**8. Calculation of values of quality indicators based on medical databases**

In this section, we briefly explain how to calculate the values of quality indicators described in the representation system by using medical databases. One can obtain an entityrelationship model (Chen, 1976) from the medical service ontology in Section 3 by translating concepts to entities and the properties between them to the relationship between entities obtained from the given concepts. Moreover, by translating the attributes of a concept to those of the entity translated from the concept, one can obtain a relational data model, which we call the global data model (GDM) of medical service ontology. In this paper, we often call an entity in GDM by a "table" and an attribute of an entity by a "column" of a table.

For example, a concept [diagnosis] of a scheduled event that is described in Figure 5 is translated to an entity in GDM, that is, it is translated to (a list of columns of) a table, as follows.


Table 3. Modification of the table 1.

Here, the parenthetic name of a column of the table above denotes the concept or one of its attributes. The columns of this table are obtained from the concept [diagnosis] and its attributes whose values (instances) are uniquely determined by an instance of [diagnosis], and the column "Diagnosis" is the primary column (the primary key) of the table. The list of columns of Table 3 is obtained from the list of all columns of Table 1 in Section 5.2 by removing the column generated from the attribute ⟨result⟩, which may have multiple values of a single diagnosis (an instance of [diagnosis]). Each attribute of a concept that may have multiple values of a single instance of the concept is translated to (a list of columns of) a table whose primary key is the attribute. For example, the attribute ⟨result⟩ is translated to the list of columns in the following table.

208 Semantics – Advances in Theories and Mathematical Models

In this section, we briefly explain how to calculate the values of quality indicators described in the representation system by using medical databases. One can obtain an entityrelationship model (Chen, 1976) from the medical service ontology in Section 3 by translating concepts to entities and the properties between them to the relationship between entities obtained from the given concepts. Moreover, by translating the attributes of a concept to those of the entity translated from the concept, one can obtain a relational data model, which we call the global data model (GDM) of medical service ontology. In this paper, we often call an entity in GDM by a "table" and an attribute of an entity by a

For example, a concept [diagnosis] of a scheduled event that is described in Figure 5 is translated to an entity in GDM, that is, it is translated to (a list of columns of) a table, as

*E1 P1* 03-11-2011 *D1* - - - *E2 P2* 03-15-2011 *D1* - - - *E3 P3* 04-06-2011 *D2* - - - *E4 P4* 05-08-2011 *D2* - - - *E5 P2* 06-09-2011 *D2* - - - *E6 P5* 07-06-2011 *D1* - - - … … … … … … …

Here, the parenthetic name of a column of the table above denotes the concept or one of its attributes. The columns of this table are obtained from the concept [diagnosis] and its attributes whose values (instances) are uniquely determined by an instance of [diagnosis], and the column "Diagnosis" is the primary column (the primary key) of the table. The list of columns of Table 3 is obtained from the list of all columns of Table 1 in Section 5.2 by removing the column generated from the attribute ⟨result⟩, which may have multiple values of a single diagnosis (an instance of [diagnosis]). Each attribute of a concept that may have multiple values of a single instance of the concept is translated to (a list of columns of) a table whose primary key is the attribute. For example, the attribute ⟨result⟩ is translated to

Staff (agent) Term (content) Device (with what) Method (how)

Date (occurring time point)

**8. Calculation of values of quality indicators based on medical databases** 

"column" of a table.

follows.

Diagnosis (diagnosis) Patient

Table 3. Modification of the table 1.

the list of columns in the following table.

(subject (of an event))


Table 4. The table generated from the attribute of the concept scheduled events [diagnosis].

As another example of a table, we describe the list of columns of a table generated from the concept [sate of life or death] in Figure 4, as follows.


Table 5. The list of columns generated from the concept of states [state of life or death] and its attributes.

The data of tables in GDM generated from the medical service ontology is obtained from data in (real) medical databases. The data of each table is obtained by one of two ways: the first way is to define mapping functions between the table and those in medical databases; the second is to define the way to calculate data from other tables in GDM plus medical databases. For example, in many cases, data of Table 3 and Table 4 is obtained by a mapping function between the tables and those in medial databases and such a mapping function can be simply defined, since most of data models in medical databases have similar tables to them. On the other hand, many medical databases should not have any table similar to Table 5. Instead of defining a mapping function between such a table and some tables in medical databases directly, one had better consider a way to calculate data from other tables in GDM (and medical databases). For example, one can obtain data of important columns of Table 5 from the table generated from the concept [death] of unscheduled event in Figure 5, as follows.


