A New Algorithm for Computing the Actions of Trigonometric and Hyperbolic Matrix Functions

A new algorithm is derived for computing the actions $f(tA)B$ and $f(tA^{1/2})B$, where $f$ is cosine, sinc, sine, hyperbolic cosine, hyperbolic sinc, or hyperbolic sine function. $A$ is an $n\times n$ matrix and $B$ is $n\times n_0$ with $n_0 \ll n$. $A^{1/2}$ denotes any matrix square root of $A$ and it is never required to be computed. The algorithm offers six independent output options given $t$, $A$, $B$, and a tolerance. For each option, actions of a pair of trigonometric or hyperbolic matrix functions are simultaneously computed. The algorithm scales the matrix $A$ down by a positive integer $s$, approximates $f(s^{-1}tA)B$ by a truncated Taylor series, and finally uses the recurrences of the Chebyshev polynomials of the first and second kind to recover $f(tA)B$. The selection of the scaling parameter and the degree of Taylor polynomial are based on a forward error analysis and a sequence of the form $\|A^k\|^{1/k}$ in such a way the overall computational cost of the algorithm is optimized. Shifting is used where applicable as a preprocessing step to reduce the scaling parameter. The algorithm works for any matrix $A$ and its computational cost is dominated by the formation of products of $A$ with $n\times n_0$ matrices that could take advantage of the implementation of level-3 BLAS. Our numerical experiments show that the new algorithm behaves in a forward stable fashion and in most problems outperforms the existing algorithms in terms of CPU time, computational cost, and accuracy.Comment: 4 figures, 16 page

Impact of adherence to individual quality-of-care indicators on the prognosis of bloodstream infection due to Staphylococcus aureus: a prospective observational multicentre cohort

Objectives To analyse the adherence and impact of quality-of-care indicators (QCIs) in the management of Staphylococcus aureus bloodstream infection in a prospective and multicentre cohort. Methods Analysis of the prospective, multicentre international S. Aureus Collaboration cohort of S. Aureus bloodstream infection cases observed between January 2013 and April 2015. Multivariable analysis was performed to evaluate the impact of adherence to QCIs on 90-day mortality. Results A total of 1784 cases were included. Overall, 90-day mortality was 29.9% and mean follow-up period was 118 days. Adherence was 67% (n = 1180/1762) for follow-up blood cultures, 31% (n = 416/1342) for early focus control, 77.6% (n = 546/704) for performance of echocardiography, 75.5% (n = 1348/1784) for adequacy of targeted antimicrobial therapy, 88.6% (n = 851/960) for adequacy of treatment duration in non-complicated bloodstream infections and 61.2% (n = 366/598) in complicated bloodstream infections. Full bundle adherence was 18.4% (n = 328/1784). After controlling for immortal time bias and potential confounders, focus control (adjusted hazard ratio = 0.76; 95% CI, 0.59–0.99; p 0.038) and adequate targeted antimicrobial therapy (adjusted hazard ratio = 0.75; 95% CI, 0.61–0.91; p 0.004) were associated with low 90-day mortality. Discussion Adherence to QCIs in S. Aureus bloodstream infection did not reach expected rates. Apart from the benefits of application as a bundle, focus control and adequate targeted therapy were independently associated with low mortality

Target trial emulation using hospital-based observational data: demonstration and application in COVID-19

Methodological biases are common in observational studies evaluating treatment effectiveness. The objective of this study is to emulate a target trial in a competing risks setting using hospital-based observational data. We extend established methodology accounting for immortal time bias and time-fixed confounding biases to a setting where no survival information beyond hospital discharge is available: a condition common to coronavirus disease 2019 (COVID-19) research data. This exemplary study includes a cohort of 618 hospitalized patients with COVID-19. We describe methodological opportunities and challenges that cannot be overcome applying traditional statistical methods. We demonstrate the practical implementation of this trial emulation approach via clone–censor–weight techniques. We undertake a competing risk analysis, reporting the cause-specific cumulative hazards and cumulative incidence probabilities. Our analysis demonstrates that a target trial emulation framework can be extended to account for competing risks in COVID-19 hospital studies. In our analysis, we avoid immortal time bias, time-fixed confounding bias, and competing risks bias simultaneously. Choosing the length of the grace period is justified from a clinical perspective and has an important advantage in ensuring reliable results. This extended trial emulation with the competing risk analysis enables an unbiased estimation of treatment effects, along with the ability to interpret the effectiveness of treatment on all clinically important outcomes.This research was funded by the German Research Foundation (original: Deutsche Forschungsgemeinschaft), grant number WO 1746/5-1.Peer ReviewedPostprint (published version

Impact of adherence to individual quality-of-care indicators on the prognosis of bloodstream infection due to Staphylococcus aureus: a prospective observational multicentre cohort

