*2.2.1. Short-term research*

### *2.2.1.1. Time study*

A continuous 24-hour researcher-administered time study was conducted over a total of fif‐ teen days during 1999 and 2000 in a gastrointestinal surgical ward in a university hospital. Of the various forms of time study techniques we adopted the researcher-administered method for the present study because on the basis of the characteristics of the ward studied, we judged that there were limits to the extent to which nurses on duty would themselves be able to keep a record of the content of the tasks in the intervals between the tasks they per‐ formed. The survey was conducted in relation to all three work shifts: 'night shift,' 'day shift' and 'evening shift.' The total number of nurses observed was 69 (Table 1).


**Table 1.** Time study period and subjects.

The ward studied was a fifty-bed ward with a staff of 23 nurses, including the head nurse. The average number of staff actually on duty on weekdays was 8.6. The ward's nursing sys‐ tem combined a three-module organization, under which ward nursing staff were divided into three groups, A, B and C, and a 'primary nursing' model, under which the same nurse was responsible for a given patient throughout, from admission to discharge (Fig. 2). When the primary nurse was not on duty, a nurse from the same group took responsibility for the patient. Information was gathered during the period of the survey on both the nurses being surveyed and the patients for whom they were responsible.

After completion of the time study, the task content recorded was coded in accordance with a specially created system of task classification and entered into a database. The nursing task classification was based on the Public Health Nurse, Midwife and Nurse Law [1948]. The four principal categories were 'clinical nursing,' 'consulting support nursing,' 'other nurs‐ ing,' and 'non-nursing tasks.' At the most detailed level, there were 92 headings altogether. The overall number of individual task action-units recorded was 46,775.

**Figure 2.** Module system and primary nursing model.

#### *2.2.1.2. Patient condition information*

responsible, and the severity of their conditions, would affect 'task times devoted to patients for whom the nurse is responsible'; second, that 'number of patients' in the nurse's charge and 'severity of their conditions' would be affected by 'number of patients by severity of condition' who were on the ward at a given time and 'number of nurses' actually available to carry out pa‐ tient care; and third, that 'number of patients by intensity of nursing care' would be affected by

**2.2. Computation of basic data required for a virtual environment based on short-term**

A continuous 24-hour researcher-administered time study was conducted over a total of fif‐ teen days during 1999 and 2000 in a gastrointestinal surgical ward in a university hospital. Of the various forms of time study techniques we adopted the researcher-administered method for the present study because on the basis of the characteristics of the ward studied, we judged that there were limits to the extent to which nurses on duty would themselves be able to keep a record of the content of the tasks in the intervals between the tasks they per‐ formed. The survey was conducted in relation to all three work shifts: 'night shift,' 'day

The ward studied was a fifty-bed ward with a staff of 23 nurses, including the head nurse. The average number of staff actually on duty on weekdays was 8.6. The ward's nursing sys‐ tem combined a three-module organization, under which ward nursing staff were divided into three groups, A, B and C, and a 'primary nursing' model, under which the same nurse was responsible for a given patient throughout, from admission to discharge (Fig. 2). When the primary nurse was not on duty, a nurse from the same group took responsibility for the patient. Information was gathered during the period of the survey on both the nurses being

After completion of the time study, the task content recorded was coded in accordance with a specially created system of task classification and entered into a database. The nursing task classification was based on the Public Health Nurse, Midwife and Nurse Law [1948]. The four principal categories were 'clinical nursing,' 'consulting support nursing,' 'other nurs‐

shift' and 'evening shift.' The total number of nurses observed was 69 (Table 1).

'patient outcomes' and 'number of patients admitted.

**research and long-term cumulative information**

*2.2.1. Short-term research*

216 Advances in Discrete Time Systems

**Table 1.** Time study period and subjects.

surveyed and the patients for whom they were responsible.

*2.2.1.1. Time study*

Patient condition information for each patient on the ward was collected and recorded daily throughout the fifteen days of the time study period. 'Patient condition information' means information that indicates a hospital patient's condition, such as how many times in the course of the day vital signs are checked, whether an artificial respirator is in use, or wheth‐ er there is any fever or bleeding. About 70 items are covered. Information collected during the day shift, at about 10 a.m., served as the base, and was incrementally updated for any patient who underwent an operation or other invasive procedure during the day shift and whose nursing intensity changed. The information recorded was entered into a database. Ultimately, the overall number of patient-shift units recorded was 2,015.

Nursing intensity, assessed daily by an experienced nurse, was included in patient condi‐ tion information. Nursing intensity is a method of classifying patient severity from two points of view – 'level of observation' and 'freedom of life' – that was proposed in 1984 in a report by the Study Group on Nursing Systems set up by the Ministry of Health, Labor and Welfare (formerly the Ministry of Health and Welfare) (Table 2). In the process of the present study, it was suggested that patient severity observations collected on the ward be‐ ing studied could be regarded as 'level of observation' for the purpose of assessing nursing intensity and these were used in carrying out our analysis.

