Medical vocabulary is complex, expanding, and convoluted not least because of the large numbers of compound terms. Formalized medical terminologies such as SNOMEDCT and ICD-10 take one of two strategies when representing medical language: so-called pre-coordination where valid compound terms are included explicitly in the terminologies and so-called post-coordination where the terminology consists of a basis and a generative function from which the compound terms may be derived. However, these notions are not used with particular precision in the literature. In this paper, we provide a formalization of the notion of coordination, a technique for estimating the degree of coordination in a given system, and an examination, based on our technique, of the coordination level of a number of major existing terminologies.
Controlled medical terminologies have long played an important role in the drive to improve
patient care, e.g., in Electronic Health Records (EHR), decision support and expert systems,
medical literature databases, and data exchange [
Term composition [24{26] or as it is more recently (in particular in the context of SNOMED
CT) called, (pre-/post-) coordination [
These discussions have led to repeated suggestions of terminologies to consist of a base of
atomic concepts, with a function, e.g., in form of a grammar or a description logic ontology,
specifying how to compose the atomic terms to form more complex terms [
Examples of pre-coordinated terms include 'Removal of External Fixation Device from Left Upper Femur, Open Approach', a procedure in ICD-10-PCS, "Removal of implanted devices from bone, femur", a procedure from ICD-9 procedures, which contains less detail (no detail on the location of the femur or the kind of approach used for the removal of the implanted device) than the procedure in ICD-10, i.e., could be considered to be less coordinated. Similarly, the procedure 'Removal of internal xation device of femur' in SNOMED CT, even though less coordinated than the procedure in ICD-10, would still be considered to be coordinated as there is potential for further decomposition, e.g., into the procedure itself, i.e., 'removal', the object that is being removed, i.e., 'internal xation device', and the location from where it is being removed, i.e., 'femur'. SNOMED CT also contains atomic terms to be used for post-coordination, for example, 'laterality' along with 'left' and 'right', but also pre-coordinated terms such as 'X-ray of left foot'.
However, so far no computational method to determine the level of coordination of terminologies has been available. In this paper, we propose a method for estimating the level of coordination of a given terminology and determine the coordination level of a number of standard terminologies. 2
Consider a simple clinical terminology, T1, that contains a single term, Back Pain, that is:
While Back Pain is atomic, that is, a single term with no substructure, it is clear from our perspective that it is a compound term. That is, it is composed of two sub-terms which themselves are clinically relevant, to wit Back and Pain which gives us an alternative terminology:
We, of course, can generate T1 from T2 via a suitable function. The simplest correct function would be a map from a subset of T2 (i.e., fBack; Paing) to the corresponding term in T1 (i.e., Back Pain). If we extend T1 and T2 we need to extend our mapping function as well: T1 = fBack Paing
T2 = fBack; Paing T10 = fBack Pain, Heart Pain, Stomach Paing
T20 = fBack, Heart, Stomach, Paing
M ap = ffBack,Paing ! Back Pain fHeart,Paing ! Heart Pain fStomach,Paing ! Stomach Paing We can also encode M ap by means of a simple grammar:
M ap2 =
Term ::= Location; ; Pain Location ::= Back | Heart | Stomach (1) (2) (3) (4)
While M ap2 is rather more illuminating than M ap or T10 and contains more information than T20 (T20 is not, by itself, su cient to generate exactly T10), it is conceptually more complicated, i.e., we have to understand a BNF style formalism. While M ap2 is very simple, it is easy to imagine situations that are inherently more complicated:
M ap3 =
Location ::= LocationWithLateralityj Back | Heart | Stomach LocationWithLaterality ::= Laterality; ; Leg
Laterality ::= Right | Left
Whole&terminology Sanc1onable&terminology Explicit&terminology
Base
The more exceptions and irregularities, the more di cult it is to come up with an exact and
yet intelligible description of the mapping, or, for that matter, a terser description. In addition,
ideally the map should only allow the construction of complex terms that are sensible for the
domain. If that is not possible, additional constraints, also known as sanctions, have to be added
to specify which compositions that can be built following the map, are meaningful, and thus are
allowed or sanctioned [
If we consider the set of compound terms generated from M ap3, there are only 5. If we include the \intermediate" terms (e.g., Right Leg), there are only 7, and if we include the base as well, there are a mere 12. Thus, the enumeration of the terms is shorter than the grammar itself, in this simple case. However, extending the set of terms with laterality causes the generated terms to grow more quickly than the base set or the grammar. And it is easy to see that terminologies with more dimensions can have even more dramatic gaps between the enumerative and the descriptive presentations of the terminology.
