=Paper=
{{Paper
|id=Vol-2137/paper_38.pdf
|storemode=property
|title=What is a Risk? A Formal Representation of Risk of Stroke for People with Atrial Fibrillation
|pdfUrl=https://ceur-ws.org/Vol-2137/paper_38.pdf
|volume=Vol-2137
|authors=Adrien Barton,Ludger Jansen,Arnaud Rosier,Jean-François Ethier
|dblpUrl=https://dblp.org/rec/conf/icbo/BartonJRE17
}}
==What is a Risk? A Formal Representation of Risk of Stroke for People with Atrial Fibrillation==
https://ceur-ws.org/Vol-2137/paper_38.pdf
What is a risk? A formal representation of risk of stroke
for people with atrial fibrillation
Adrien Barton1,* Ludger Jansen2, Arnaud Rosier3 and Jean-François Ethier1,3,*
GRIIS, Université de Sherbrooke, Québec, Canada
1
Ruhr University Bochum and University of Rostock, Germany
2
3
INSERM UMR_S 1138 Eq 22, Paris Descartes University, Paris, France
ABSTRACT One principle of BFO is the strict separation between uni-
We propose a framework for the representation of medical risks in the versals and their instances. We write names of instances as
context of the OBO Foundry using the Web Ontology Language (OWL). The
framework is developed for the use case of risk of stroke for people with
well as relations between instances in bold, and names of uni-
atrial fibrillation, for which we distinguish three classes of dispositions: the versals and defined classes in italics. When first introduced,
atrial fibrillation disease; the risk of stroke for a human who has atrial fi- names of universals will be prefixed by the name of the
brillation; and the risk of stroke over 12 months for a human who has atrial source ontology (e.g., “BFO:Disposition”), unless the context
fibrillation. The latter is quantified by risk estimates, which are informa-
tional entities extracted from documents – such as journal articles – and to
makes it obvious.
which epistemic probability values can be assigned. We discuss the refer- The OBO Foundry compliant Ontology of Biological and
ence-class problem (i.e., the possibility to have several risk estimates with Clinical Statistics (OBCS; Zheng et al., 2016) defines Abso-
different epistemic probabilities for the same individual, depending on the lute risk as a subclass of IAO:Information content entity
reference class the risk estimate is based on) and clarify the philosophical
(“ICE” for short). However, arguably, a person with atrial fi-
hypotheses on which this dispositional framework is based.
brillation has a risk to get a stroke independently of whether
or not there exists some ICE estimating his risk to get a
1 INTRODUCTION
stroke. The risk itself has rather a dispositional character: an
Risks of adverse outcomes are ubiquitous in the medical do- instance of risk of an adverse outcome of type A may be re-
main and have a central importance. An older population with alized by an instance of A, but it may also never be realized;
complex combinations of chronic diseases and many medica- however, whether it is realized or not, the risk still exists. For
tions makes simple deterministic treatment decisions diffi- this reason, this paper formalizes risks as dispositions that can
cult. Instead, clinicians need to assess, manage, and balance be estimated by a specific kind of ICE, risk estimates, and the
risks much more explicitly than ever before. It would there- risk probability values as assigned to these risk estimates.
fore be valuable if ontologies aiming at adequately represent- We begin by distinguishing two types of dispositions: the
ing medical knowledge could formalize such risks. This pa- disease of atrial fibrillation on the one hand, and the risk of
per contributes to this aim by proposing a framework for the stroke of a human who has atrial fibrillation on the other
representation of risks, illustrated by the risk of stroke in peo- (Sect. 2). We then show how a probability can be assigned to
ple with atrial fibrillation. More specifically, we propose a a risk of stroke in 12 months for a human with atrial fibrilla-
representation of absolute risks, such as a 3.2% risk of stroke tion (Sect. 3). A discussion and conclusion follow.
