Beyond age as a con ounde
Ch onological age, biological age, and causali y
Lau en Gau ie ∗
Sep embe 2025
Abs ac
In da a analysis, age is usually conside ed a po en ial con ounde and
he e lex is o con ol o i , o example as a co a ia e in a eg ession
model o as a s a i ying ac o .
Heal h esea ch ocusing on longe i y in es iga es how a heal hy s a e
can be main ained o ex ended as we age. I makes a dis inc ion be-
ween ch onological age, measu ing o a ions o he Ea h a ound i sel
and a ound he Sun, and biological age, a loosely de ined concep wi h
di e en mani es a ions – he abili y o di ide and epai issues, he p o-
duc ion o p o eins suppo ing issue s uc u e, he abili y o elimina e
oxins, mi ochond ial heal h, o mu a ion load.
A ene o heal hy aging esea ch is ha biological age can be in-
luenced unlike ch onological age. Fo da a analysis, s a is ics, o causal
in e p e a ion o machine lea ning models, his means ha he de aul ec-
ommenda ion o con ol o age as a po en ial con ounde may no longe
apply when biological age is in ol ed. Biological age can also be a medi-
a o , o a collide . When he la e , he a iable mus no be con olled
in he analysis.
In oduc ion
This a icle ocuses on causal app oaches o da a analysis when a a iable ep-
esen ing a “biological age” is conside ed. While machine lea ning is good a
inding associa ions in he da a mos o en by using he mos da a a ailable,
he unde lying in en o many da a and s a is ical analysis e o s is o assess
o model he causal e ec o an exposu e on an ou come. In ha scena io,
he challenge lies in how addi ional a iables besides exposu e and ou come a e
handled in an analysis, as hei ea men may g ea ly a ec he quali y o ha
es ima e. In some cases, mishandling hese a iables can c ea e “da a mi ages”
and lead o misleading conclusions. Fo example, sign e e sal obse ed in Simp-
son’s pa adox may o igina e om media o s and collide s, wo causal s uc u es
desc ibed below, inco ec ly included in a model. The inco po a ion o subjec
ma e expe ise ea ly in he p ocess, and he help o causal easoning, can help
a oid pi alls.
∗A icle published on Subs ack a h ps://onlyques ions.subs ack.com/p/beyond-age-as-a-
con ounde
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When looking a pa ien da a, “age” can be one such addi ional a iable
and i migh be among he mos equen ly adjus ed a iables in obse a ional
s udies. Fo example, he a icle “Why and how o con ol o age in occupa-
ional epidemiology”[1], explains ha age is iewed as a po en ial con ounde
in mos s udies, and should he e o e be con olled. Fo example, by including
i as a co a ia e in a eg ession model, o s a i ying he analysis (i.e., spli ing
he da a in o age g oups).
Howe e , age can ep esen wo phenomena:
• Ch onological age is a measu e o plane a y-scale obse a ions, such as he
numbe o he Ea h’s o a ions a ound he sun o on i s own axis.
• Biological age, ha is a measu e o biological senescence. This is a loosely
de ined concep and he e a e likely di e en measu es o i . Fo exam-
ple, he abili y o di ide and epai issues, he p oduc ion o p o eins
suppo ing issue s uc u e, he abili y o elimina e oxins, mi ochond ial
heal h, o mu a ion load.
Ch onological age is conside ed o be immune o any ex e nal in luence,
which makes he de aul o con ol o i a sensible one. On he o he hand,
biological age does no ha e ha p ope y — Resea ch on longe i y and aging
ac ually ies o ind ways o in luence he biological age. Howe e , he ch ono-
logical age obse ed can be causally connec ed o exposu e and ou come s udied,
c ea ing a selec ion bias called a collide s bias. The causal decomposi ion in o
a Di ec ed Acyclic G aph (DAG) will indica e whe e cau ion should be exe -
cised and how ch onological and biological age should be used in an analysis.
The s eng h o he ela ionship be ween ch onological and biological age can
be especially impo an when conside ing an analy ical app oach.
Exposu e, ou come, and age
Ques ion: exposu e → ou come?
A equen ques ion o in e es is: does an exposu e, e.g., a speci ic ea men ,
die , o en i onmen ac o s, causes, o a he con ibu es o, an ou come o
in e es ? I ha is he case, wha a e he di ec ion and s eng h o ha e ec .
In heal h s udies, his can be “does ea men X help cu e disease Y”, o “does
li es yle X inc ease he isk o de eloping heal h issue Y”.
Causal g aphs a e Di ec ed Acyclic G aphs (DAGs), whe e he a ow means
“causes”, “con ibu es o”, o “in luences”. Wha we a e looking o is o de ine
quan i a i ely he a ow be ween exposu e and ou come in Figu e 1.
