*Copula Modelling of Agitation-Sedation (A-S) in ICU: Threshold Analysis of Nurses'… DOI: http://dx.doi.org/10.5772/intechopen.105753*

The first patient (patient 8) in **Table 2** is a good WPB tracker and the second (patient 27) a poor WPB tracker both studied in [20, 21], for which the upper tail thresholds of the nurses'scores using copulas were established, in a pilot study of these 2 patients using copula mathematics. We also refer the reader to Hudson's chapter in this book "Modelling Agitation-Sedation (A-S) in ICU: an Empirical Transition and Time to event analysis of poor and good tracking between nurses scores and automated A-S measures" [22].

The corresponding WPB% values for patient 8 and patient 27 are 87.5% and 43.7%, respectively (**Table 2**). 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 12 poor trackers (**Table 1**). Noteworthy also is that the A-S time series of these two patients examined (P8 and P27) were of disparate lengths patient 8 had 10,561 time points and patient 27, had 13,441 time points. The full set of patients studied had a range of [3001-25,261] time points of automated dose assessments.

Patient 18 (good tracker) with a WPB% of 93.8% and patient 28 (poor tracker) with WPB% of 50.8% (**Table 3**) were studied in detail in [20, 21], 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 (see also [27–29]).

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 exhibit an increased total number of violations.

The total number of WPB-based violations is greater for the poor trackers than for the good trackers, and it is the poor trackers that tend to have longer ICU times. There are three approximate categories of patient ICU time: 50�64, 113�128, and 205–256, and 19 of the 36 patients have an ICU time of ≤64.
