The computation of multiple roots of a polynomial using structure preserving matrix methods.

Solving polynomial equations is a fundamental problem in several engineering and science fields. This problem has been handled by several researchers and excellent algorithms have been proposed for solving this problem. The computation of the roots of ill-conditioned polynomials is, however, still drawing the attention of several researchers. In particular, a small round off error due to floating point arithmetic is sufficient to break up a multiple root of a polynomial into a cluster of simple closely spaced roots. The problem becomes more complicated if the neighbouring roots are closely spaced. This thesis develops a root finder to compute multiple roots of an inexact polynomial whose coefficients are corrupted by noise. The theoretical development of the developed root solver involves the use of structured matrix methods, optimising parameters using linear programming, and solving least squares equality and nonlinear least squares problems. The developed root solver differs from the classical methods, because it first computes the multiplicities of the roots, after which the roots are computed. The experimental results show that the developed root solver gives very good results without the need for prior knowledge about the noise level imposed on the coefficients of the polynomial

A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix

A non-linear structure preserving matrix method for the computation of a structured low rank approximation S((f) over bar , (g) over bar) of the Sylvester resultant matrix S(f , g) of two inexact polynomials f = f(y) and g = g(y) is considered in this paper. It is shown that considerably improved results are obtained when f (y) and g(y) are processed prior to the computation of S((f) over bar , (g) over bar), and that these preprocessing operations introduce two parameters. These parameters can either be held constant during the computation of S((f) over bar , (g) over bar), which leads to a linear structure preserving matrix method, or they can be incremented during the computation of S((f) over bar, (g) over bar), which leads to a non-linear structure preserving matrix method. It is shown that the non-linear method yields a better structured low rank approximation of S((f) over bar , (g) over bar) and that the assignment of f (y) and g(y) is important because S((f) over bar , (g) over bar) may be a good structured low rank approximation of S(f, g), but S((f) over bar , (g) over bar) may be a poor structured low rank approximation of S (g f) because its numerical rank is not defined. Examples that illustrate the differences between the linear and non-linear structure preserving matrix methods, and the importance of the assignment off (y) and g(y), are shown. (C) 2010 Elsevier B.V. All rights reserved

Prognostic accuracy of triage tools for adults with suspected COVID-19 in a prehospital setting: an observational cohort study

BACKGROUND: Tools proposed to triage patient acuity in COVID-19 infection have only been validated in hospital populations. We estimated the accuracy of five risk-stratification tools recommended to predict severe illness and compared accuracy to existing clinical decision making in a prehospital setting. METHODS: An observational cohort study using linked ambulance service data for patients attended by Emergency Medical Service (EMS) crews in the Yorkshire and Humber region of England between 26 March 2020 and 25 June 2020 was conducted to assess performance of the Pandemic Respiratory Infection Emergency System Triage (PRIEST) tool, National Early Warning Score (NEWS2), WHO algorithm, CRB-65 and Pandemic Medical Early Warning Score (PMEWS) in patients with suspected COVID-19 infection. The primary outcome was death or need for organ support. RESULTS: Of the 7549 patients in our cohort, 17.6% (95% CI 16.8% to 18.5%) experienced the primary outcome. The NEWS2 (National Early Warning Score, version 2), PMEWS, PRIEST tool and WHO algorithm identified patients at risk of adverse outcomes with a high sensitivity (>0.95) and specificity ranging from 0.3 (NEWS2) to 0.41 (PRIEST tool). The high sensitivity of NEWS2 and PMEWS was achieved by using lower thresholds than previously recommended. On index assessment, 65% of patients were transported to hospital and EMS decision to transfer patients achieved a sensitivity of 0.84 (95% CI 0.83 to 0.85) and specificity of 0.39 (95% CI 0.39 to 0.40). CONCLUSION: Use of NEWS2, PMEWS, PRIEST tool and WHO algorithm could improve sensitivity of EMS triage of patients with suspected COVID-19 infection. Use of the PRIEST tool would improve sensitivity of triage without increasing the number of patients conveyed to hospital

LMIC-PRIEST: Derivation and validation of a clinical severity score for acutely ill adults with suspected COVID-19 in a middle-income setting.

