**7. Examples of quality indicators in the representation system**

A quality indicator is a barometer to evaluate a medical service. We regard it as a combination of an objective graph and a quantifying concept. In this subsection, we describe one of the typical quality indicators "stomach cancer 5-year survival rate" with objective graphs and a quantifying concept. This indicator is defined to be the rate of the number of patients diagnosed with stomach cancer surviving 5 years after diagnosis among the number of patients diagnosed with stomach cancer. Thus, the numerator and the denominator of the indicator can be described to be objective graphs � and �\* in Figure 6 and Figure 7, respectively. Thus, one can describe the quality indicator by using �, �\*, and the quantifying concept ⫷cardinality rate⫸ as the graph in Figure 8 on the next page.

We will show another example of a quality indicator "the average length of the hospital stays for stomach cancers". The following figure denotes a set of hospital stays for stomach cancer treatments that have stomach cancer operations by laparotomies.

206 Semantics – Advances in Theories and Mathematical Models

For a finite set S and a subset S\* of S, the rate of the total number of S\* among the total numbers of S obtained in the same way as that to calculate the total number of S\* is called a rate of S\* among S. In particular, the rate of the cardinality of S\* among that of S is called the cardinality rate of S\* among S. Moreover, the rate of the total attribute number of S\* with respect to *A1,..., An* and *f* among that of S with respect to the same attributes and the same

The quantifying concept ⫷cardinality rate⫸ is regarded as a function that has the following

In contrast, the quantifying concept ⫷total attribute number rate⫸ is regarded as a function

⫷total attribute number rate⫸ outputs the rate of the total attribute number of [[�]] with respect to *A1,..., An* and f among that of [[�\*]] with respect to the same attributes and the

For concept S, attributes *A1,..., An* of S, and attribute quantifier function f, the ratio of the total attribute number of S with respect to *A1,..., An* and f and the cardinality of S is called the average of the value of S with respect to *A1,..., An* of *f*. The quantifying concept ⫷average⫸ is regarded as a function that has the same input data as that of ⫷total attribute number⫸

A quality indicator is a barometer to evaluate a medical service. We regard it as a combination of an objective graph and a quantifying concept. In this subsection, we describe one of the typical quality indicators "stomach cancer 5-year survival rate" with objective graphs and a quantifying concept. This indicator is defined to be the rate of the number of patients diagnosed with stomach cancer surviving 5 years after diagnosis among the number of patients diagnosed with stomach cancer. Thus, the numerator and the denominator of the indicator can be described to be objective graphs � and �\* in Figure 6 and Figure 7, respectively. Thus, one can describe the quality indicator by using �, �\*, and the quantifying concept ⫷cardinality rate⫸ as the graph in Figure 8 on the next page.

We will show another example of a quality indicator "the average length of the hospital stays for stomach cancers". The following figure denotes a set of hospital stays for stomach

and that outputs the average of the value of S with respect to *A1,..., An* of *f*.

**7. Examples of quality indicators in the representation system** 

cancer treatments that have stomach cancer operations by laparotomies.

attribute quantifier function is called the total attribute number rate.

**6.2 Rate** 

data as input data:

1. An objective graph �, and 2. A segment �\* of �.

1. An objective graph �, 2. A segment �\* of �,

**6.3 Average** 

that has the following data as input data:

4. *f*: *C1*⨯...⨯*Cn*→*R*,, where *Ci* := {*s.Ai*|s∈[[�]]}.

3. Attributes *A1,..., An* of C(�), and

same attribute quantifier function.

Fig. 8. Quality indicator "Stomach cancer 5-year survival rate".

Fig. 9. Objective graph describing Hospital stays for stomach cancers.

To be more precise, Figure 9 denotes the set of hospital stays that have admissions with purposes treatments of stomach cancers and operations for stomach cancers by laparotomies. By using the objective graph above, the quantifying concept ⫷average⫸ (cf. Section 6.3) and a function that assigns to two dates the number of days between the two dates, one can obtain the quality indicator "the average length of the hospital stays for stomach cancers", as follows.

Fig. 10. Quality indicator "The average length of the hospital stays for stomach cancers"

In Figure 10, the objective graph in Figure 9 is the first input data of ⫷average⫸, two attributes ⟨starting time point⟩ and ⟨terminating time point⟩ of the concept [hospital stay] are assigned as second input data of ⫷average⫸, and the function that assigns to two dates the number of days between the two dates is the third input data of ⫷average⫸ (see Section 6.3).

Representation System for Quality Indicators by Ontology 209

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

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

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,

Starting time point (starting time point)

Date

(occurring time point)

Event (terminating event)

*Rs1 E1* stomach cancer *Rs2 E2* stomach cancer *Rs3 E3* stomach cancer *Rs4 E4* gastric ulcer *Rs5 E5* stomach cancer *Rs6 E6* gastric varices *Rs7 E6* duodenal ulcer *…* … …

Diseases (the range of result)

Terminating time

Truth value (service)

(terminating time

point

point)

Diagnosis (diagnosis)

concept [sate of life or death] in Figure 4, as follows.

Event (starting event)

Result (result)

State of life or death (state of life or death)

its attributes.

as follows.

Patient

(subject (of an event))

… … …

*F1 P2* 11-10-2011 *F2 P5* 12-12-2011

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.

Death (death) Patient (subject (of a state))
