**2. Data and methods**

This chapter models the agitation-sedation profiles of Agitation and Sedation (A-S) profiles of 37 patients were collected at the Christchurch Hospital, Christchurch

School of Medicine and Health Sciences, NZ. Two measures were recorded for each patient: (1) the nurses' ratings of a patient's agitation level and (2) an automated sedation dose (see **Figure 1**). Infusion data were recorded using an electronic drug infusion device for all admitted ICU patients during a nine-month observation period and required more than 24 hours of sedation. Infusion data containing less than 48 hours of continuous data, or data from patients whose sedation requirements were extreme, such as those with severe head injuries, were excluded [9, 10]. A total of 37 ICU patients met these requirements and were enrolled in the study. Classification of patients into poor and good trackers, as based on the Wavelet Probability Bands (WPB) are given in **Table 2**. The so-called good tracker delineates the scenario where the nurse's rating scores remains within the (time based) 90% coverage of wavelet probability band (WPB) based on the simulated dose profiles [9, 10]. Poor tracking delineates the scenario where the nurses rating scores remain outside the (time based) 90% coverage of wavelet probability band (WPB) for a significant portion of time based on the simulated dose profiles [13, 14].

By way of illustration we consider four patients from the pool of 37 patients**. Tables 1** and **3** summarise each of these four patients' WPB tracker status, time to first, second and third violation outside the WPB bands [9], their total number of violations over ICU stay and patient's time in ICU, along with their specific WPB% value. Display of their line profiles of *nurses' rating* of A-S in relation to drug infusion *dose* over time, for each of the 4 patients (P8, P27, P18, P28) are given in **Figures 2**–**4**.

The first patient (patient 8) in **Table 3** is a good WPB tracker and the second a poor WPB tracker (patient 27), studied in depth in [28], for which upper tail thresholds of the nurses'scores using copulas were established. We also refer the reader also to Hudson & Tursunalieva's chapter in this book entitled "Copula thresholds and modelling Agitation-Sedation (A-S) in ICU: analysis of nurses scores of A-S and automated drug infusions by protocol" [27]. The corresponding WPB% values for patient 8 and patient 27 are 87.5% and 43.7%, respectively (**Table 3**). Overall, the minimum, median and maximum WPB% values for the 24 good trackers is (58.8%, 87.5%, 96.9%) and (47.3%, 64.8%, 77.3%) for the 13 poor trackers (**Table 2**). Noteworthy also is that the A-S time series of these two patients examined (P8 and P27) were of disparate lengths - patient eight had 10,561 time points and patient 27, 13,441 time points. The full 37 patients studied had a range of [3001–25,261] time points.

#### **Figure 1.**

*Diagram of the feedback loop employing nursing staff's feedback of subjectively assessed patient agitation through the infusion controller (diagram is sourced from Chase et al. [14]).*


*Modelling Agitation-Sedation (A-S) in ICU: An Empirical Transition and Time to Event… DOI: http://dx.doi.org/10.5772/intechopen.105480*

#### **Table 2.**

*Patient numbers of the poor trackers according to the criteria of 4 studies. Developed earlier in [11–14]. Low WPB 90% indicates a poor tracker by Kang's WPB diagnostics [9, 10].*


#### **Table 3.**

*Time to the patient-specific 1st violation V1, second violation V2 and third violation V3, total number of violations, total ICU time and WPB% values.*

Patient 18 (good tracker) with a WPB% of 93.8% and patient 28 (poor tracker) with WPB% of 50.8% (**Table 1**) were studied in detail in [28], for which both upper and lower tails/thresholds of over or under-estimation of agitation levels by the nurses rating were established using copula dependence analytics [29], refer also to [27].

Patients vary according to their length of stay in ICU and consequently differ in their opportunity for violations to occur. The good trackers generally have shorter ICU time and thus less chance to exibit an increased total number of violations. An indication of how the strata (good versus poor tracker), the patient's total number of violations and a patient's time in ICU interact, can be visualied in **Figure 5**. The total number of WPB based violations is clearly greater for the poor trackers than for the

**Figure 2.**

*Line plot of nurses' rating of patient agitation and the automated sedation dose for patient 8 (good tracker).*

**Figure 3.**

*Line plot of nurses' rating of patient agitation and the automated sedation dose for patient 27 (good tracker).*

**Figure 4.**

*Line plot and WPB% band for patient 18 (LHS) and 28 (RHS, poor tracker).*

good trackers, and it is the poor trackers that tend to have longer ICU times. Also from the scatterplot in **Figure 5** there seems to be three approximate categories of patient ICU time: 50–64, 113–128 and 205–256. The majority of patients (28 (76%)) have ≤40 violations (RHS of **Figure 5**), 19 (51%) patients have an ICU time of ≤64 (**Table 4**).

Accordingly, for ICU time categorised and coded as: 0 = [50,64], 1 = [113,128], and 2 = [205,256], the total violations profile according to tracking status, displayed in **Figure 6**, shows that the total number of violations is significantly higher for the poor trackers, particularly when ICU time > 205. Noteworthy, is that the majority of patients 28 (76%) have ≤40 violations (RHS of **Figure 6**), whereas 19 (51%) patients have an ICU time ≤ 64 (**Table 4**). **Figure 7** displays the histogram of the number of violations where a violation is defined as a nurse's A-S rating outside the patient's WPB control band. We note that the majority of the time, in excess of >75% of the 370 violation counts are below a count of five violations (**Figure 7**).

*Modelling Agitation-Sedation (A-S) in ICU: An Empirical Transition and Time to Event… DOI: http://dx.doi.org/10.5772/intechopen.105480*

#### **Figure 5.**

*Total number of violations by WPB tracking status [9] and ICU time.*


**Table 4.**

*Patient tracker status by ICU time: 0 = 50–64, 1 = 113–128, 2 = 205–256.*

#### **Figure 6.**

*Total number of violations by 3 levels of ICU time (LHS) and boxplot of poor good tracker time to 3rd violation by ICU time: 0 = [50,64], 1 = [113,128], 2 = [205,256].*

For the state-space analysis described in Section 3 each patient's total ICU time is broken into 10 bins, where each bin represents 10% of the patients' total time in ICU; i.e., Bin 1: 0–10%, Bin 2: 11–20% etc. For the 37 patients, we thus have 370 bins, i.e. 370 counts of violations. The 10% interval approach is used due to the large variation in time in ICU between the WPB-based good versus poor strata [9] - noting that some poor trackers have times up to 256, whereas good trackers are mostly limited to 64–128. Given these bins, patients' A-S states can then be defined in terms of the total number of violations or jumps outside the WPB bands that occur during each 10% interval of a patient's total ICU time. The randon, outcome event of A-S status is then the number of violations that over time.
