**9. Related works**

210 Semantics – Advances in Theories and Mathematical Models

Starting time point (starting time point)

Terminating time

Truth value (service)

(terminating time

point

point)

Event (terminating event)

*S1 P2* - *F1* - 11-09-2011 True *S2 P2 F1* - 11-10-2011 - False *S3 P5* - *F2* - 12-11-2011 True *S4 P5 F2* - 12-12-2011 - False … … … … … … …

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

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.

automatically calculate the value of quality indicators based on the data in the MD.

Table-7.Starting-time-point < Table-3.Date + "5-years" (\*)

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

*<sup>i</sup>* denotes the tuple in Table 2 (see 5.2).

Moreover, they are calculated by using Tables 2, 3, 4 and 7, as follows.

 Table-2.Patient=Table-3.Patient and Table-3.Diagnosis=Table-4.Diagnosis and Table-4.Disease="stomach cancer" and

 Table-2.Patient=Table-7.Patient and Table-7.Truth-value="False" and

 Table-2.Patient=Table-3.Patient and Table-3.Diagnosis=Table-4.Diagnosis and

Not exists \* from Table-7 where

*<sup>1</sup>*, *tuple23*}, where each tuple*<sup>2</sup>*

Table-4.Disease="stomach cancer"

*<sup>3</sup>*}.

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

Patient (subject (of a state))

[[ॳ]] = select \* from Table-2 where

[[ॳ\*]] = select \* from Table-2 where

*<sup>1</sup>*, *tuple22*, *tuple2*

= {*tuple2*

= {*tuple2*

Event (starting event)

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

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

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 evaluate and compare medical services among hospitals.

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 indicators and/or to define them accurately.

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 calculating accurate values of the quality indicators among multiple hospitals.

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 databases.