Table 6. The table generated from the concept [death] and its attributes.

For example, one can obtain data of Table 5 from Table 6, as follows.

Representation System for Quality Indicators by Ontology 211

more than 5 years after the date of an event of diagnosis" in a coherent way, which is not

It is important to fairly evaluate or compare the qualities of medical services that hospitals provide in order to improve the services. To this end, the qualities of medical services must be identified and adequate methods must be found to measure these qualities accurately (Donabedian, 1966). Quality indicators, which are quantitative criteria for the evaluation of medical services, have been attracting attention (Mainz, 2003). Many quality indicators already have been defined by standards organizations and projects such as IQIP (IQIP,

However, as we mentioned in Section 1, although many good quality indicators have been developed, at least the following two issues remain for using quality indicators to fairly

The first issue is that, while many quality indicators (of medical services) are defined by terms in relation to medical care, many medical databases are developed from the aspect of accounting management. Moreover, many medical databases are developed in the vendors' or hospitals' own schema. Therefore, to calculate the values of quality indicators or to define them, it is often necessary for medical staffs to collaborate with system engineers who manage or developed the medical databases. However, the gaps in their knowledge and viewpoints often prevent them from collaborating to calculate the values of quality

The second issue is that many words for medical services have meanings that differ according to the hospital or community of the medical staff. For example, at least in our country, the meaning of "new patients" or "inpatients" sometimes differs according to the medical staff in some hospitals, even though the hospitals may belong to the same hospital group. Such different interpretations of words also prevent medical staffs from coherently

The proposed representation system of quality indicators helps to define quality indicators and calculate their values in a coherent manner that is based on the data in medical

It is important to describe quality indicators that have no ambiguity of interpretation and to calculate their values accurately in a coherent way. To this end, we introduce a representation system of quality indicators, which consists of (i) an ontology of medical services, (ii) objective graphs to represent the objectives of quantification and an interpretation of objective graphs as sets, and (iii) quantifying concepts. We also briefly explain the whole image of our theoretical framework to define quality indicators and to calculate their values. Moreover, we explain a way to calculate the values of quality

indicators based on the medical databases through an example of a quality indicator.

calculating accurate values of the quality indicators among multiple hospitals.

2011), MHA (Scheiderer, 1995), and OECD (Mattke et al, 2006).

evaluate and compare medical services among hospitals.

indicators and/or to define them accurately.

difficult to establish.

**9. Related works** 

databases.

**10. Conclusion** 


Table 7. Data generated from the data of Table 6.

By the interpretation of Section 5, one can perform a query on the GDM from a given objective graph ॳ by translating the condition of [[ॳ]] in a way based on relational calculus (Abiteboul et al, 1995), since the condition of [[ॳ]] is defined as a formula in first-order logic on the concepts and properties, and all properties are so simple that one can translate them to queries on the GDM automatically. Therefore, for a given medical database MD, if one has a suitable mapping between the data model on the MD and the GDM, one can automatically calculate the value of quality indicators based on the data in the MD.

For example, we calculate the value of the quality indicator "stomach cancer 5-year survival rate" in Section 7 based on data in Tables 2, 3, 4 and 7. Let ॳ be the objective graph of Figure 6 in Section 4.2, and let ॳ\* be the objective graph in Figure 7. Thus, by the definition of the interpretation of objective graphs in Section 5, [[ॳ]] and [[ॳ\*]] can be considered to be sets of tuples in the table generated from the concept [patient], that is, Table 2 in Section 3.2. Moreover, they are calculated by using Tables 2, 3, 4 and 7, as follows.



 = {*tuple2 <sup>1</sup>*, *tuple2 <sup>3</sup>*}, where each tuple*<sup>2</sup> <sup>i</sup>* denotes the tuple in Table 2 (see 5.2).


= {*tuple21*, *tuple22*, *tuple23*}.

Thus, the value of "stomach cancer 5-year survival rate" is calculated to be 2/3.

Note that all condition expressions in the queries above besides (\*) are directly translated from the definitions of [[ॳ]] and [[ॳ\*]]. On the other hand, the condition expression (\*) is obtained from the condition "the date of the state of life or dead with truth value true is more than 5 years after the date of an event of diagnosis" in a coherent way, which is not difficult to establish.