In general, a terminology (even idealised as complete) will not be fully enumerative or fully descriptive. Instead, given a set of base terms that are truly atomic, we can project a structure between the basis and the total terminological space generated from that basis. (Note, that if we allow for arbitrary iteration of base terms in a compound term, then the full space will be in nite.) Figure 1 illustrates a slightly idealised structure of a representation of a vocabulary. The \real" vocabulary, that is the set of terms which are meaningful for a domain, corresponds to the sanctioned terminology. A terminology might include a degree of pre-coordination in the form of an explicit set of coordinated terms without fully covering the vocabulary. This might be because the terminology is incomplete or that there are some compound terms which are so common or signi cant that the terminology designer wanted to make them more salient. Finally, there may be terms in the basis or explicit terminology which are not domain signi cant, at least, in isolation.
Note that this sort of phenomenon is not limited to terminologies per se. For example, we might have a hierarchical terminology where the hierarchical relations are themselves aspects of the coordination. (It is easy to see that we could generate a term plus a list of parent terms via a mapping function.) Similarly, we might be generating forms from a base \vocabulary" of form elements, and so on.
Furthermore, the map could be described in any number of formalisms, for example, by a description logic ontology.
With this picture, it is straightforward to articulate the classic trade o s between pre- and post-coordinated terminologies. A post-coordinated vocabulary has the possibility of 1) being more \compressed" in size but also 2) it can be expressed in a more perspicuous way. Instead of having a huge pile of terms, we can isolate important subgroups of terms and characterise them by their contribution to a mapping function. This can potentially support more e ective review for correctness and completeness of the terminology itself and of systems that make use of it, as well as just lowering the cost of maintenance (since we have \fewer things" to look at or connect to other parts of a system).
Contrariwise, while we might have fewer things to look at, each thing might be signi cantly more complex. The correctness of a coordination function with respect to the sanctioned vocabulary might be quite di cult to determine. Furthermore, the execution of the coordination function to generate or validate a term might be expensive in computational resources, and it might not be obvious \how much" of some section of the vocabulary to manifest for a particular situation. 3 3.1
Intuitively, coordination is a process of inductive composition, that is, a coordination of a (base) terminology is a recursively de ned function over that terminology. Since we can de ne such functions arbitrarily over any given basis, just identifying coordinations with recursively de ned sets is not particularly illuminating. In our case, the point of coordination is to capture some speci c set of terms (i.e., exactly the meaningful ones).
De nition 1. A vocabulary, V, is a set of terms such that each term is meaningful wrt to a domain and the set is exhaustive of such terms.
\Meaningfulness" is domain and application speci c.
De nition 2. A terminology T is a coordination of another terminology T' just in case there is a function, f , which is a recursive de nition of T' with the base cases all lying in T and T' V. We call f the coordinating or coordination function. We call T 0 the basis of the coordination or the coordinated terminology.
In the most natural instance, a term is a string and a canonical coordinating function constructs a new term by concatenating the old ones. For our current purposes, it su ces to be this narrow.
Clearly, a coordination can, but does not have to, contain its basis. It may also only contain part of its basis. For example, a terminology might not contain left on its own even though left is part of its basis. For the target application, left might not be meaningful on its own. Furthermore, we can arrange coordinations in a partial order and there is always the possibility of exactly capturing V.
De nition 4. A coordination, T , is saturated or fully coordinated if T = V.
A saturated coordination might still be extensible, i.e., there are still desired terms not in the coordination, but any extension requires an extension to the basis. It is highly likely that few terminologies are saturated, especially if we allow for all clinically meaningful, i.e., sanctionable terms.
De nition 5. The coordination factor (relative to a basis) of T is the size of T / the size of the basis.
It might be the case that there are several possible bases or that the true basis is unknown. In the rst case, a given coordination factor might not be determinate. In the second case, it might not be precise.