BackgroundUneven vaccination and less resilient health care systems mean hospitals in LMICs are at risk of being overwhelmed during periods of increased COVID-19 infection. Risk-scores proposed for rapid triage of need for admission from the emergency department (ED) have been developed in higher-income settings during initial waves of the pandemic.MethodsRoutinely collected data for public hospitals in the Western Cape, South Africa from the 27th August 2020 to 11th March 2022 were used to derive a cohort of 446,084 ED patients with suspected COVID-19. The primary outcome was death or ICU admission at 30 days. The cohort was divided into derivation and Omicron variant validation sets. We developed the LMIC-PRIEST score based on the coefficients from multivariable analysis in the derivation cohort and existing triage practices. We externally validated accuracy in the Omicron period and a UK cohort.ResultsWe analysed 305,564 derivation, 140,520 Omicron and 12,610 UK validation cases. Over 100 events per predictor parameter were modelled. Multivariable analyses identified eight predictor variables retained across models. We used these findings and clinical judgement to develop a score based on South African Triage Early Warning Scores and also included age, sex, oxygen saturation, inspired oxygen, diabetes and heart disease. The LMIC-PRIEST score achieved C-statistics: 0.82 (95% CI: 0.82 to 0.83) development cohort; 0.79 (95% CI: 0.78 to 0.80) Omicron cohort; and 0.79 (95% CI: 0.79 to 0.80) UK cohort. Differences in prevalence of outcomes led to imperfect calibration in external validation. However, use of the score at thresholds of three or less would allow identification of very low-risk patients (NPV ≥0.99) who could be rapidly discharged using information collected at initial assessment.ConclusionThe LMIC-PRIEST score shows good discrimination and high sensitivity at lower thresholds and can be used to rapidly identify low-risk patients in LMIC ED settings

Training and testing of a gradient boosted machine learning model to predict adverse outcome in patients presenting to emergency departments with suspected covid-19 infection in a middle-income setting.

COVID-19 infection rates remain high in South Africa. Clinical prediction models may be helpful for rapid triage, and supporting clinical decision making, for patients with suspected COVID-19 infection. The Western Cape, South Africa, has integrated electronic health care data facilitating large-scale linked routine datasets. The aim of this study was to develop a machine learning model to predict adverse outcome in patients presenting with suspected COVID-19 suitable for use in a middle-income setting. A retrospective cohort study was conducted using linked, routine data, from patients presenting with suspected COVID-19 infection to public-sector emergency departments (EDs) in the Western Cape, South Africa between 27th August 2020 and 31st October 2021. The primary outcome was death or critical care admission at 30 days. An XGBoost machine learning model was trained and internally tested using split-sample validation. External validation was performed in 3 test cohorts: Western Cape patients presenting during the Omicron COVID-19 wave, a UK cohort during the ancestral COVID-19 wave, and a Sudanese cohort during ancestral and Eta waves. A total of 282,051 cases were included in a complete case training dataset. The prevalence of 30-day adverse outcome was 4.0%. The most important features for predicting adverse outcome were the requirement for supplemental oxygen, peripheral oxygen saturations, level of consciousness and age. Internal validation using split-sample test data revealed excellent discrimination (C-statistic 0.91, 95% CI 0.90 to 0.91) and calibration (CITL of 1.05). The model achieved C-statistics of 0.84 (95% CI 0.84 to 0.85), 0.72 (95% CI 0.71 to 0.73), and 0.62, (95% CI 0.59 to 0.65) in the Omicron, UK, and Sudanese test cohorts. Results were materially unchanged in sensitivity analyses examining missing data. An XGBoost machine learning model achieved good discrimination and calibration in prediction of adverse outcome in patients presenting with suspected COVID19 to Western Cape EDs. Performance was reduced in temporal and geographical external validation

Exploring variation in ED attendances and acute hospital admissions for Ambulatory Care Sensitive Conditions

Poster presented at the Royal College of Emergency Medicine Annual Scientific Conference 2023.Ethics approval was obtained from the University of Sheffield Research Ethics Committee (Reference Number 050058).</p