over 12 months for people with atrial fibrillation (Nielsen et
al., 2016). 2 DIFFERENTIATING RISK DISPOSITION
This formalization is expressed in the Web Ontology Lan- AND DISEASE
guage (OWL), in the context of the OBO Foundry (Smith et
al., 2007). The OBO Foundry is one of the most comprehen- The OGMS (Ontology for General Medical Science) consid-
sive collections of interoperable ontologies in the biomedical ers a Disease as a BFO:Disposition (Scheuermann, Ceusters
domain, built on the upper ontology Basic Formal Ontology & Smith, 2009). Röhl & Jansen (2011) developed an axio-
(BFO) 2.0 (Arp, Smith & Spear, 2015). A few ontologies matisation of dispositions in the context of BFO. In this
have formalized the notion of medical risk; see Uciteli et al. model, a disposition is a BFO:Dependent continuant that in-
(2016) for a recent account (though not in the context of the heres_in his bearer (which is the bearer_of this property), a
OBO Foundry), as well as a review of former accounts. How- Material entity, and may be realized (realized_in) via a pro-
ever, there is currently no comprehensive account of the no- cess. The realization process has the material entity as a par-
tion of risk in the OBO Foundry ontologies. ticipant (has_participant), and the disposition is triggered by
(has_trigger) some event or process. Finally, according to
*To whom correspondence should be addressed: ethierjf@gmail.com;
adrien.barton@gmail.com
1
Barton et al.
BFO, a disposition has_material_basis some entity. For ex- These pathological processes lead to the development of a
ample, the fragility of a glass is formalized as a disposition blood clot in Jones’ atrium, which is a new disorder. This
inhering in the glass, that may be realized by a breaking pro- blood clot is the bearer of a disposition to dislodge and mi-
cess when some form of stress (the trigger) happens; moreo- grate, which is at some point realized by the process of the
ver, the fragility exists because of some molecular structure blood clot migrating to the brain. The migrating clot has then
of the glass, which is its material basis. a disposition to get stuck in a cerebral artery - by contrast to
The OGMS model considers Disease as a disposition re- dissolve. When it gets stuck, the blood flow is blocked and
alized_in a Disease course that has as parts some Pathologi- strokeJones happens.
cal process. The material basis of a disease is a Disorder in On top of the disposition afJones, Jones is also the bearer of
the organism. For example, the disease epilepsy is seen as a another disposition: the risk of stroke riskJones,Stroke, which is
disposition to have a disease course composed by various ep- realized by his stroke:
ileptic crises (pathological processes), because of some dis-
riskJones,Stroke inheres_in Jones
order in the brain.
The OGMS model is applied to cardiovascular diseases by riskJones,Stroke realized_in strokeJones
the Cardiovascular Disease Ontology (CVDO; Barton et al., riskJones,Stroke is an instance of RiskAF,Stroke, the class of risks
2014). It formalizes the atrial fibrillation disease Atrial fibril- of stroke for humans with atrial fibrillation, which is itself a
lation as a disposition realized by a disease course that has as subclass of Risk:
parts some processes of atrial fibrillation:
Risk subClassOf Disposition
Atrial fibrillation subClassOf Disease
RiskAF,Stroke subClassOf Risk
Atrial fibrillation process subClassOf Pathological pro-
cess RiskAF,Stroke subClassOf (inheres_in some HumanAF)
Atrial fibrillation subClassOf (realized_in some Disease HumanAF subClassOf (bearer_of some RiskAF,Stroke)
course and (has_part some Atrial fibrillation process))
RiskAF,Stroke subClassOf (realized_in only Stroke)
This matches to an ambiguity in the natural language
An instance of RiskAF,Stroke may be realized by one or sev-
term “atrial fibrillation”: it refers sometimes to a pathological
eral instance(s) of stroke, or may remain unrealized. To clar-
process of atrial fibrillation (namely, irregular, uncoordinated
ify the triggers of RiskAF,Stroke, we need to use BFO:History.
contractions of the atria of the heart), and sometimes to a dis-
BFO defines the history of a material entity as the “process
ease – a disposition exceeding a given threshold (Scheuer-
that is the sum of the totality of processes taking place in the
mann et al., 2009) to atrial fibrillation processes.