It is possible that we have the following situation: 1. There is a basis, B 2. a terminology, T , which is what is physically manifested and delivered, 3. another terminology Ttotal, which is the complete set of terms for the application or domain (i.e., Ttotal, is saturated) where B T Ttotal. In this case, T is partially pre-coordinated (since it is less coordinated than its saturation). The pre-coordinated terms might be the most frequently used, or the most convenient for use, or they might form a more intuitive basis of the full coordination. Speculatively, we might expect that the coordination factor (relative to B) of Ttotal to be an order of magnitude greater than that of T in a nicely designed system. 3.2
Approach for estimating level of coordination in medical terminologies
It is not immediate how to determine the amount of coordination in a given terminology,
especially if we are aiming at the inherent amount of coordination. This requires determining the
smallest basis for the terminology and even highly factored systems may not be minimal. In more
typical cases or in highly pre-coordinated terminologies, the basis may never have been made
explicit. Estimates for the size of the basis of medical terminologies have varied widely between
20,000 and 1,000,000 [
However, we can attempt to estimate the amount of coordination in existing terminologies by parsing and analysing the terms explicitly present in the terminology. To obtain loose lower and upper bounds of the size of the basis for each terminology, we have analysed the full descriptions of the terminologies listed in Table 1 using two di erent approaches, described in the following. For the purpose of this analysis we were only interested in the level of coordination of the core terms of each terminology, therefore chose to ignore synonyms that are available for some of the terminologies analysed. Approach 1: We have tokenized the descriptions by breaking them up into separate tokens using the Apache Lucene1 standard tokenizer. On the one hand, this approach results in single tokens to be considered as part of the basis that domain experts would potentially not consider to be part of the basis (e.g., stop words, such as 'of', 'the', 'in', and words that do not make sense on their own in the context of the terminology, e.g., 'due', 'using', or 'object'). On the other hand, concepts that domain experts might consider to be part of the base, but that consist of multiple tokens are missed (e.g., 'blood group', 'cardiac arrest', or 'foreign body').
Approach 2: Some stop words, such as 'of', 'and', 'with', or 'by'2 and punctuations, such as ',', can be considered as indicators for pre-coordination of a term. Following this intuition, we have broken up the descriptions into the parts that are separated by any of these stop words and commas while excluding these words from the basis. Following this approach, for example, the term 'entire superior segment of left lower lobe of lung', a term specifying a body structure in SNOMED CT, is broken up into 'entire superior segment', 'left lower lobe', and 'lung'. However, if laterality, such as 'left' and 'right' is considered to be part of the basis, 'left lower lobe' could further be broken up into 'left' and 'lower lobe', the latter of which could potentially be further broken up into 'lower' and 'lobe'. Examples where this approach is successful in identifying what could be considered atomic concepts include 'fracture of pelvis' (i.e., 'fracture', 'pelvis') in NCIt, 'incision and drainage of perianal abscess' (i.e., 'incision', 'drainage', 'perianal abscess') procedure in SNOMED CT, or 'removal of drainage device from lower back, percutaneous endoscopic approach' (i.e., 'removal', 'drainage device', 'lower back', 'percutaneous endoscopic approach') procedure in ICD-10-PCS.
For each terminology, we then identi ed the set of unique terms or atomic concepts, i.e., the basis B of the terminology produced by each of the two approaches. Once we have the size of the basis, it is easy to determine the coordination factor of the terminology (see De nition 5).
In addition to the coordination factor itself, there are other measures that can provide indications of the level of coordination of the terminologies. These include the length of the descriptions with respect to the number of tokens or atomic concepts of the base, and the usage of the tokens or atomic concepts of the base, i.e., how many of the concepts in the base are used in the pre-coordinated terms and how often they are used. In case of the former, longer terms suggest higher levels of coordination, and for the latter, more frequent usage of a greater number of concepts of the base also suggest higher levels of coordination. In contrast, in a predominantly post-coordinated terminology, the average length of the descriptions would be expected to be fairly short and none or very little re-use of the concepts of the base would be expected.
