Function theory related to H∞ control

We define Γ(E), a subset of C³, related to the structured singular value μ of 2x2 matrices. μ is used to analyse performance and robustness of linear feedback systems in control engineering. We find a characterisation for the elements of Γ(E) and establish a necessary and sufficient condition for the existence of an analytic function from the unit disc into Γ(E) satisfying an arbitrary finite number of interpolation conditions. We prove a Schwarz Lemma for Γ(E) when one of the points in Γ(E) is (0,0,0), then we show that in this case, the Carathéodory and Kobayashi distances between the two points in Γ(E) coincide. We also give a characterisation of the interior, the topological boundary and the distinguished boundary of Γ(E), then we define Γ(E)-inner functions and show that if there exists an analytic function from the unit disc into Γ(E) that satisfies the interpolating conditions, then there is a rational Γ(E)-inner function that interpolates.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Best-practice prevention alone or with conventional or biological caries management for 3- to 7-year-olds:the FiCTION three-arm RCT

Background Historically, lack of evidence for effective management of decay in primary teeth has caused uncertainty, but there is emerging evidence to support alternative strategies to conventional fillings, which are minimally invasive and prevention orientated. Objectives The objectives were (1) to assess the clinical effectiveness and cost-effectiveness of three strategies for managing caries in primary teeth and (2) to assess quality of life, dental anxiety, the acceptability and experiences of children, parents and dental professionals, and caries development and/or progression. Design This was a multicentre, three-arm parallel-group, participant-randomised controlled trial. Allocation concealment was achieved by use of a centralised web-based randomisation facility hosted by Newcastle Clinical Trials Unit. Setting This trial was set in primary dental care in Scotland, England and Wales. Participants Participants were NHS patients aged 3–7 years who were at a high risk of tooth decay and had at least one primary molar tooth with decay into dentine, but no pain/sepsis. Interventions Three interventions were employed: (1) conventional with best-practice prevention (local anaesthetic, carious tissue removal, filling placement), (2) biological with best-practice prevention (sealing-in decay, selective carious tissue removal and fissure sealants) and (3) best-practice prevention alone (dietary and toothbrushing advice, topical fluoride and fissure sealing of permanent teeth). Main outcome measures The clinical effectiveness outcomes were the proportion of children with at least one episode (incidence) and the number of episodes, for each child, of dental pain or dental sepsis or both over the follow-up period. The cost-effectiveness outcomes were the cost per incidence of, and cost per episode of, dental pain and/or dental sepsis avoided over the follow-up period. Results A total of 72 dental practices were recruited and 1144 participants were randomised (conventional arm, n = 386; biological arm, n = 381; prevention alone arm, n = 377). Of these, 1058 were included in an intention-to-treat analysis (conventional arm, n = 352; biological arm, n = 352; prevention alone arm, n = 354). The median follow-up time was 33.8 months (interquartile range 23.8–36.7 months). The proportion of children with at least one episode of pain or sepsis or both was 42% (conventional arm), 40% (biological arm) and 45% (prevention alone arm). There was no evidence of a difference in incidence or episodes of pain/sepsis between arms. When comparing the biological arm with the conventional arm, the risk difference was –0.02 (97.5% confidence interval –0.10 to 0.06), which indicates, on average, a 2% reduced risk of dental pain and/or dental sepsis in the biological arm compared with the conventional arm. Comparing the prevention alone arm with the conventional arm, the risk difference was 0.04 (97.5% confidence interval –0.04 to 0.12), which indicates, on average, a 4% increased risk of dental pain and/or dental sepsis in the prevention alone arm compared with the conventional arm. Compared with the conventional arm, there was no evidence of a difference in episodes of pain/sepsis among children in the biological arm (incident rate ratio 0.95, 97.5% confidence interval 0.75 to 1.21, which indicates that there were slightly fewer episodes, on average, in the biological arm than the conventional arm) or in the prevention alone arm (incident rate ratio 1.18, 97.5% confidence interval 0.94 to 1.48, which indicates that there were slightly more episodes in the prevention alone arm than the conventional arm). Over the willingness-to-pay values considered, the probability of the biological treatment approach being considered cost-effective was approximately no higher than 60% to avoid an incidence of dental pain and/or dental sepsis and no higher than 70% to avoid an episode of pain/sepsis. Conclusions There was no evidence of an overall difference between the three treatment approaches for experience of, or number of episodes of, dental pain or dental sepsis or both over the follow-up period

