**4. Conclusions**

Copulas were successfully implemented to capture non-linear dependence, and establish the presence of lower (LT) and/or upper tail (UT) dependence between the nurses' A-S rating and the automated sedation dose (**Figure 20**). Establishing the presence of tail dependence and patient-specific lower and/or upper thresholds for areas with different agitation intensities has significant implications for effective administration of sedatives. Copulas unique to the poor trackers were the Survival BB7 and Rotated Tawn type 1, 180. Unique copula types of the good trackers were Clayton, BB8, and t copula. To the best fit copulas, we established for each patients' bivariate score and dose trajectories regions of mild, moderate, and severe agitation and their lower and upper tail thresholds, if any, in the dependence, relationship via K-plots and our novel equation relating patient's nurses'score to dose. We found that for lower tail dependence, nurses tend to underestimate the patient's agitation in the moderate agitation zone. In the mild agitation zone, nurses tend to assign a rating that is, on average, 0.30 to 0.45 points lower than expected for the patient's given agitation. For upper tail dependence nurses tend to either moderately or strongly underestimate patient's agitation in the moderate agitation zone; but in periods of severe agitation, tend to overestimate a patient's agitation. When both lower and upper tails exist, nurses tend to strongly underestimate agitation in the moderate zone and then tend to still underestimate agitation in mild agitation periods; but in the severe zone nurses tend to overestimate agitation on average by 0.34 points. We also determined the

#### **Figure 19.**

*P35 poor tracker with a lower tail - copula plot, main* tau, *K- plot and tail* tau *(upper panel); best fit line(s) (lower panel) relating P35 nurses' score with dose. LT tail* tau *= 0.74, LT dose threshold = 0.72 and LT score threshold = 0.66.*

#### **Figure 20.**

*P27 poor tracker with no tails- copula plot, main* tau = *0.70, K- plot and tail* tau *(upper panel); best fit line (lower panel) relating P27 nurses' score with dose.*

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

number of occurrences over the patient's total ICU stay, where nurses tend to under/ over- estimate agitation. Finding thresholds and regions of mismatch between the nurses'scores and sedation dose potentially provides a way to improved alerting systems for over/under-sedation. Our approach lends credence to augmenting conventional RASS and SAS agitation measures with semi-automated systems and identifying thresholds and regions of deviance for alerting increased risk.