To evaluate the length of the descriptions, we have calculated the distribution of terms with a particular number of tokens as identi ed using the rst approach as well as the maximum, median and average number of atomic concepts in terms as determined by approach 2. To determine the usage of the concepts in the basis, we have calculated the maximum, median and average occurrence of tokens and atomic concepts determined by both approaches, as well as the number and percentage of tokens that appear only in a single term, along with the average length of those terms with respect to its number of tokens. We expect that not all members of the base contribute equally to the pre-coordination of a terminology, i.e., some tokens might appear more frequently than others and a number of them might only be used once. In the case of terminologies that support post-coordination, some of the tokens that appear only once might be atomic concepts to be used for post-coordination, but others might be tokens that are only used very rarely. To 1 http://lucene.apache.org 2 complete list: f"and", "at", "by", "for", "from", "in", "into", "no", "not", "non", "of", "on", "or", "with", "within", "without"g gain an insight into the change in level of coordination of a terminology during its life cycle, we have analysed the coordination factor and the sizes of the base (using approach 1) and the whole explicit terminology of 115 versions of the NCI thesaurus released almost every month between late 2003 and July 2013.
Unfortunately, determining the saturated coordination is not possible without out of band
knowledge of the coordinating function. This might be given by a set of rules or by examining
the pattern of use in a large application. It is not clear whether we can give an interesting loose
estimation: If we allow arbitrary repetition of base terms in coordinated terms, then we have
an in nite number of possible terms. If we disallow repetition, the total possible set of terms is
exponential in the size of the basis. It is highly unlikely that the true saturated coordination is
remotely close in size to the potential term space, as most combinations of terms from the basis
will be clinically nonsensical [
Where available, we collected the OWL representation of ontologies (SNOMED CT, NCIt, FMA,
and Gene Ontology), in all other cases we collected the source les from the terminologies listed
in Table 1. The terminologies are grouped according to their contents, with the rst group
containing SNOMED CT and NCI thesaurus (NCIt) representing general terminologies. The second
group covers diagnosis descriptions and contains ICD-9-CM, ICD-10-CM and the corresponding
subsets disorder and ndings of SNOMED CT as well as the Clinical Observations Recording
and Encoding (CORE) subset [
The distributions of terms with a certain number of tokens as determined using approach 1 are shown in Figure 2. The increase in the length of the terms in ICD suggest an increase in the level of coordination in both cases, ICD procedure and diagnosis between the last release of ICD-9 in 2012 and the most recent release of ICD-10. Di erences can also be observed between the CORE subset of SNOMED CT and the corresponding whole set of terms as illustrated in the case of SNOMED CT and CORE SNOMED CT, as well as the corresponding subsets for disorder and nding, with the terms in the CORE subset tending to be shorter, and potentially less coordinated. A comparison of the distributions of tokens of a particular length between SNOMED CT in Figure 2 and NCIt in Figure 4, NCIt appears to be less coordinated.
The results of the analysis of the size of each terminology as well as the size of the corresponding basis, the median and maximum length of the terms and the coordination factor with respect to the basis determined using both approaches 1 and 2 are shown in Table 2. Table 3 presents the results of the usage analysis of the terminologies, i.e., how many members of the base occur in how many terms and how many members of the basis occur only once.
Considering that SNOMED CT supports and encourages post-coordination, its
coordination factor is perhaps higher than expected, in particular when compared to pre-coordinated
terminologies such as LOINC. However, evaluations of SNOMED CT suggest that it contains a
mixture of pre-coordinated terms and atomic terms that can be post-coordinated (e.g., [
SNOMED CT disorder CORE SNOMED CT disorder
ICD-‐9 2012 diagnosis ICD-‐10-‐CD 2014 diagnosis SNOMED CT
CORE SNOMED CT
SNOMED CT finding CORE SNOMED CT finding ICD-‐9 2012 procedure ICD-‐10-‐PCS 2014 procedure 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 18.00% 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Fig. 2. Distribution of terms with a certain number of tokens, x-axis: number of tokens, y-axis: percentage of terms in the terminology with number of tokens 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 SNOMED CT disorder
SNOMED CT finding 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
ICD diagnosis Terminology
An observation that applies to both terminologies for which subsets of frequently used terms could be obtained (SNOMED CT and LOINC) is that the coordination factor of the frequently used terms are signi cantly lower than those of the whole terminology, even when the corresponding subsets for the categories in SNOMED (disorder and nding) are considered. In the case of SNOMED this could suggest that the most frequently used terms are atomic concepts that are being post-coordinated, however, as LOINC does not support post-coordination, this does not apply to LOINC.
