**3.2 Visuals, tail dependence, taus, dose/score thresholds of 10 patients**

Details of equations, copulas and visualisations will focus on the following list of 10 patients given in **Tables 8 and 9**. Visualisations comprise patients'score and dose trajectories with associated 95% WPB bands, copula plots, K-plots, along with associated equations, relevant tau for tails and a clear delineation dose and nurses'score thresholds related to upper and lower tails, when they exist. Specifically lower and upper tail tau (τ) values, their percentile positions in the patient bivariate trajectories of length in ICU, associated lower and/or upper tail thresholds for the infusion dose and nurse's score threshold are given in **Table 8**. **Table 9** gives the associated equation parameters contrasting linear correlation (r) with our novel copula-tail based approach. **Figures 11** and **12** display the bivariate trajectories and 90% WPB bands of the patients. Full set of equations and tail thresholds are given in **Tables A.1** and **A.2** in the Appendix.

#### **Figure 7.**

*P32 a poor tracker with 2 tails - copula plot, main* tau, *K- plot and tail* taus *(upper panel); best fit line(s) (lower panel). LT* tau *= 0.73, UT* tau *= 0.40, (LT, UT) dose threshold = (3.90, 7.02), (LT, UT) score threshold = (3.62, 7.63).*

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

#### **Figure 8.**

*P28 poor tracker with a lower tail - copula plot, main* tau, *K- plot and tail* tau *(upper panel); best fit line(s) (lower panel) relating P28 nurses' score with dose. LT tail* tau *= 0.79, LT dose threshold = 1.70 and LT score threshold = 1.20.*

#### **Figure 9.**

*P25 good tracker with 2 tails - copula plot, main region* tau *K-plot, and tail* taus *(upper panel); best fit line(s) (lower panel) LT* tau *= 0.06, UT* tau *= 0.06, and (LT, UT) dose threshold = (2.68, 4.43), with (LT, UT) score threshold = (2.41, 3.94).*

#### **Figure 10.**

*P37 good tracker with upper tail - copula plot, main* tau, *K- plot and tail* tau *(upper panel); best fit line(s) (lower panel) relating P37 nurses' A-S score with dose. UT* tau *= 0.77, UT dose threshold = 2.53, and UT nurse score threshold = 2.99.*


#### **Table 8.**

*Upper and/or lower tail positions (percentiles) and associated lower/upper thresholds for dose and nurses' A-S score.*