By integrating the time study database and the patient condition information database on the basis of 'day of survey,' 'shift,' 'nurse ID' and 'patient ID,' we created a data set that made it possible to tell which nurse had spent how much time performing what tasks for patients in what condition. We assumed that among the task actions, subject patients would be available for nursing task classifications from 10101 to 301T1.

The names of nurses and patients included in the survey records, as well as any other items of information from which it would be possible to identify individuals, were all coded and only if this used for analysis after the information had been made secure.


sults were as follows. Average daily number of patients on the ward was 44.2, and the standard deviation (SD) was 2.3. The greatest number of patients on the ward at one time was 49, the smallest 42. The average number of patients for whom one nurse was respon‐ sible was 4.9. The largest number was 7, the smallest 3. A total of 281 patterns of change in nursing intensity was abstracted from the HIS information in relation to admissions to

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From the data set obtained by integrating time study data and patient condition informa‐ tion, we calculated, for individual nurses on the day shift, time spent on 'patients for whom the nurse is responsible,' time spent on 'other patients,' time spent on 'other duties' and 'rest time.' Results showed that the greatest amount of task time was spent on 'patients for whom the nurse is responsible.' Next came 'other patients' and 'other duties,' almost the same amount of time being spent on each. Average rest time was less than the 60-minute rest peri‐

the ward in question in the year 2000.

*2.3.2. Task times by purpose*

od stipulated by law (Table 3).

**Table 3.** Recorded statistical quantities for task times by purpose.

**Figure 3.** Correlations between task times by purpose.

**Table 2.** Nursing intensity.

#### *2.2.2. Long-term cumulative information*

#### *2.2.2.1. Information concerning patient outcomes*

In order to understand over-all patterns of change in nursing intensity for the patients on the ward being studied, we obtained information from the HIS (Hospital Information Sys‐ tem) under the headings 'date of admission,' 'date of discharge,' 'date of update ofnursing intensity,' and 'nursing intensity' covering the period from January 1, 2000, to December 31, 2000. This information was obtained in addition to the patient condition information gath‐ ered during the time study period.

'Pattern of change in nursing intensity' shows the outcome for a given patient. We defined it in terms of the number of days for which the patient was hospitalized and any changes in nursing intensity during that period. Pattern of change in nursing intensity varies according to individ‐ ual factors, such as the disease from which the patient is suffering, surgical procedures under‐ gone, and medical treatment. For example, patient J is in hospital for 3 days. On the first day nursing intensity is B, on the second day C, and again on the third day C. The pattern of change in nursing intensity for this patient is 'BCC.' Patient S is in hospital for four days. On the first two days nursing intensity is A, and on the remaining two days B. The pattern of change of nursing intensity for this patient is 'AABB.' It is no exaggeration to say that, except in the cases of patients where there is no clinical pathway variance, each individual patient exhibits a unique pattern of change in nursing intensity during the period of hospitalization.

#### **2.3. Basic data**

Basic data required for the creation of a virtual environment was calculated from a shortterm survey and a long-term cumulative information survey.

#### *2.3.1. Ward environment*

On the basis of time study data and patient condition information, we found recorded statistical values relating to the number of patients admitted to the ward studied. The re‐ sults were as follows. Average daily number of patients on the ward was 44.2, and the standard deviation (SD) was 2.3. The greatest number of patients on the ward at one time was 49, the smallest 42. The average number of patients for whom one nurse was respon‐ sible was 4.9. The largest number was 7, the smallest 3. A total of 281 patterns of change in nursing intensity was abstracted from the HIS information in relation to admissions to the ward in question in the year 2000.

#### *2.3.2. Task times by purpose*

**Table 2.** Nursing intensity.

218 Advances in Discrete Time Systems

**2.3. Basic data**

*2.3.1. Ward environment*

*2.2.2. Long-term cumulative information*

ered during the time study period.

*2.2.2.1. Information concerning patient outcomes*

In order to understand over-all patterns of change in nursing intensity for the patients on the ward being studied, we obtained information from the HIS (Hospital Information Sys‐ tem) under the headings 'date of admission,' 'date of discharge,' 'date of update ofnursing intensity,' and 'nursing intensity' covering the period from January 1, 2000, to December 31, 2000. This information was obtained in addition to the patient condition information gath‐

'Pattern of change in nursing intensity' shows the outcome for a given patient. We defined it in terms of the number of days for which the patient was hospitalized and any changes in nursing intensity during that period. Pattern of change in nursing intensity varies according to individ‐ ual factors, such as the disease from which the patient is suffering, surgical procedures under‐ gone, and medical treatment. For example, patient J is in hospital for 3 days. On the first day nursing intensity is B, on the second day C, and again on the third day C. The pattern of change in nursing intensity for this patient is 'BCC.' Patient S is in hospital for four days. On the first two days nursing intensity is A, and on the remaining two days B. The pattern of change of nursing intensity for this patient is 'AABB.' It is no exaggeration to say that, except in the cases of patients where there is no clinical pathway variance, each individual patient exhibits a

Basic data required for the creation of a virtual environment was calculated from a short-

On the basis of time study data and patient condition information, we found recorded statistical values relating to the number of patients admitted to the ward studied. The re‐

unique pattern of change in nursing intensity during the period of hospitalization.

term survey and a long-term cumulative information survey.