Dual bronchodilators in Bronchiectasis study (DIBS): protocol for a pragmatic, multicentre, placebo-controlled, three-arm, double-blinded, randomised controlled trial studying bronchodilators in preventing exacerbations of bronchiectasis

INTRODUCTION: Bronchiectasis is a long-term lung condition, with dilated bronchi, chronic inflammation, chronic infection and acute exacerbations. Recurrent exacerbations are associated with poorer clinical outcomes such as increased severity of lung disease, further exacerbations, hospitalisations, reduced quality of life and increased risk of death. Despite an increasing prevalence of bronchiectasis, there is a critical lack of high-quality studies into the disease and no treatments specifically approved for its treatment. This trial aims to establish whether inhaled dual bronchodilators (long acting beta agonist (LABA) and long acting muscarinic antagonist (LAMA)) taken as either a stand-alone therapy or in combination with inhaled corticosteroid (ICS) reduce the number of exacerbations of bronchiectasis requiring treatment with antibiotics during a 12 month treatment period. METHODS: This is a multicentre, pragmatic, double-blind, randomised controlled trial, incorporating an internal pilot and embedded economic evaluation. 600 adult patients (≥18 years) with CT confirmed bronchiectasis will be recruited and randomised to either inhaled dual therapy (LABA+LAMA), triple therapy (LABA+LAMA+ICS) or matched placebo, in a 2:2:1 ratio (respectively). The primary outcome is the number of protocol defined exacerbations requiring treatment with antibiotics during the 12 month treatment period. ETHICS AND DISSEMINATION: Favourable ethical opinion was received from the North East-Newcastle and North Tyneside 2 Research Ethics Committee (reference: 21/NE/0020). Results will be disseminated in peer-reviewed publications, at national and international conferences, in the NIHR Health Technology Assessments journal and to participants and the public (using lay language). TRIAL REGISTRATION NUMBER: ISRCTN15988757

Alternative to prophylactic antibiotics for the treatment of recurrent urinary tract infections in women: multicentre, open label, randomised, non-inferiority trial.

OBJECTIVE: To test and compare the efficacy of methenamine hippurate for prevention of recurrent urinary tract infections with the current standard prophylaxis of daily low dose antibiotics. DESIGN: Multicentre, open label, randomised, non-inferiority trial. SETTING: Eight centres in the UK, recruiting from June 2016 to June 2018. PARTICIPANTS: Women aged ≥18 years with recurrent urinary tract infections, requiring prophylactic treatment. INTERVENTIONS: Random assignment (1:1, using permuted blocks of variable length via a web based system) to receive antibiotic prophylaxis or methenamine hippurate for 12 months. Treatment allocation was not masked and crossover between arms was allowed. MAIN OUTCOME MEASURE: Absolute difference in incidence of symptomatic, antibiotic treated, urinary tract infections during treatment. A patient and public involvement group predefined the non-inferiority margin as one episode of urinary tract infection per person year. Analyses performed in a modified intention-to-treat population comprised all participants observed for at least six months. RESULTS: Participants were randomly assigned to antibiotic prophylaxis (n=120) or methenamine hippurate (n=120). The modified intention-to-treat analysis comprised 205 (85%) participants (antibiotics, n=102 (85%); methenamine hippurate, n=103 (86%)). Incidence of antibiotic treated urinary tract infections during the 12 month treatment period was 0.89 episodes per person year (95% confidence interval 0.65 to 1.12) in the antibiotics group and 1.38 (1.05 to 1.72) in the methenamine hippurate group, with an absolute difference of 0.49 (90% confidence interval 0.15 to 0.84) confirming non-inferiority. Adverse reactions were reported by 34/142 (24%) in the antibiotic group and 35/127 (28%) in the methenamine group and most reactions were mild. CONCLUSION: Non-antibiotic prophylactic treatment with methenamine hippurate might be appropriate for women with a history of recurrent episodes of urinary tract infections, informed by patient preferences and antibiotic stewardship initiatives, given the demonstration of non-inferiority to daily antibiotic prophylaxis seen in this trial. TRIAL REGISTRATION: ISRCTN70219762

