Copula Modelling of Agitation-Sedation (A-S) in ICU: Threshold Analysis of Nurses’ Scores of A-S and Automated Drug Infusions by Protocol

Abstract

Pain management is increasingly recognised as a formal medical subspecialty worldwide. Empirical distributions of the nurses’ ratings of a patient’s pain and/or agitation levels and the administered dose of sedative are often positively skewed, and if the joint distribution is non-elliptical, then high nurses’ ratings of a patient’s agitation levels may not correspond to the true occurrences of patient’s agitation-sedation (A-S). Copulas are used to capture such nonlinear dependence between skewed distributions and check for the presence of lower (LT) and/or upper tail (UT) dependence between the nurses’ A-S rating and the automated sedation dose, thus finding thresholds and regions of mismatch between the nurse’s scores and automated sedation dose, thereby suggesting a possible way forward for an improved alerting system for over- or under-sedation. We find for LT 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 severity. For UT dependence in the moderate agitation zone, nurses tend to either moderately or strongly underestimate patient’s agitation, but in periods of severe agitation, nurses tend to overestimate a patient’s agitation. 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.