Differentiability, Porosity and Doubling in Metric Measure Spaces

We show if a metric measure space admits a differentiable structure then porous sets have measure zero and hence the measure is pointwise doubling. We then give a construction to show if we only require an approximate differentiable structure the measure need no longer be pointwise doubling

Editor's Choice - Bypass versus Angioplasty for Severe Ischaemia of the Leg (BASIL) Prospective Cohort Study and the Generalisability of the BASIL-2 Randomised Controlled Trial

OBJECTIVE: The Bypass versus Angioplasty in Severe Ischaemia of the Leg-2 (BASIL-2) randomised controlled trial has shown that, for patients with chronic limb threatening ischaemia (CLTI) who require an infrapopliteal (IP) revascularisation a vein bypass (VB) first revascularisation strategy led to a 35% increased risk of major amputation or death when compared with a best endovascular treatment (BET) first revascularisation strategy. The study aims are to place the BASIL-2 trial within the context of the CLTI patient population as a whole and to investigate the generalisability of the BASIL-2 outcome data.METHODS: This was an observational, single centre prospective cohort study. Between 24 June 2014 and 31 July 2018, the BASIL Prospective Cohort Study (PCS) was performed which used BASIL-2 trial case record forms to document the characteristics, initial and subsequent management, and outcomes of 471 consecutive CLTI patients admitted to an academic vascular centre. Ethical approval was obtained, and all patients provided fully informed written consent. Follow up data were censored on 14 December 2022.RESULTS: Of the 238 patients who required an infrainguinal revascularisation, 75 (32%) had either IP bypass (39 patients) or IP BET (36 patients) outside BASIL-2. Seventeen patients were initially randomised to BASIL-2. A further three patients who did not have an IP revascularisation as their initial management were later randomised in BASIL-2. Therefore, 95/471 (20%) of patients had IP revascularisation (16% outside, 4% inside BASIL-2). Differences in amputation free survival, overall survival, and limb salvage between IP bypass and IP BET performed outside BASIL-2 were not subject to hypothesis testing due to the small sample size. Reasons for non-randomisation into the trial were numerous, but often due to anatomical and technical considerations.CONCLUSION: CLTI patients who required an IP revascularisation procedure and were subsequently randomised into BASIL-2 accounted for a small subset of the CLTI population as a whole. For a wide range of patient, limb, anatomical and operational reasons, most patients in this cohort were deemed unsuitable for randomisation in BASIL-2. The results of BASIL-2 should be interpreted in this context.</p

Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial

SummaryBackground Azithromycin has been proposed as a treatment for COVID-19 on the basis of its immunomodulatoryactions. We aimed to evaluate the safety and efficacy of azithromycin in patients admitted to hospital with COVID-19.Methods In this randomised, controlled, open-label, adaptive platform trial (Randomised Evaluation of COVID-19Therapy [RECOVERY]), several possible treatments were compared with usual care in patients admitted to hospitalwith COVID-19 in the UK. The trial is underway at 176 hospitals in the UK. Eligible and consenting patients wererandomly allocated to either usual standard of care alone or usual standard of care plus azithromycin 500 mg once perday by mouth or intravenously for 10 days or until discharge (or allocation to one of the other RECOVERY treatmentgroups). Patients were assigned via web-based simple (unstratified) randomisation with allocation concealment andwere twice as likely to be randomly assigned to usual care than to any of the active treatment groups. Participants andlocal study staff were not masked to the allocated treatment, but all others involved in the trial were masked to theoutcome data during the trial. The primary outcome was 28-day all-cause mortality, assessed in the intention-to-treatpopulation. The trial is registered with ISRCTN, 50189673, and ClinicalTrials.gov, NCT04381936.Findings Between April 7 and Nov 27, 2020, of 16 442 patients enrolled in the RECOVERY trial, 9433 (57%) wereeligible and 7763 were included in the assessment of azithromycin. The mean age of these study participants was65·3 years (SD 15·7) and approximately a third were women (2944 [38%] of 7763). 2582 patients were randomlyallocated to receive azithromycin and 5181 patients were randomly allocated to usual care alone. Overall,561 (22%) patients allocated to azithromycin and 1162 (22%) patients allocated to usual care died within 28 days(rate ratio 0·97, 95% CI 0·87–1·07; p=0·50). No significant difference was seen in duration of hospital stay (median10 days [IQR 5 to >28] vs 11 days [5 to >28]) or the proportion of patients discharged from hospital alive within 28 days(rate ratio 1·04, 95% CI 0·98–1·10; p=0·19). Among those not on invasive mechanical ventilation at baseline, nosignificant difference was seen in the proportion meeting the composite endpoint of invasive mechanical ventilationor death (risk ratio 0·95, 95% CI 0·87–1·03; p=0·24).Interpretation In patients admitted to hospital with COVID-19, azithromycin did not improve survival or otherprespecified clinical outcomes. Azithromycin use in patients admitted to hospital with COVID-19 should be restrictedto patients in whom there is a clear antimicrobial indication

A Comparison of Clinical Outcomes Between Primary Bypass and Secondary Bypass After Failed Plain Balloon Angioplasty in the Bypass versus Angioplasty for Severe Ischaemia of the Limb (BASIL) Trial.

OBJECTIVE Chronic limb threatening ischaemia (CLTI) is a growing global health problem. The UK NIHR HTA funded BASIL trial is still the only randomised controlled trial to have compared a "bypass surgery first" with a "plain balloon angioplasty (PBA) first" strategy for the management of CLTI. In patients who were likely to survive for 2 years and had a suitable vein, primary bypass (PB) was associated with better clinical outcomes. Furthermore, PBA was associated with a high technical and clinical failure rate and many went on to have secondary bypass (SB). This study aimed at comparing clinical outcomes following PB and SB in the BASIL trial. METHODS Demographic, procedural, and outcome data were obtained from the BASIL case report forms. Outcomes were amputation free survival (AFS), limb salvage (LS), overall survival (OS), and freedom from revascularisation (FFR). The SB cohort comprises patients whose first trial intervention was PBA and who subsequently underwent bypass during follow up. The PB cohort comprises those patients whose first trial intervention was bypass. RESULTS The 190 PB and 49 SB patients were well matched except that the SB patients were more likely to be current smokers. At a median of 7 years, PB was associated with better AFS (PB 60% vs. SB 40%; HR 1.58, p = .04), LS (PB 85% vs. SB 73%, p = .06), and OS (PB 68% vs. 51%, p = .06). FFR was equivalent (PB 53% vs. 53%, p = .3). CONCLUSION In the BASIL trial, clinical outcomes following PB were significantly better than in patients undergoing SB after failed PBA. Prior to treating patients with CLTI with primary PBA, clinicians should consider that if this should fail, the outcome of attempted subsequent bypass is likely to be significantly worse than if PB were attempted