A signi cant increase in the coordination factor can be observed for both, the diagnosis and
the procedure codes between ICD-9 and ICD-10, with the former increasing from 2.48 to 12.79
and the latter from 1.80 to 53.51 (for approach 1) with the base decreasing in size in the case
of the latter. ICD-10 aims to contain an as complete as possible list of variations of diagnoses
and procedures, with, in particular the procedures being descriptions of the procedures rather
than their names [
In contrast, the percentage of those that occur only in a single term is surprisingly high across the majority of the other terminologies (around 50%) with the median length of the terms in which these rarely used tokens appear suggesting that these are not only atomic concepts to be used for post-coordination, which is only supported by SNOMED CT. 25,000" 20,000" 15,000" 10,000" 5,000"
Number'of'terms'with'' a'given'length'of'' numbers'of'tokens'
The results of the analysis of the NCI thesaurus, namely the observed change in coordination factor, increase in size of the base as well as the whole terminology and the changes in the distribution of terms with a particular number of tokens are shown in Figures 3 and 4. In comparison to the change in coordination factor observed between ICD-9 and ICD-10, the coordination factor of NCIt does not change signi cantly over time. However, the plot of the coordination factor over time on the left hand side of Figure 3 suggests that e orts are being undertaken to reduce the level of coordination of NCIt, which is followed by an increase of the co-ordination factor, most likely due to new terms being added to the NCI thesaurus. The reductions in the level of coordination do not correlate with signi cant reductions in the size of the terminology or the length of the terms, as can be seen by the steady increase of both (see on the right hand side of Figure 3 and Figure 4). 5
The key advantage of our technique for determining the coordination factor along with
supporting measures providing indications for the level of coordination is that it is done completely
analytically and computationally. No domain expertise or manual inspection of a sample of
terms (a la [
The coordination level has previously been suggested as a quality measure for terminologies
[
Di erent levels of coordination in di erent terminologies have also been shown to cause issues
or require additional work when mapping between terminologies (e.g., [
In case of terminologies that are being adapted from pre-coordinated to post-coordinated terminologies, the measures presented here enable a continuous assessment of the progress made in the conversion process.
As the analysis presented here suggests that most commonly used terms have a lower coordination factor than the terminology, highly coordinated terms might deserve some analysis to determine the reasons for their limited usage and whether they could be removed from the terminology or whether they are pre-coordinated terms of post-coordinated most commonly used terms.
In addition to having a measure for assessing the level of coordination in terminologies, the
basis that is obtained as part of the process presented here, can also be utilised further. The
analysis of the usage of the basis can highlight tokens or atomic concepts that are rarely used,
and perhaps deserve further analysis to decide whether they should be included in the basis, or
whether some pre-coordinated terms have been missed. The basis itself could prove useful for
the maintenance and development of the terminology. For example, an agreed canonical basis
of the preferred names for the atomic concepts to be used with synonyms could be utilised to
ensure that the preferred term is used, and not one of the multiple synonyms. For example,
inconsistencies in term usage, such as in the ndings in SNOMED CT 'Amputated big toe' and
'Cock-up deformity of great toe' where the big toe is called big toe in one nding and great toe in
the other nding. The same inconsistency can be observed in FMA, e.g., 'Dorsal surface of great
toe' and 'Eponychium of big toe'. Other examples include the representation of ordinal numbers,
which are written out in some terms and written as numbers in other terms within the same
terminology. This inconsistent usage could be one reason for the observed high percentage of
rarely used tokens in the basis. In NCIt, the following terms can be found: 'Cardiac Arrest' and
'CTCAE Grade 5 Asystole'. Using the Uni ed Medical Language System (UMLS) [
In addition to the basis, a coordination function could furthermore help to ensure that the order in which the pre-coordinated complex terms are created is consistent, e.g., in ICD-10, a diagnosis called 'Abrasion, left great toe' can be found, with the laterality associated with the great toe, without the explicit mention of the foot to which the great toe belongs. In contrast, the diagnosis called 'Fused toes, left foot' lists the corresponding foot and assigned the laterality to the foot rather than the toes. These inconsistencies make maintenance and usage of terminologies harder, and could be avoided with the identi cation and then usage of coordination functions.