From the data set obtained by integrating time study data and patient condition informa‐ tion, we calculated, for individual nurses on the day shift, time spent on 'patients for whom the nurse is responsible,' time spent on 'other patients,' time spent on 'other duties' and 'rest time.' Results showed that the greatest amount of task time was spent on 'patients for whom the nurse is responsible.' Next came 'other patients' and 'other duties,' almost the same amount of time being spent on each. Average rest time was less than the 60-minute rest peri‐ od stipulated by law (Table 3).



**Figure 3.** Correlations between task times by purpose.

Fig. 3 shows that there was a strong negative correlation between time spent on 'tasks relat‐ ing to patients for whom the nurse is responsible' and time spent on 'tasks relating to other patients' and 'other tasks,' and that the correlation of 'rest time' with other task items was low. It appears at first glance that the correlation coefficient between 'tasks relating to other patients' and 'other tasks' is high at 0.727, but the partial correlation coefficient of the two is 0.019 and almost no direct correlation was observed. We were therefore able to judge that this was a spurious correlation influenced by 'tasks relating to patients for whom the nurse is responsible.' In other words, what this shows is that the relationship between the two is not such that when one increases the other decreases, but such that when time spent on 'pa‐ tients for whom the nurse is responsible' increases, the two decrease together.

nurse is responsible' as the dependent variable. When formulating a plan for the creation of a virtual environment, we entered the factor 'nursing intensity' as an independent variable on the assumption that task time devoted to patients for whom a nurse is responsible would be affected by patient severity. Bearing in mind that changes in shift time and in the number of nurses actually on duty on a shift would also have a great effect on care time devoted to

Investigation of a Methodology for the Quantitative Estimation of Nursing Tasks on the Basis of Time Study Data

The subject of analysis consisted of records, extracted from the data set created by integrat‐ ing time study data and patient condition information, which revealed responsibility rela‐ tionships between nurses and patients. The data extracted related to a total of 425 patients (a

patients, we included the factor 'shift' as well.

A multiple regression analysis model is generally formulated as

tween an intercept *β*0 in (1) and independent variables.

ducing randomness for each 'patient' with respect to the intercept.

formed with regard to the dependent variable.

*y* =*β*<sup>0</sup> + *β*1*x*<sup>1</sup> + ⋯ + *β<sup>p</sup> xp*

where *y* is a dependent variable, there are *p* independent variables {*xk* } that have fixed ef‐ fects and *ε* is margin of error. As opposed to this, Multilevel Analysis (Jones, 1991; Gold‐ stein, 2003) is a method of estimating parameters (coefficients) in which, by assuming random effects resulting from a given phenomenon *j*, it is possible to take into account inter‐ nal correlations between data with the same value for *j* in relation to the correlation {*β<sup>k</sup>* } be‐

Because the time study survey periods were continuous, the same patients were included in different shifts in the data set relating to 425 patients subject to analysis. This means that there were elements that affected the care time, which is a variable dependent on patient identity (i.e., there were internal correlations in the data), although it was difficult to treat these ele‐ ments as regular fixed effects, as in the case of the patient's bodily strength or personality.

In order to estimate parameters having variable effects that explained these internal correla‐ tions, we constructed, for the purposes of this study, a model for the estimation of task time devoted to patients for whom the nurse was responsible using Multilevel Analysis, intro‐

Rather than a model in which the actual care times are regressed in their original dimen‐ sions, we judged that the optimal model was one in which logistic conversion was per‐

Because it is a mathematical model for explaining task times, when the estimated expected value *y* is negative, there is a marked lack of conformance of the times. For this reason, it is

+ *ε* (1)

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total of 57 nurses on 57 shifts).

*3.1.1. Multilevel analysis*

*3.1.2. Optimal model*

Our reasons were as follows.

### **2.4. Construction of a virtual ward environment**

In accordance with the plan formulated under 2.1, a virtual ward environment was created according to the following procedure:

**1.** Construction of a model for estimation of task time devoted to patients for whom the nurse is responsible.

Construct a model to estimate the kinds of factors that influence care time devoted to a given patient.

**2.** Calculation of number of patients for whom one nurse is responsible and of care time

Determine which patients a given nurse is responsible for and find the total task time spent by that nurse on patients for whom she is responsible.

**3.** Estimation of task time by purpose

On the basis of the total task time devoted to 'patients for whom the nurse is responsi‐ ble' calculated under 2., estimate time spent on 'patients for whom the nurse is not re‐ sponsible,' 'other tasks,' and 'rest time,' all of which are correlated.

#### **2.5. Test experiments in virtual ward environment**

In the virtual environment we had created, we carried out the following test experiments and investigated the difference from actual data.