Figu e 1: Minimimal DAG wi h Exposu e and Ou come.
A pa h o answe he ques ion wi h da a equi es in o ma ion abou each
indi iduals’ exposu e and ou come. How o ob ain ha da a, ei he selec ing i
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om a la ge da ase o unning a s udy o acqui e i , is ou -o -scope o his
pos bu i is ul ima ely connec ed o some o he poin s below abou pe o m-
ing an analysis o he da a. The da a is expec ed o con ain he in o ma ion
ha can answe he ques ion, and possibly indica e he p esence o addi ional
associa ions ha a e help ul o include in he analysis. In he con ex o people
o pa ien s, age is a equen ly collec ed addi ional “ hi d a iable”.
Age decomposi ion
Be o e p oceeding, i is wo h asking ou sel es wha we mean by “age” o in end
o measu e wi h i . Fo example, longe i y esea ch is an exci ing b oad a ea in
heal h esea ch ha in i ed hinking abou heal hy aging in con as o me e
age. This b ings us o he gene ic no ion o “biological age” as some biological
measu e o senescence. The biological age does no necessa ily ha e an abso-
lu e uni o measu e, and could be a ac ion o expec ed li espan a bi h, o
some measu e o accumula ed damage, physiological age, cellula age, o molec-
ula age. The e a e e en a gumen s o hinking abou di e en biological ages
ha could be, o example o gan speci ic[2]. Ou unde s anding o biological
age g a i a es a ound nine en a i e hallma ks o aging[3] (genomic ins abili y,
elome e a i ion, epigene ic al e a ions, loss o p o eos asis, de egula ed nu i-
en sensing, mi ochond ial dys unc ion, cellula senescence, s em cell exhaus ion,
and al e ed in e cellula communica ion) bu he science o ully alida e and
unde s and he unde lying biology o all o hem is needed[4]. Fo simplici y
his a icle conside s one gene al no ion o biological age o simplici y, and in
some examples one o he bioma ke s o i (DNA me hyla ion).
The age eco ded in census da a, popula ion s udies, heal h egis ies, ad-
minis a i e heal h claims, o elec onic heal h eco ds is he “calenda age”,
o ch onological age. The uni o ha numbe can be exp essed in numbe o
o a ions he Ea h pe o med a ound he sun, he numbe o days and nigh s,
o depending on he la i ude he numbe o season cycles expe ienced.
Figu e 2: Minimal DAG wi h Ch onological and Biological Age.
Calenda age and biological age ha e an unequi ocal causal dependency: he
calenda age will in luence he biological age. The e e se is no possible, as i
would o he wise imply ha biological in e en ions could ha e an in luence on
plane a y mechanics o he possibili y o ime a el. Mo e gene ally, no causal
a ow can poin owa d ch onological age (Figu e 2).
On he o he hand, biological age, o a he ma ke s o i , could be a ec ed
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by o he a iables. In causal DAG ep esen a ions, a ows could poin owa d
hem. O he age- ela ed a iables such as “age a diagnosis”, “age a ini ia ion
o ea men ”, o “age a en ollmen ” could also be poin ed o in a causal DAG
bu , al hough hey u he highligh he impo ance being e y speci ic abou
wha “age” means, his sho a icle will no discuss hem.
Wi h ha dis inc ion be ween ch onological age and biological age in mind,
we a e eady o e iew h ee majo causal pa e ns whe e age can be a “ hi d
a iable”, and how o handle i in an analysis.
Age as a hi d a iable
The las hi y yea s ha e wi nessed signi ican p og ess in he de ini ion o
causal e ec s, and hei es ima ion. S a is icians, econome icians, and epi-
demiologis s ha e emb aced hese de elopmen s, bu he applica ion o causal
in e ence is s ill wo king i s way h ough some ields, scien i ic communi ies, o
cu icula abou da a analysis.
Addi ional possible a iables will exis in mos si ua ions, al hough no nec-
essa ily measu ed o a ailable in he da ase , and some imes he in o ma ion
hey con ain expose bias in he da a. When such a iables a e p esen , a p io i
causal s uc u es de i ed om subjec ma e expe ise will guide whe he hey
should be inco po a ed in o he analysis o ob ain he desi ed e ec es ima e
and a oid inco ec conclusions. We conside h ee causal pa e ns in ol ing
an addi ional a iable: he con ounde , he media o , and he collide [5]. Dis-
inguishing ch onological age om biological age can help e eal which one is
p esen .
The Con ounde
A con ounde is a a iable ha causally a ec s he ou come and is also as-
socia ed wi h he exposu e al hough no necessa ily causal - o example, no
andomly dis ibu ed be ween ea men and con ol g oups. The g aph o a
classic con ounde is shown in Figu e 3.
