**2. Framework for definition and calculation of quality indicators**

We first show a whole image of the framework for definition and calculation of quality indicators.

From the user's point of view, the framework consists of (I) a representation system of quality indicators, (II) medical databases in hospitals, and (III) mapping systems that connect a certain global data model with data models of real medical databases.

Figure 1 below indicates the relationship between the representation system, medical databases, mapping systems and stakeholders of the frameworks. Users of the framework, who intend to evaluate medical services of hospitals that are associated with the framework, first define quality indicators with the representation system. Quality indicators are described to be diagrams with nodes and arrows, which are concepts and properties defined in an ontology we call Medical Service Ontology (MSO). In order to define quality indicators with the representation system, knowledge engineers, medical staffs and system engineers of medical databases collaborate in developing MSO in advance. Concepts and properties in MSO are translated to a virtual data model called the Global Data Model (GDM), which is 194 Semantics – Advances in Theories and Mathematical Models

 The second advantage is that the representation language enables one to transform qualitative expressions into quantitative ones based on reasonable rationales and processes. The reasonable rationales and processes are provided by the fundamental

 The final advantage is that, since a quality indicator expressed by the representation language has the accurate semantics, one can calculate the value of the quality indicator via given medical databases. In this chater, we show a way to calculate the value of a

We finally introduce several examples of quality indicators that show that the representation language provides accurate and easily understandable expressions to quality

This chapter is an extended version of (Takaki et al., 2012), which is obtaiend from it by adding more detailed explanations and examples to demonstrate the working of the

The remainder of this chapter is organized as follows. Section 2 briefly explains our framework to define quality indicators and to calculate their values based on the data in medical databases. Section 3 explains an ontology called the "medical service ontology". Sections 4 and 5 explain objective graphs and their interpretation based on a set theoretic interpretation of graphs. Section 6 explains quantifying concepts. Section 7 introduces an example of a quality indicator in the proposed representation system. Section 8 briefly explains a way to calculate the values of quality indicators based on the medical databases.

We first show a whole image of the framework for definition and calculation of quality

From the user's point of view, the framework consists of (I) a representation system of quality indicators, (II) medical databases in hospitals, and (III) mapping systems that

Figure 1 below indicates the relationship between the representation system, medical databases, mapping systems and stakeholders of the frameworks. Users of the framework, who intend to evaluate medical services of hospitals that are associated with the framework, first define quality indicators with the representation system. Quality indicators are described to be diagrams with nodes and arrows, which are concepts and properties defined in an ontology we call Medical Service Ontology (MSO). In order to define quality indicators with the representation system, knowledge engineers, medical staffs and system engineers of medical databases collaborate in developing MSO in advance. Concepts and properties in MSO are translated to a virtual data model called the Global Data Model (GDM), which is

word in a quality indicator.

indicators.

indicators.

theory of quantifications of concepts.

quality indicator that is expressed by our language.

proposed representation system of quality indicators.

Section 9 explains related works, and Section 10 concludes this chapter.

**2. Framework for definition and calculation of quality indicators** 

connect a certain global data model with data models of real medical databases.

has multiple meanings. In fact, we use a lot of words, each of that has multiple meanings. For example, the word "the first visit" has the meaning that differs among hospitals. So, we need to clarify the meanings of the words that constitute quality indicators, and the representation language enables one to clarify the meaning of each translated to data models in medical databases in hospitals by the mapping system. In order to calculate values of quality indicators defined by the representation system, they are translated to query programs of tables (=data models) of medical databases through a certain interpretation and mappings in mapping systems. In many cases, the mapping systems are developed by system engineers who maintain the medical databases. By using the framework, users can define quality indicators and calculate the values of them without knowing structures of local medical databases.

Fig. 1. Whole image of the framework for definition and calculation of quality indicators.

From a theoretical point of view, the framework consists of (i) the representation system, (ii) interpretations of components of the representation system, and (iii) several mappings that connect a database schema generated from MSO defined in the next section and other database schemas of given medical databases (see also Section 8). Also the representation system consists of (i) Medical Service Ontology, (ii) objective graphs, and (iii) quantifying concepts. Figure 2 below indicates how to define quality indicators and calculate values of them based on the representation system, the interpretations and the mappings.

A quality indicator is represented to be a graph obtained by combining objective graphs and a quantifying concept. An objective graph is a graph that expresses a set of patients, events (in a hospital) or other things such as "a set of patients who had operations for stomach cancers" or "a set of operations on patients with stomach cancers". An objective graph is constructed based on vocabularies in MSO. On the other hand, a quantifying concept is a function from a concept or a set of instances of a concept that is expressed by an objective graph to a numerical value. For example, a quality indicator "average length of hospital stays of patients who had operations for stomach cancers" is represented by an objective

Representation System for Quality Indicators by Ontology 197

developed based on an ontology developing tool called the "Semantic Editor" (Hasida,

We first define concepts in the medical service ontology. Concepts in MSO are used as vocabularies to describe quality indicators. Many quality indicators are described as the number, the rate or the average of (a) set(s) of patients or events in hospitals that are in a state. Moreover, many patients, events and states (of patients) can be characterized by them. Thus, concepts of stakeholders (especially, patients), events and states (of patients) are

We introduce main concepts in MSO, as follows. Because of space limitations, we define some main concepts only. We describe a concept by the [name of a concept]. The concepts

[hospital admission], [hospital discharge],[diagnosis], [medical examination], [test],

[number of years], [number of months],[number of weeks], [number of days]

A concept can be regarded as a set of instances of a given concept. Thus, we often identify

2011).

**3.1 Concepts** 

particularly important.

below are indicated by brackets.

2.1. Concepts of events with terms: [hospital stay], [hospital visit] 2.2. Concepts of events with no terms 2.2.1. Concepts of scheduled events:

[operation], [prescription]

[death], [bedsore], [falling]

4. Concepts of organizations: [department], [facility], [hospital]

3. Concepts of states:

5. Concepts of items:

6. Concepts of methods:

7. Concepts of diseases:

 8.1. Concepts of time points: [date], [clock time] 8.2. Concepts of terms:

 [disease] 8. Concept of time

2.2.2. Concepts of unscheduled events:

[state of age], [state of life or death], [state of disease]

[medicine], [clinical instrument], [medical device]

the concept [patient] with the set of instances of that patient.

[method], [cure], [method of examination]

1. Concepts of stakeholders: [patient], [medical staff] 2. Concepts of events

Fig. 2. Representation Language of Quality Indications and their values.

graph that expresses a set of hospital stays of patients who had operations for stomach cancers and a quantifying concept that calculate the average of length of the hospital stays for a given set of hospital stays.

In a coherent manner, concepts and properties in MSO are translated to tables or columns in them in GDM. Also an objective graph is translated to a query on GDM through a mathematical interpretation defined in Section 5. Moreover, by mappings between GDM and data models of local medical databases, tables and queries on GDM are translated to those in the local medical databases. On the other hand, a quantifying concept is translated to an algorithm to enumerate tuples of the tables that are obtained to be the results of the tables and queries above and/or to calculate data of them. Finally, the value of a quality indicator is calculated to be the result of the algorithm, queries and data above.

In this chapter, we focus on the representation system of quality indicators.
