Copula modelling of agitation-sedation rating of ICU patients: towards monitoring and alerting tools

Agitation-Sedation (A-S) cycling in critically ill intensive care unit (ICU) patients is damaging to health. Sedation quality is assessed by nurses and may suffer from subjectivity in their judgment and lead to sub-optimal sedation. Therefore, the use of quantitative modelling to enhance understanding of the A-S system is a key tool for optimising sedation management. Inadequate assessment of the agitation associated with clinical outcomes may lead to under or over-sedation and harm a patient's wellbeing. 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 the high nurses' ratings of a patient's agitation levels may not correspond to the occurrences of patient's A-S profile with large infusion dose. Copulas measure nonlinear dependencies capturing the dependence between skewed distributions. Therefore, the aim is to use a copula-based dependence measure between the nurses' rating of patients' agitation level, and the automated sedation dose to identify patient-specific thresholds that separate the regions of mild, moderate, and severe agitation intensities. Delineating the occurrences with different agitation intensities allows us to establish the regions where nurses' rating has stronger or weaker correlation with the automated sedation dose. This pilot study modelled agitation-sedation profiles of two patients collected at Christchurch Hospital, Christchurch School of Medicine and Health Sciences, NZ, from the pool of 37 patients. Classification of patients into poor and good trackers based on Wavelet Probability Bands (WPB). One of the patients is a poor tracker and the other patient is a good tracker. The best-fitting copula shows t hat t he dependency structure between the nurses rating of a patients agitation level and the administered dose of sedative for both patients has an upper and lower tail. More specifically, a correlation between the nurses rating of a patients agitation severity and the administered dose of the sedative is the strongest when patients are expressing signs of a mild agitation, namely in the lower tail region (below the lower threshold for nurses' rating: 1.1 for poor tracker and 1.3 for good tracker) and weakest when patients are expressing signs of a severe agitation, namely in the upper tail region (above the upper threshold for nurses' rating: 2.6 for poor tracker and 6.1 for good tracker). The results show that for a good tracker, the nurses' rating of the patients' agitation levels has strong positive correlation with the administered dose of the sedative for low and mild agitation severity. For a poor tracker, the nurses' rating of the patients' agitation levels has strong positive correlation with the administered dose of the sedative only for low agitation severity. In addition, incorporating the tail dummy variables improved predictions of the nurses' rating by increasing the adjusted R2 values by 28%. Moreover, the percentage of lower and upper tail observations that are common with the lower and upper WPBs is higher for the poor tracker than the good tracker. However, the percentage of observations that are common to both the main region (the region associated with moderate agitation intensity) and within WPB is higher for the good tracker compared to the poor tracker. In this paper we have accounted for non-linear relationships between the two variables, finding thresholds and regions of mismatch between the nurse's scores and sedation dose, thereby suggesting a possible way forward for an improved alerting system for over/under-sedation. Establishing the presence of tail dependence and patient-specific thresholds for areas with different agitation intensities has significant implications for the effective administration of sedatives.