spatiotemporal region occupied by a material entity or site,
Consider a human Jones, who has an atrial fibrillation dis-
including processes on the surface of the entity or within the
ease (“AF” for short) afJones – an instance of the universal
cavities to which it serves as host” (Arp, Smith and Spear,
Atrial fibrillation. Jones is an instance of HumanAF, the class
2015). We define History-part as the class of temporal parts
of humans with atrial fibrillation:
of the history of any material object:
HumanAF equivalentClass Human and (bearer_of some
History-part equivalentClass (part_of some History)
Atrial fibrillation)
In our formalization, RiskAF,Stroke is triggered by any His-
Suppose that afJones leads to the process instance stroke-
tory-part of its bearer:
Jones (an instance of the universal Stroke) through the follow-
ing scenario. There is some fibrosis in Jones’ atrial myocar- RiskAF,Stroke subClassOf (has_trigger some History-part)
dium (the disorder atrium_fibrosisJones), which is the mate-
This way, risks of stroke are dispositions that are always
rial basis of the disposition afJones:
triggered. However, RiskAF,Stroke is not a sure-fire disposition
afJones inheres_in Jones (that is, a disposition that is always realized when triggered),
but a tendency (that is, a disposition that is not always real-
afJones has_material_basis atrium_fibrosisJones
ized when triggered; Jansen 2007; Röhl & Jansen, 2011).
afJones is realized by a (long) disease course af_courseJones, The material basis of riskJones,Stroke is a disorder that has as
that encompasses various pathological processes, including part Jones’ fibrosis, but also other entities. As a matter of fact,
several episodes of atrial fibrillation (ppaf,1,...,ppaf,n): Jones can have a stroke because of his atrial fibrillation, but
also because of various random or progressive factors, such
afJones realized_in af_courseJones
as the regular senescence of his blood vessels.
For every iÎ[1,n]: af_courseJones has_part ppaf,i
2
What is a risk? A formal representation of risk of stroke
for people with atrial fibrillation
riskJones,Stroke has_material_basis some (Disorder and By contrast to RiskAF,Stroke which is triggered by all history-
has_part atrium_fibrosisJones and has_part senes- parts of its bearer, RiskAF,12m,Stroke is only triggered by all 12-
cent_blood_vesselsJones) months-long history-parts of its bearer:
Thus, the disease afJones and the risk riskJones,Stroke are not RiskAF,12m,Stroke subClassOf (has_trigger some
the same disposition: even if they both inhere in Jones, they History-part12m)
have distinct material basis and distinct realizations – namely,
In order to determine how a probability can characterize
af_courseJones vs. strokeJones. (The OGMS model leaves
RiskAF,12m,Stroke, we need to clarify the ontological status of
open the question whether pathological processes that are
probabilities.
caused - or partially caused - by earlier pathological process
of a disease course are also part of this disease course; thus, 3.2 What are the probabilities?
it is an open question whether strokeJones is a part of Standardly, objective and epistemic interpretations of proba-
af_courseJones; see Barton et al. 2014 for a discussion. In any bilities are distinguished (Hájek, 2012). Objective probabili-
case, those two instances are distinct entities.) ties are meant to characterize the world independently of our
knowledge of it, while epistemic interpretations consider
3 PROBABILITY ASSIGNMENTS TO RISK probabilities to describe our knowledge of the world: epis-
DISPOSITIONS temic probabilities can be defined as degrees of belief or de-
We can now turn to the representation of a probability assign- grees of confidence.
ment to a risk of stroke. For this purpose, we first discuss the Consider for example a biased coin that has three times
entity characterized by a probability assignment, then discuss more chances to fall on heads than on tails. The objective
the nature of probabilities at play, and finally formalize the probability of the coin falling on heads is ¾, and its objective
probability assignment to a risk estimate. probability to fall on tails is ¼. If Mr. Green knows about the
coin’s bias, he should assign epistemic probabilities with the
3.1 What kind of entity do risk probabilities
same values: ¾ to heads and ¼ to tails; this is a consequence
characterize? of a principle of rationality called the “principal principle”
Nielsen et al. (2016) studied a nationwide cohort of patients (Lewis, 1980). However, if Mr. White is not aware of this
for which the overall ischemic stroke rate was 3.20 per 100 bias and thinks that the coin is balanced, he would assign ep-
person-years. However, this value 3.2% does not relate only istemic probabilities ½ to heads and ½ to tails. Epistemic
to a proportion in this cohort: we can infer from this infor- probabilities can be operationalized as rational, hypothetical
mation that an unspecified human from the same population betting coefficients – that is, coefficients indicating which
with atrial fibrillation has a 3.2% probability to have a stroke odds should be considered as acceptable by the agent to bet
over 12 months – even, of course, if he was not one of the on the occurrence of heads or tails (Maher, 1997).