Objectives: To analyse the adherence and impact of quality-of-care indicators (QCIs) in the management of Staphylococcus aureus bloodstream infection in a prospective and multicentre cohort. Methods: Analysis of the prospective, multicentre international S. Aureus Collaboration cohort of S. Aureus bloodstream infection cases observed between January 2013 and April 2015. Multivariable analysis was performed to evaluate the impact of adherence to QCIs on 90-day mortality. Results: A total of 1784 cases were included. Overall, 90-day mortality was 29.9% and mean follow-up period was 118 days. Adherence was 67% (n = 1180/1762) for follow-up blood cultures, 31% (n = 416/ 1342) for early focus control, 77.6% (n = 546/704) for performance of echocardiography, 75.5% (n = 1348/ 1784) for adequacy of targeted antimicrobial therapy, 88.6% (n = 851/960) for adequacy of treatment duration in non-complicated bloodstream infections and 61.2% (n = 366/598) in complicated blood-stream infections. Full bundle adherence was 18.4% (n = 328/1784). After controlling for immortal time bias and potential confounders, focus control (adjusted hazard ratio = 0.76; 95% CI, 0.59-0.99; p 0.038) and adequate targeted antimicrobial therapy (adjusted hazard ratio = 0.75; 95% CI, 0.61-0.91; p 0.004) were associated with low 90-day mortality. Discussion: Adherence to QCIs in S. Aureus bloodstream infection did not reach expected rates. Apart from the benefits of application as a bundle, focus control and adequate targeted therapy were inde-pendently associated with low mortality. Francesc Escrihuela-Vidal, Clin Microbiol Infect 2023;29:498 (c) 2022 The Authors. Published by Elsevier Ltd on behalf of European Society of Clinical Microbiology and Infectious Diseases

Impact of adherence to individual quality-of-care indicators on the prognosis of bloodstream infection due to Staphylococcus aureus: a prospective observational multicentre cohort

© 2022 The Authors. Published by Elsevier Ltd on behalf of European Society of Clinical Microbiology and Infectious Diseases. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).[Objectives] To analyse the adherence and impact of quality-of-care indicators (QCIs) in the management of Staphylococcus aureus bloodstream infection in a prospective and multicentre cohort.[Methods] Analysis of the prospective, multicentre international S. Aureus Collaboration cohort of S. Aureus bloodstream infection cases observed between January 2013 and April 2015. Multivariable analysis was performed to evaluate the impact of adherence to QCIs on 90-day mortality.[Results] A total of 1784 cases were included. Overall, 90-day mortality was 29.9% and mean follow-up period was 118 days. Adherence was 67% (n = 1180/1762) for follow-up blood cultures, 31% (n = 416/1342) for early focus control, 77.6% (n = 546/704) for performance of echocardiography, 75.5% (n = 1348/1784) for adequacy of targeted antimicrobial therapy, 88.6% (n = 851/960) for adequacy of treatment duration in non-complicated bloodstream infections and 61.2% (n = 366/598) in complicated bloodstream infections. Full bundle adherence was 18.4% (n = 328/1784). After controlling for immortal time bias and potential confounders, focus control (adjusted hazard ratio = 0.76; 95% CI, 0.59–0.99; p 0.038) and adequate targeted antimicrobial therapy (adjusted hazard ratio = 0.75; 95% CI, 0.61–0.91; p 0.004) were associated with low 90-day mortality.[Discussion] Adherence to QCIs in S. Aureus bloodstream infection did not reach expected rates. Apart from the benefits of application as a bundle, focus control and adequate targeted therapy were independently associated with low mortality.The ISAC-01 study did not receive dedicated funding. Funding for data acquisition of patients who were also enrolled in the ARREST study was provided by the United Kingdom National Institute for Health Research Health Technology Assessment. The funding organizations had no influence on the design of the study, the collection, analysis and interpretation of the data as well as the decision to approve publication of the finished manuscript. A.S.W. is supported by the National Institutes of Health Research Biomedical Research Centre, Oxford. L.E.L.C. and J.R.B. are supported by Plan Nacional de I + D + I 2013-2016 and Instituto de Salud Carlos III, Subdirección General de Redes y Centros de Investigación Cooperativa, Ministerio de Economía, Industria y Competitividad, Spanish Network for Research in Infectious Diseases (RD16/0016/0001)-co-financed by European Development Regional Fund ‘A way to achieve Europe, Operative program Intelligent Growth 2014-2020’. G.T. is supported by the Wellcome trust.Peer reviewe

Bias due to censoring of deaths when calculating extra length of stay for patients acquiring a hospital infection

Abstract Background In many studies the information of patients who are dying in the hospital is censored when examining the change in length of hospital stay (cLOS) due to hospital-acquired infections (HIs). While appropriate estimators of cLOS are available in literature, the existence of the bias due to censoring of deaths was neither mentioned nor discussed by the according authors. Methods Using multi-state models, we systematically evaluate the bias when estimating cLOS in such a way. We first evaluate the bias in a mathematically closed form assuming a setting with constant hazards. To estimate the cLOS due to HIs non-parametrically, we relax the assumption of constant hazards and consider a time-inhomogeneous Markov model. Results In our analytical evaluation we are able to discuss challenging effects of the bias on cLOS. These are in regard to direct and indirect differential mortality. Moreover, we can make statements about the magnitude and direction of the bias. For real-world relevance, we illustrate the bias on a publicly available prospective cohort study on hospital-acquired pneumonia in intensive-care. Conclusion Based on our findings, we can conclude that censoring the death cases in the hospital and considering only patients discharged alive should be avoided when estimating cLOS. Moreover, we found that the closed mathematical form can be used to describe the bias for settings with constant hazards