiss her or should I wait for her to kiss me?” A June morning, assessing the situation In this vein, it is somewhat striking how little ‘life experience’ accumulates over evolutionary-range time intervals: same teenagers struggle with the same ‘demons’, despite hundreds of similar generations before them going through the same experiences: very little ‘species-level knowledge’ gets passed down (i.e. not much cohort effect’ in this manner!).

References

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