patients in the cohort. Therefore, as we will now argue, the Suppose that the 3.2% value would be an objective proba-
probability 3.2% also characterizes a certain property of Hu- bility that could be assigned to the disposition RiskAF,12m,Stroke.
manAF: their risk to have a stroke over 12 months. We would then have:
Dispositions are natural targets for probability assign-
ments (Barton et al. 2012). However, we cannot assign the RiskAF,12m,Stroke subClassOf (has_objective_probability
0.032)
probability 3.2% to the disposition RiskAF,Stroke. As a matter of
fact, 3.2% is the probability of a human with AF to have a This would imply that for every r instance_of
stroke over 12 months – but RiskAF,Stroke does not have any RiskAF,12m,Stroke:
ontological connection with 12-months-long processes.
r has_objective_probability 0.032
To solve this issue, let’s define History-part12m as the sub-
class of History-part with a 12 months-long duration. Let’s Thus, all people with AF would have an objective proba-
now introduce RiskAF,12m,Stroke the class of risks of a human bility 3.2% to have a stroke over 12 months. However, this
with AF to get a stroke over 12 months, that we also formalize cannot be the case: many people with AF have a lower or
as a Risk – and therefore, a disposition: higher objective probability to have a stroke over 12 months,
depending on various factors (see below the section 4.2 on
RiskAF,12m,Stroke subClassOf Risk
CHADS2 and CHADSVASC scores). Therefore, we would
Like with RiskAF,Stroke, there is an instance of RiskAF,12m,Stroke rather interpret 3.2% as an epistemic probability that charac-
inhering in any person with AF; and those instances can only terizes the rational degree of confidence, given the evidence
be realized by a stroke: provided by Nielsen et al. (2016), that a person with AF
HumanAF subClassOf (bearer_of some RiskAF,12m,Stroke) would have a stroke over 12 months. We will now propose a
RiskAF,12m,Stroke subClassOf (realized_in only Stroke) formalization along those lines.
3
Barton et al.
3.3 Epistemic probability assignment a person who has AF (in the absence of additional infor-
We define the relation object_of as the inverse of mation).
IAO:is_about (Ceusters & Smith, 2010), which relates an
ICE to what it is about. We introduce the class Risk estimate 4 DISCUSSION
as a subclass of ICE. Let risk_estimateAF,12m,Stroke,Niel- 4.1 The reference class problem
sen_et_al._(2016) be the following instance of Risk estimate: the
As mentioned in section 3.2, all patients with atrial fibrilla-
estimate of the risk of a human with atrial fibrillation to have
tion do not have the same objective probability of stroke. The
a stroke over 12 months, extracted from the article Nielsen et
CHADS2 score (congestive heart failure, hypertension, age ³
al. (2016)1:
75 years, diabetes mellitus, stroke) is a tool that has been de-
RiskAF,12m,Stroke subClassOf (object_of veloped to predict the risk of stroke in patients with atrial fi-
risk_estimateAF,12m,Stroke,Nielsen_et_al._(2016)) brillation by stratifying patients into risk groups (Gage et al.,
2001). It was later expanded into the CHA2DS2-VASc score
To represent the assignment of the probability 3.2% to this
(Lip et al., 2010; written “CHADSVASC” from now on),
risk estimate, we use two OBI relations (which are currently
which includes three additional risk factors: vascular disease,
being formalized by the OBI development team), the object
age 65-74 years, and female sex.