Dual bronchodilators in Bronchiectasis study (DIBS): protocol for a pragmatic, multicentre, placebo-controlled, three-arm, double-blinded, randomised controlled trial studying bronchodilators in preventing exacerbations of bronchiectasis

Introduction: Bronchiectasis is a long-term lung condition, with dilated bronchi, chronic inflammation, chronic infection and acute exacerbations. Recurrent exacerbations are associated with poorer clinical outcomes such as increased severity of lung disease, further exacerbations, hospitalisations, reduced quality of life and increased risk of death. Despite an increasing prevalence of bronchiectasis, there is a critical lack of high-quality studies into the disease and no treatments specifically approved for its treatment. This trial aims to establish whether inhaled dual bronchodilators (long acting beta agonist (LABA) and long acting muscarinic antagonist (LAMA)) taken as either a stand-alone therapy or in combination with inhaled corticosteroid (ICS) reduce the number of exacerbations of bronchiectasis requiring treatment with antibiotics during a 12 month treatment period. Methods: This is a multicentre, pragmatic, double-blind, randomised controlled trial, incorporating an internal pilot and embedded economic evaluation. 600 adult patients (≥18 years) with CT confirmed bronchiectasis will be recruited and randomised to either inhaled dual therapy (LABA+LAMA), triple therapy (LABA+LAMA+ICS) or matched placebo, in a 2:2:1 ratio (respectively). The primary outcome is the number of protocol defined exacerbations requiring treatment with antibiotics during the 12 month treatment period. Ethics and dissemination: Favourable ethical opinion was received from the North East—Newcastle and North Tyneside 2 Research Ethics Committee (reference: 21/NE/0020). Results will be disseminated in peer-reviewed publications, at national and international conferences, in the NIHR Health Technology Assessments journal and to participants and the public (using lay language). Trial registration number: ISRCTN15988757

Cost-effectiveness of methenamine hippurate compared with antibiotic prophylaxis for the management of recurrent urinary tract infections in secondary care: a multicentre, open-label, randomised, non-inferiority trial.

OBJECTIVES: To estimate the cost-effectiveness of methenamine hippurate compared with antibiotic prophylaxis in the management of recurrent urinary tract infections. DESIGN: Multicentre, open-label, randomised, non-inferiority trial. SETTING: Eight centres in the UK, recruiting from June 2016 to June 2018. PARTICIPANTS: Women aged ≥18 years with recurrent urinary tract infections, requiring prophylactic treatment. INTERVENTIONS: Women were randomised to receive once-daily antibiotic prophylaxis or twice-daily methenamine hippurate for 12 months. Treatment allocation was not masked and crossover between arms was allowed. PRIMARY AND SECONDARY OUTCOME MEASURES: The primary economic outcome was the incremental cost per quality-adjusted life year (QALY) gained at 18 months. All costs were collected from a UK National Health Service perspective. QALYs were estimated based on responses to the EQ-5D-5L administered at baseline, 3, 6, 9, 12 and 18 months. Incremental costs and QALYs were estimated using an adjusted analysis which controlled for observed and unobserved characteristics. Stochastic sensitivity analysis was used to illustrate uncertainty on a cost-effectiveness plane and a cost-effectiveness acceptability curve. A sensitivity analysis, not specified in the protocol, considered the costs associated with antibiotic resistance. RESULTS: Data on 205 participants were included in the economic analysis. On average, methenamine hippurate was less costly (-£40; 95% CI: -684 to 603) and more effective (0.014 QALYs; 95% CI: -0.05 to 0.07) than antibiotic prophylaxis. Over the range of values considered for an additional QALY, the probability of methenamine hippurate being considered cost-effective ranged from 51% to 67%. CONCLUSIONS: On average, methenamine hippurate was less costly and more effective than antibiotic prophylaxis but these results are subject to uncertainty. Methenamine hippurate is more likely to be considered cost-effective when the benefits of reduced antibiotic use were included in the analysis. TRIAL REGISTRATION NUMBER: ISRCTN70219762