Figu e 3: Minimal g aph ep esen a ion showing a con ounde pa e n. A DAG
would ha e an a ow om Con ounde o Exposu e.
S udies abou he e ec o d inking co ee on heal h can p o ide examples
o con ounde s[6]. Fo example, a simple obse a ion o co ee consump ion
and lung cance could conclude ha i is a isk ac o . Howe e , smoking is
a con ounde as smoke s end o consume mo e co ee. The nega i e e ec o
co ee on lungs disappea s as soon as he smoking s a us is accoun ed o .
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Whene e a con ounde is p esen , i MUST be con olled[7].
Example o age as a con ounde
Age is iewed as a po en ial con ounde by de aul and should he e o e be con-
olled. I we keep co ee d inking as he exposu e o in e es , an obse a ional
s udies in es iga ing he e ec o co ee on cause-speci ic mo ali y may conside
ha co ee d inking pa e ns change wi h age and he isk o diseases is a ec ed
by “age”. This makes “age” a con ounde , and con olling o i is hen needed.
We ha e no conside ed he decomposi ion o age men ioned p e iously, and
i we do he DAG could look like in Figu e 4.
Figu e 4: Age decomposi ion and con ounde .
Ch onological age has an in luence on co ee d inking, while biological age
has an e ec on he p e alence o diseases, he e o e disease-speci ic mo ali y.
In his case he g aph does no adically change how one should handle “age”
in an analysis. Ch onological age can be used as a con ounde , and a measu e
o biological age could op ionally be ea ed as a modi ie and included in he
analysis o educe he a iance o he e ec es ima e.
The Media o
A media o “media es” he e ec by being on a causal pa h be ween exposu e
and ou come. I can be on he unique causal pa h be ween exposu e and ou -
come ( ull media ion), o be in addi ion o a di ec e ec o exposu e on he
ou come. Figu e 5 shows a DAG o a media o when a di ec e ec o he
exposu e on ou come:
The g aph o he pa e n is simila o he con ounde pa e n, wi h he
a ow be ween exposu e and he addi ional a iable, now a media o , in he
o he di ec ion.
Whe he o con ol o a media o a iable depends on he spe-
ci ic ques ion o be answe ed. I he o al e ec o exposu e on he
ou come is he objec i e, i should no be con olled. Howe e , i
he objec i e o dis inguish be ween di ec and media ed e ec o
exposu e, hen one should con ol o he media o .
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Figu e 5: Minimal DAG showing a media o pa e n.
Example o age as a media o
When we s a conside ing “age” as composi e o calenda and biological age,
causal e ec s in o “age” become possible.
Fo example, le ’s assume ha we wan o in es iga e he e ec o alcohol
consump ion (exposu e) as isk ac o o de eloping cogni i e diseases (ou -
come). The gene al no ion o age is epo ed o in luence o be in luenced by
he ollowing a iables:
exposu e → age: alcohol has a epo ed e ec on ma ke s o cellula aging
(DNA me hyla ion[8])
age → exposu e: d inking pa e ns a e also epo ed o e ol e wi h age, and
he exac pa e n is coho -speci ic[9]
age → ou come: Cellula aging is epo ed o ha e e ec on cogni ion[10]
I keeping a gene al no ion o “age”, he g aph would ge a bidi ec ional a ow
(Figu e 6). This is simila o one o he con ounde pa e ns shown ea lie , bu
aises he ques ion o di ec ionali y i ch onological age is somehow implied.
Figu e 6: Bi-di ec ional causal a ow be ween Age and Exposu e.
Decomposing “age” in o ch onological age and biological age as we ha e
shown esol es he causal issue (no hing can a ec ch onological age), and we
ob ain he upda ed g aph in Figu e 7.
The gene al ule would be ha i he o al e ec o exposu e on he ou come
is wan ed, ch onological age is a con ounde and should he e o e be con olled.
I a mo e g anula unde s anding o he causal pa hway is needed, o example,
o de elop a diagnosis es ha would u ilize DNA me hyla ion-based aging,
hen a mo e sophis ica ed analysis is equi ed o de e mine di ec and indi ec
e ec s and quan i y he con ibu ion o biological age o he ou come. Howe e ,
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Figu e 7: Decomposi ion o Age in o Ch onological Age and Biological esol es
he bi-di ec ionali y in Figu e 6.
he s eng h o he coupling be ween ch onological age and biological age, ha is
how s ongly hey a e co ela ed, will ma e . I he co ela ion is high, and he
con ounde (ch onological age) is uly a con ounde wi h signi ican coupling
wi h exposu e and ou come, con olling o he coun ounde will amoun o
pa ially con ol o he media o as well, and his a ec he quali y o ou
e ec es ima e. In ha case, a clean es ima e o he o al e ec can be difficul
o achie e wi h simple co a ia e adjus men echniques. Mo e sophis ica ed
me hods such as media ion analysis a e hen necessa y.