property has_value_specification (that relates an infor-
Let HumanAF2 be the class of humans with atrial fibrilla-
mation content entity to an OBI:Value specification) and the
tion and a CHADSVASC score of 2 (“AF2” for short). We
datatype property has_specified_value (that relates a value
can introduce a class of dispositions RiskAF2,12m,Stroke, the risk
specification to its numerical value). As a shortcut, let’s in-
of stroke over 12 months for people with AF2:
troduce here the datatype property has_value defined as
has_value_specification o has_specified_value. We can RiskAF2,12m,Stroke equivalentClass
then write: (RiskAF,12m,Stroke and inheres_in some HumanAF2)
risk_estimateAF,12m,Stroke,Nielsen_et_al._(2016) Nielsen et al. (2016) state that the rate of stroke over 12
has_value 0.032 months among patients in the sample who had AF2 was
1.97%. Therefore, there is an instance risk_esti-
Informally, if R is a risk and re is a risk estimate, (R sub-
mateAF2,12m,Stroke,Nielsen_et_al._(2016) such that:
ClassOf object_of re) and (re has_value p) mean together
that according to the risk estimate re, it is rational to assign RiskAF2,12m,Stroke subClassOf object_of
an epistemic probability p to the risk R. risk_estimateAF2,12m,Stroke,Nielsen_et_al._(2016)
The evidence for the estimate is documented in Niel-
risk_estimateAF2,12m,Stroke,Nielsen_et_al._(2016)
sen_et_al._(2016), an instance of IAO:Journal article has_value 0.0197
(which is, in turn, a subclass of IAO:Document). To formally
relate this journal article with risk_estimateAF,12m,Stroke,Niel- Suppose that Jones has AF2. Jones is the bearer of the risk
sen_et_al._(2016), we introduce a relation extracted_from, whose to get a stroke over 12 months riskJones,12m,Stroke. Since
domain is Information content entity and whose range is Doc- Jones instance_of HumanAF2, his risk to get a stroke over 12
ument. If r is a risk estimate and j is a document, r ex- months is an instance of the class of risks to get a stroke over
tracted_from j implies that j participates in a IAO:Planned 12 months for people with AF2:
process whose specified output is r: riskJones,12m,Stroke instance_of RiskAF2,12m,Stroke
extracted_from subRelationOf and therefore:
(is_specified_output_of o has_participant)
riskJones,12m,Stroke object_of
Then, we can state: risk_estimateAF2,12m,Stroke,Nielsen_et_al._(2016)
risk_estimateAF,12m,Stroke, Nielsen_et_al._(2016) extracted_from Moreover, since HumanAF2 subClassOf HumanAF,
Nielsen_et_al._(2016)
Jones instance_of HumanAF. Therefore, his risk to get a
Altogether, the relations we have introduced here and in stroke over 12 months is an instance of the class of risks to
section 3.1 mean that a risk estimate is extracted from Nielsen get a stroke over 12 months for people with AF:
et al. (2016), according to which it is rational to assign a 3.2% riskJones,12m,Stroke instance_of RiskAF,12m,Stroke
epistemic probability to the risk of stroke over 12 months for
and therefore:
1
As in OWL the term “value” is used in a class restriction to introduce an RiskAF,12m,Stroke subClassOf (object_of value risk_estimateAF,12m,Stroke,Niel-
individual after an object property, this could more specifically be written as sen_et_al._(2016))
4
What is a risk? A formal representation of risk of stroke
for people with atrial fibrillation
riskJones,12m,Stroke object_of who have a stroke over 12 months – tends towards 0.032 as
risk_estimateAF,12m,Stroke,Nielsen_et_al._(2016) the size of the sequence tends towards infinity.
Thus, riskJones,12m,Stroke is the object of two different esti- This conception raises the issue of what it means to have a
mates with two different probability values (0.032 and representative sequence of hypothetical instances of
0.0197), based on two different reference classes (AF or RiskAF,12m,Stroke inhering in hypothetical instances of HumanAF.
