**1. Introduction**

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> We have not yet established a proper methodology to accurately evaluate the quality of medical services, although such a method is necessary for fair comparison between hospitals and/or improvement in the quality of medical services. The reason is that such a methodology needs a reasonable way to transform qualitative properties of medical services such as doctors' skill or patient satisfaction into quantitative properties that are measurable by data existing in medical databases, but, it has not yet been researched sufficiently. In general, it is not easy to fairly evaluate abstract things such as intelligence and performances by measuring quantitative aspects of them although we often have opportunities to evaluate such things. Moreover, even though we have quantitative properties denoting some useful properties, we need a proper method to accurately represent such quantitative properties in order to make users understand the definitions of the properties correctly.

> In this chapter, we introduce a representation system of quality indicators. Quality indicators are barometers that indicate processes, results and/or other things of medical services numerically, in order to evaluate medical services. The representation system helps to define quality indicators and to calculate their values in a coherent manner that is based on the data in medical databases. The representation system primarily consists of three parts. The first one is an ontology to define concepts related to medical services. The second one is a set of graphs that express the targets of quality indicators. We call these graphs "objective graphs". The third one is a set of "quantifying concepts" that abstract the quantities of the subjects. The proposed system represents a quality indicator as a combination of an objective graph and a quantifying concept.

> An objective graph can be interpreted as a set of instances of a concept. The set is defined by the properties described by the labels of the arrows in the graph. We also explain the interpretation of objective graphs for the sets in this paper.

The representation language provides the following advantages.

 The first advantage is that by representing a quality indicator with the representation system one can avoid the problem that occurs from a word in the quality indicator that

Representation System for Quality Indicators by Ontology 195

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

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

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

knowing structures of local medical databases.

and the mappings.

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 word in a quality indicator.


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

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 proposed representation system of quality indicators.

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