The FiCTION trial: child oral health-related quality of life and dental anxiety across 3 treatment strategies for managing caries in young children.

Objectives: The FiCTION Trial compared co-primary outcomes (dental pain and/or infection) and secondary outcomes (child oral health-related quality of life [COHRQOL], child dental anxiety, cost-effectiveness, caries development/progression and acceptability) across 3 treatment strategies (Conventional with Prevention (C+P); Biological with Prevention (B+P); Prevention Alone (PA)) for managing caries in children in primary care. COHRQOL and child dental anxiety experiences are reported upon here. Methods: A multi-centre, 3-arm parallel group, unblinded patient-randomised controlled trial of 3-7-year-olds treated under NHS contracts was conducted in 72 general dental practices in England, Wales and Scotland. Child participants (with at least one primary molar with dentinal caries) were randomised (1:1:1) to one of three treatment arms with the intention of being managed according to allocated arm for three years (minimum 23 months). Randomisation was via a centrally-administered system using random permuted blocks of variable length. At baseline and final visit, accompanying parents/caregivers completed a parental questionnaire including COHRQOL (16 item P-CPQ-16), and at every visit child-and parental-questionnaire-based data were collected for child-based dental trait and state anxiety. Statistical analyses were conducted on complete cases from the modified intention to treat (mITT) analysis set. Results: 1144 children were randomised (C+P: 386; B+P: 381; PA: 377). The mITT analysis set included the 1058 children who attended at least one study visit (C+P: 352; B+P: 352; PA: 354). Median follow-up was 33.8 months (IQR 23.8, 36.7). The P-CPQ-16 overall score could be calculated after simple imputation at both baseline and final visit for 560 children (C+P: 189; B+P: 189; PA: 182). There was no evidence of a difference in the estimated adjusted mean P-CPQ-16 at the final visit which was, on average, 0.3 points higher (97.5% CI: -1.1 to 1.6) in B+P than C+P and 0.2 points higher, on average, (97.5% CI: 1.2 to 1.5) in PA than for C+P. Child dental trait anxiety and child dental state anxiety, measured at every treatment visit, showed no evidence of any statistically or clinically significant difference between arms in adjusted mean scores averaged over all follow-up visits. Conclusions: The differences noted in COHRQOL and child-based dental trait and dental state anxiety measures across 3 treatment strategies for managing dental caries in primary teeth were small, and not considered to be clinically meaningful. The findings highlight the importance of including all 3 strategies in a clinician’s armamentarium, to manage childhood caries throughout the young child’s life and achieve positive experiences of dental care

Additional file 3 of Acipimox in Mitochondrial Myopathy (AIMM): study protocol for a randomised, double-blinded, placebo-controlled, adaptive design trial of the efficacy of acipimox in adult patients with mitochondrial myopathy

Additional file 3. PIS Summary

Additional file 1 of Acipimox in Mitochondrial Myopathy (AIMM): study protocol for a randomised, double-blinded, placebo-controlled, adaptive design trial of the efficacy of acipimox in adult patients with mitochondrial myopathy

Additional file 1. Informed consent form

Additional file 2 of Acipimox in Mitochondrial Myopathy (AIMM): study protocol for a randomised, double-blinded, placebo-controlled, adaptive design trial of the efficacy of acipimox in adult patients with mitochondrial myopathy

Additional file 2. Participant information sheet