AF2): this is the reference class problem (Hájek, 2007). This Indeed, several factors can influence the risk of having a
is ontologically sound: if Dr. Khan only knows that Jones has stroke – in particular those involved in the CHADSVASC
AF, it is rational for him, based on Nielsen et al. (2016), to score: hypertension, age ³ 75 years, etc. It makes sense to
assign a probability 3.2% to the risk that Jones will have a speak of a representative sequence of instances only by ref-
stroke over 12 months; and if Dr. Patel knows in addition that erence to an actual population pop0: to be representative of
Jones has a CHADSVASC score of 2, then it is rational for pop0, the sequence seq0 should involve the same proportions
him, based on Nielsen et al. (2016), to assign a probability of as in pop0 of people with hypertension, of people older than
1.97% to this risk. 75 years, etc. But this implies that the probability 0.032
However, this raises practical difficulties. It might seem at would characterize the actual population pop0 (that is, a col-
first sight rational, for a computer system who has the infor- lection of human particulars – cf. Jansen & Schulz, 2011) ra-
mation that Jones has a CHADSVASC score of 2, to always ther than a subclass of Human. This is a possible orientation,
give precedence to the 1.97% risk estimation over the 3.2% pursed by Barton, Ethier, Duvauferrier & Burgun (2017) to
estimation, as it is based on more specific factors. However, formalize indicators of diagnostic performance.
other criteria may matter. For example, if both values had This article has used an alternative interpretation of prob-
been obtained from different studies, the 3.2% could be con- abilities as epistemic in nature. This interpretation makes the
sidered as a more reliable value for other reasons – such as a formalization simpler in the present context, as it enables to
smaller 95% confidence interval. relate a probability estimate to a universal of human. Future
Moreover, different articles relating about different co- work will need to discuss further the articulation between the
horts or samples might give risk estimates with different val- objective and epistemic probability views, and compare the
ues of the same risk class. They might give also risk estimates strengths of each.
for risk classes that are not included into each others. Suppose 4.3 Generalization of this formalization
that Jones has atrial fibrillation and is a smoker, and that we Note that this formalization can be adapted to represent a risk
know two data from two different cohorts: the probability pAF during a process that is not characterized by its duration (such
that someone with atrial fibrillation will have a stroke during as 12 months), but by some other characteristics. Imagine for
ten years; and the probability pSmoker that a smoker will have example that we want to represent the probability p that a hu-
a stroke during ten years. There is no easy way to decide man with AF would have a stroke during a hospitalization
which epistemic probability is the best to estimate Jones’ risk, process; we would then introduce the risk riskJones,Hospitaliza-
or how they should be weighted in a common probability es-
tion,Stroke that Jones would have a stroke during a hospitaliza-
timate. Note however that this is a classical issue for proba- tion process, and assign the probability p to its risk estimate
bilistic reasoning, independent of the ontological representa- (the class of triggers of this risk would be the class of history-
tion chosen here. parts of Jones that temporally span any of his hospitalization
4.2 Articulating objective and epistemic proba- process).
bilities
5 CONCLUSION
We have seen earlier that we could not formalize in OWL
3.2% as an objective probability assigned to RiskAF,12m,Stroke, This article has shown how a specific risk and its various
as it would imply that every instance of this risk probability estimates could be formalized in the context of
(riskJones,12m,Stroke, riskHubbard,12m,Stroke, etc.) would have the the OBO Foundry. We took the example of the risk of stroke
same objective probability – which is false. for people with AF over 12 months RiskAF,12m,Stroke, which was
An alternative reading would be to interpret the objective formalized as a disposition. The article introduced risk_esti-
probability 3.2% in line of Barton, Burgun & Duvauferrier mateAF,12m,Stroke,Nielsen_et_al._(2016), related (by the relation ex-
(2012) as assigned only to the universal RiskAF,12m,Stroke, but tracted_from) to the instance of Journal article Niel-
not to its instances – a conception that is not straightforwardly sen_et_al._(2016). It was also related (by the relation
implementable in OWL. Informally, this assignment would is_about) to the risk RiskAF,12m,Stroke, which was itself related
be elucidated as follows: in a hypothetical, representative se- to the following relevant classes: humans with atrial fibrilla-
quence seq0 of instances of RiskAF,12m,Stroke inhering in hypo- tion HumanAF (by the relation inheres_in); 12-months-long
thetical instances of HumanAF, the proportion of those risks history-parts History-part12m (by the relation has_trigger);
who are realized – that is, the proportion of those humans and Stroke (by the relation realized_in).