The Collide
A collide is close o he causal opposi e o a con ounde . I is a a iable ha
is a ec ed by bo h exposu e and ou come. This las pa e n migh be he leas
in ui i e o he h ee pa e ns we conside o his a icle. The DAG looks is
shown in Figu e 8.
Figu e 8: Minimal DAG wi h a collide pa e n.
In con as o a con ounde , con olling o a collide in oduces bias and can
dis o he measu ed associa ion be ween he exposu e and ou come. Be kson’s
pa adox[11] can be a mani es a ion o his, and his pa e n is conside ed a
o m o selec ion bias. The his o ical example looked a isk ac o s o diseases
among in-pa ien hospi alized popula ions: bo h isk ac o s inc eased he odds
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o being hospi alized ( he collide ), leading o a spu ious nega i e associa ion
be ween hem.
Whene e a collide is p esen , i mus NOT be con olled.
Ch onological and biological ages as con ounde and collide
Unlike Ch onological Age, Biological Age migh be in luenceable. I i is a ec ed
by bo h he exposu e and he ou come i hen becomes a collide . We can hink
o a pu a i e example using again alcohol consump ion as he exposu e, and
DNA Me hyla ion as a measu e o Biological Age. Ou ques ion is he e ec
o Alcohol Consump ion on In lamma ion[12]. We al eady ha e he e ec o
alcohol on DNA me hyla ion, o which we add ha In lamma ion causes DNA
damage and a ec me hyla ion[13]. To comple e he example, we can add ha
ch onological age has a di ec e ec , o a he an e ec no media ed by DNA
Me hyla ion, on in lamma ion[14].
Figu e 9: Age decomposi ion sepa a es coun ounde and collide pa e ns.
The decomposi ion is shown in Figu e 9: we a e now in a si ua ion wi h a
con ounde ha mus be con olled and a collide ha mus no be con olled.
He e again, he s eng h o he co ela ion be ween con ounde and collide will
in luence how complex he si ua ion is, and wha can be a pa h o wa d:
• I con ounde and collide a e no e y co ela ed, in o ma ion “leakage”
abou he collide will be limi ed and he con ounde should be simply
con olled o .
• I he co ela ion is oo high o he leakage unaccep able, look o an
ano he a iable han he con ounde ha is no angled wi h he collide
• I con ounde and collide a e highly co ela ed, bias and a iance can
dis o d he es ima e. Simple co a ia e adjus men is hen no sufficien
and mo e ad anced causal modeling is equi ed. Fo example, s uc u al
equa ion modeling. De ailing hese echniques is well beyond he scope o
his a icle.
O he wise, jus as much as he s eng h o he associa ion be ween Ch ono-
logical Age and Biological Age ma e s, he “s eng h o he con ounde ” can
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in luence wha is a good cou se o ac ion. As ha s eng h diminishes he
impo ance o he collide in he sys em inc eases.
Biological age as a collide
We can also ind a possible example whe e Biological Age could be a collide
and Ch onological Age no longe a con ounde , using ai pollu ion o he ex-
posu e and as hma o he ou come. The g aph is sligh ly mo e complex, wi h
he causal e ec o Ai Pollu ion on As hma likely media ed by In lamma ion
when ine pa icles and ozone a e in ol ed, and In lamma ion will a ec DNA
Me hyla ion. When DNA-binding chemical pollu an s such as he ones ound
in ehicle exhaus a e in ol ed, hey will ha e an e ec on DNA Me hyla ion
pa e ns. The DAG o his is shown in Figu e 10.
Figu e 10: Example o o Biological Age as a collide .
Unde he causal assump ions ep esen ed by he g aphical model abo e,
Ch onological Age does no a ec exposu e o ou come. I is no longe a con-
ounde , and con olling o i can be done bu i is an unnecessa y s ep, possi-
bly adding a bu den o da a collec ion o missing alues handling. Howe e , i
As hma has an e ec on DNA Me hyla ion ha is no media ed by In lamma ion
hen Biological Age should no be added as a simple co a ia e o s a i ica ion
ac o when looking a he associa ion be ween Ai Pollu ion and As hma. In
ha case, Biological Age becomes a collide and i mus no be con olled.
Res ic ing on ch onological age inducing a collide bias
While ch onological age is impe ious o in luences, i can s ill be in ol ed in
a collide pa e n. Whene e mo ali y is in ol ed, he o he wise inexo able
p og ession o ch onological age is ine i ably s opped. I exposu e and ou come
ha e an e ec on su i al, hen i is a collide and ch onological age can become
a p oxy o i .
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