A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure

Ceftazidime-avibactam versus meropenem in nosocomial pneumonia, including ventilator-associated pneumonia (REPROVE): a randomised, double-blind, phase 3 non-inferiority trial

Background: Nosocomial pneumonia is commonly associated with antimicrobial-resistant Gram-negative pathogens. We aimed to assess the efficacy and safety of ceftazidime-avibactam in patients with nosocomial pneumonia, including ventilator-associated pneumonia, compared with meropenem in a multinational, phase 3, double-blind, non-inferiority trial (REPROVE). Methods: Adults with nosocomial pneumonia (including ventilator-associated pneumonia), enrolled at 136 centres in 23 countries, were randomly assigned (1:1) to 2000 mg ceftazidime and 500 mg avibactam (by 2 h intravenous infusion every 8 h) or 1000 mg meropenem (by 30-min intravenous infusion every 8 h) for 7-14 days; regimens were adjusted for renal function. Computer-generated randomisation codes were stratified by infection type and geographical region with a block size of four. Participants and investigators were masked to treatment assignment. The primary endpoint was clinical cure at the test-of-cure visit (21-25 days after randomisation). Non-inferiority was concluded if the lower limit of the two-sided 95% CI for the treatment difference was greater than -12·5% in the coprimary clinically modified intention-to-treat and clinically evaluable populations. This trial is registered with ClinicalTrials.gov (NCT01808092) and EudraCT (2012-004006-96). Findings: Between April 13, 2013, and Dec 11, 2015, 879 patients were randomly assigned. 808 patients were included in the safety population, 726 were included in the clinically modified intention-to-treat population, and 527 were included in the clinically evaluable population. Predominant Gram-negative baseline pathogens in the microbiologically modified intention-to-treat population (n=355) were Klebsiella pneumoniae (37%) and Pseudomonas aeruginosa (30%); 28% were ceftazidime-non-susceptible. In the clinically modified intention-to-treat population, 245 (68·8%) of 356 patients in the ceftazidime-avibactam group were clinically cured, compared with 270 (73·0%) of 370 patients in the meropenem group (difference -4·2% [95% CI -10·8 to 2·5] ). In the clinically evaluable population, 199 (77·4%) of 257 participants were clinically cured in the ceftazidime-avibactam group, compared with 211 (78·1%) of 270 in the meropenem group (difference -0·7% [95% CI -7·9 to 6·4]). Adverse events occurred in 302 (75%) of 405 patients in the ceftazidime-avibactam group versus 299 (74%) of 403 in the meropenem group (safety population), and were mostly mild or moderate in intensity and unrelated to study treatment. Serious adverse events occurred in 75 (19%) patients in the ceftazidime-avibactam group and 54 (13%) patients in the meropenem group. Four serious adverse events (all in the ceftazidime-avibactam group) were judged to be treatment related. Interpretation: Ceftazidime-avibactam was non-inferior to meropenem in the treatment of nosocomial pneumonia. These results support a role for ceftazidime-avibactam as a potential alternative to carbapenems in patients with nosocomial pneumonia (including ventilator-associated pneumonia) caused by Gram-negative pathogens. Funding: AstraZeneca

A randomized, blinded, multicenter trial of lipid-associated amphotericin B alone versus in combination with an antibody-based inhibitor of heat shock protein 90 in patients with invasive candidiasis

BACKGROUND: Mycograb (NeuTec Pharma) is a human recombinant monoclonal antibody against heat shock protein 90 that, in laboratory studies, was revealed to have synergy with amphotericin B against a broad spectrum of Candida species. METHODS: A double-blind, randomized study was conducted to determine whether lipid-associated amphotericin B plus Mycograb was superior to amphotericin B plus placebo in patients with culture-confirmed invasive candidiasis. Patients received a lipid-associated formulation of amphotericin B plus a 5-day course of Mycograb or placebo, having been stratified on the basis of Candida species (Candida albicans vs. non-albicans species of Candida). Inclusion criteria included clinical evidence of active infection at trial entry plus growth of Candida species on culture of a specimen from a clinically significant site within 3 days after initiation of study treatment. The primary efficacy variable was overall response to treatment (clinical and mycological resolution) by day 10. RESULTS: Of the 139 patients enrolled from Europe and the United States, 117 were included in the modified intention-to-treat population. A complete overall response by day 10 was obtained for 29 (48%) of 61 patients in the amphotericin B group, compared with 47 (84%) of 56 patients in the Mycograb combination therapy group (odds ratio [OR], 5.8; 95% confidence interval [CI], 2.41-13.79; P<.001). The following efficacy criteria were also met: clinical response (52% vs. 86%; OR, 5.4; 95% CI, 2.21-13.39; P<.001), mycological response (54% vs. 89%; OR, 7.1; 95% CI, 2.64-18.94; P<.001), Candida-attributable mortality (18% vs. 4%; OR, 0.2; 95% CI, 0.04-0.80; P = .025), and rate of culture-confirmed clearance of the infection (hazard ratio, 2.3; 95% CI, 1.4-3.8; P = .001). Mycograb was well tolerated. CONCLUSIONS: Mycograb plus lipid-associated amphotericin B produced significant clinical and culture-confirmed improvement in outcome for patients with invasive candidiasis

Clinical factors associated with a Candida albicans Germ Tube Antibody positive test in Intensive Care Unit patients

Background: Poor outcomes of invasive candidiasis (IC) are associated with the difficulty in establishing the microbiological diagnosis at an early stage. New scores and laboratory tests have been developed in order to make an early therapeutic intervention in an attempt to reduce the high mortality associated with invasive fungal infections. Candida albicans IFA IgG has been recently commercialized for germ tube antibody detection (CAGTA). This test provides a rapid and simple diagnosis of IC (84.4% sensitivity and 94.7% specificity). The aim of this study is to identify the patients who could be benefited by the use of CAGTA test in critical care setting. Methods: A prospective, cohort, observational multicentre study was carried out in six medical/surgical Intensive care units (ICU) of tertiary-care Spanish hospitals. Candida albicans Germ Tube Antibody test was performed twice a week if predetermined risk factors were present, and serologically demonstrated candidiasis was considered if the testing serum dilution was >= 1: 160 in at least one sample and no other microbiological evidence of invasive candidiasis was found. Results: Fifty-three critically ill non-neutropenic patients (37.7% post surgery) were included. Twenty-two patients (41.5%) had CAGTA-positive results, none of them with positive blood culture for Candida. Neither corrected colonization index nor antifungal treatment had influence on CAGTA results. This finding could corroborate that the CAGTA may be an important biomarker to distinguish between colonization and infection in these patients. The presence of acute renal failure at the beginning of the study was more frequent in CAGTA-negative patients. Previous surgery was statistically more frequent in CAGTA-positive patients. Conclusions: This study identified previous surgery as the principal clinical factor associated with CAGTA-positive results and emphasises the utility of this promising technique, which was not influenced by high Candida colonization or antifungal treatment. Our results suggest that detection of CAGTA may be important for the diagnosis of invasive candidiasis in surgical patients admitted in ICU.This study has been supported by a Pfizer research gran