5
Barton et al.
This representation of risk of stroke for patients with atrial Barton, A., Rosier, A., Burgun, A., & Ethier, J.-F. (2014) The Cardiovascu-
fibrillation could also be used to stratify patients into risk lar Disease Ontology. In Garbacz, P. & Kutz, O. (eds), Proceedings of
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SWRL rules (Rosier, 2015). This would also provide formal Systems (FOIS 2014). IOS Press, Amsterdam, pp. 409–414.
definitions of classes HumanAF1, HumanAF2, etc. Gage, B.F., Waterman, A.D., Shannon, W., Boechler, M., Rich, M.W., &
This paper has shown how a specific example of probabil- Radford, M.J. (2001) Validation of clinical classification schemes for
ity assignment to a risk – the risk of stroke over 12 months of predicting stroke: results from the National Registry of Atrial Fibrilla-
a patient with atrial fibrillation – could be formalized. Future tion. Jama, 285, 2864–2870.
work will need to systematize, using OBO-Foundry relations, Hájek, A. (2007) The reference class problem is your problem too. Synthese,
the relations involving the classes Risk or Risk estimate. Elab- 156, 563–585.
orating on the work of Barton & Jansen (2016), a relation of Hájek, A. (2012) Interpretations of Probability. In Zalta, E.N. (ed), The Stan-
disposition-parthood could also be introduced to represent ford Encyclopedia of Philosophy, Winter 2012. edn.
the connection between the risk of a human with AF to have Jansen, L. (2007) Tendencies and other realizables in medical information
a stroke (RiskAF,Stroke) and the risk of a human with AF to have sciences. The Monist, 90, 534–554.
a stroke over 12 months (RiskAF,12m,Stroke). Jansen, L. & Schulz, S. (2011) Grains, components and mixtures in biomed-
The formalization presented in this paper relies on two hy- ical ontologies. J. Biomed. Semant., 2, S2.
potheses. The first is that for every class of material objects Lewis, D. (1980) A Subjectivist’s Guide to Objective Chance. In Studies in
O, and every classes of processes T and R, there exists a class Inductive Logic and Probability. University of California Press, pp. 83–
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ified class of triggers and R as maximally specified class of Lip, G.Y., Nieuwlaat, R., Pisters, R., Lane, D.A., & Crijns, H.J. (2010) Re-
realizations; and O, T and R together constitute the conditions fining clinical risk stratification for predicting stroke and thromboem-
of identity of this disposition. This hypothesis was used to bolism in atrial fibrillation using a novel risk factor-based approach: the
define RiskAF,12m,Stroke (from the classes HumanAF, History- euro heart survey on atrial fibrillation. Chest, 137, 263–272.
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position d can happen during a trigger t – not necessarily just Stroke and thromboembolic event rates in atrial fibrillation according to
after the trigger ended. Thus, riskJones,12m,Stroke could be real- different guideline treatment thresholds: a nationwide cohort study. Sci.
ized during a 12-months-long history part that acted as a trig- Rep., 6, 1–7.
ger. Finally, this formalization raises the wider philosophical Röhl, J. & Jansen, L. (2011) Representing dispositions. J. Biomed. Semant.,
issue whether the risk of stroke RiskHuman,Stroke could be clas- 2, S4.
sified as a kind of disease, given OGMS definition of disease. Rosier, A. (2015) Raisonnement automatique basé ontologies appliqué à la
hiérarchisation des alertes en télécardiologie. (doctoral dissertation,
ACKNOWLEDGEMENTS Rennes 1)
We thank three anonymous reviewers for their feedback. AB Scheuermann, R.H., Ceusters, W., & Smith, B. (2009) Toward an ontologi-
acknowledges financial support by the “bourse de fellowship cal treatment of disease and diagnosis. In Proceedings of the 2009 AMIA
du département de médecine de l’université de Sherbrooke” Summit on Translational Bioinformatics. San Francisco CA, pp. 116–
and the “CIHR funded Quebec SPOR Support Unit”. 120.
Smith, B., Ashburner, M., Rosse, C., Bard, J., Bug, W., … & Lewis, S.
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