Part of the book: Discrete Wavelet Transforms
Part of the book: Discrete Wavelet Transforms
Part of the book: Discrete Wavelet Transforms
A new approach to assess synchronicity developed in this chapter is a novel bivariate extension of the generalised mixture transition distribution (MTDg) model (we coin this B-MTD). The aim of this chapter is to test MTDg an extended MTD with interactions model and its bivariate extension of MTD (B-MTD) to investigate synchrony of flowering of four Eucalypts species—E. leucoxylon, E. microcarpa, E. polyanthemos and E. tricarpa over a 31 year period. The mixture transition distribution (MTDg) is a method to estimate transition probabilities of high order Markov chains. Our B-MTD approach allows us the derive rules of thumb for synchrony and asynchrony between pairs of species, e.g. flowering of the four species. The latter B-MTD rules are based on transition probabilities between all possible on and off flowering states from previous to current time. We also apply MTDg modelling using lagged flowering states and climate covariates as predictors to model current flowering status (on/off) to assess synchronisation using residuals from the resultant models via our adaptation of Moran’s classic synchrony statistic. We compare these MTDg (with covariates)-based synchrony measures with our B-MTD results in addition to those from extended Kalman filter (EKF)-based residuals.
Part of the book: Probability, Combinatorics and Control
Sedation in the intensive care unit (ICU) is challenging, as both over- and under-sedation are detrimental. Optimal sedation and analgesic strategies, are a challenge in ICU and nurses play a major role in assessing a patient’s agitation levels. Assessing the severity of agitation is a difficult clinical problem as variability related to drug metabolism for each patient. Multi-state models provide a framework for modelling complex event histories. Quantities of interest are mainly the transition probabilities e.g. between states, that can be estimated by the empirical transition matrix (ETM). Such multi-state models have had wide applications for modelling complex courses of a disease. In this chapter the ETM of multi-state and counting process (survival analytic) models which use the times for ICU patients to transition to varying states of violations (a violation being a carer’s agitation rating outside so-called wavelet-probability bands (WPB)) confirm the utility of defining so-called trackers and non-trackers according to WPB-based control limits and rules. ETM and multi-state modelling demonstrate that these control-limit scoring approaches are suitable for developing more advanced optimal infusion controllers and coding of nurses A-S scores. These offer significant clinical potential of improved agitation management and reduced length of stay in critical care.
Part of the book: Recent Advances in Medical Statistics
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.
Part of the book: Recent Advances in Medical Statistics