Monomial discrete valuations in k[[X]]

Let v be a rank m discrete valuation of k[[X1,...,Xn]] with dimension n-m. We prove that there exists an inmediate extension L of K where the valuation is monomial. Therefore we compute explicitly the residue field of the valuation

Association between convalescent plasma treatment and mortality in COVID-19: a collaborative systematic review and meta-analysis of randomized clinical trials.

Funder: laura and john arnold foundationBACKGROUND: Convalescent plasma has been widely used to treat COVID-19 and is under investigation in numerous randomized clinical trials, but results are publicly available only for a small number of trials. The objective of this study was to assess the benefits of convalescent plasma treatment compared to placebo or no treatment and all-cause mortality in patients with COVID-19, using data from all available randomized clinical trials, including unpublished and ongoing trials (Open Science Framework, https://doi.org/10.17605/OSF.IO/GEHFX ). METHODS: In this collaborative systematic review and meta-analysis, clinical trial registries (ClinicalTrials.gov, WHO International Clinical Trials Registry Platform), the Cochrane COVID-19 register, the LOVE database, and PubMed were searched until April 8, 2021. Investigators of trials registered by March 1, 2021, without published results were contacted via email. Eligible were ongoing, discontinued and completed randomized clinical trials that compared convalescent plasma with placebo or no treatment in COVID-19 patients, regardless of setting or treatment schedule. Aggregated mortality data were extracted from publications or provided by investigators of unpublished trials and combined using the Hartung-Knapp-Sidik-Jonkman random effects model. We investigated the contribution of unpublished trials to the overall evidence. RESULTS: A total of 16,477 patients were included in 33 trials (20 unpublished with 3190 patients, 13 published with 13,287 patients). 32 trials enrolled only hospitalized patients (including 3 with only intensive care unit patients). Risk of bias was low for 29/33 trials. Of 8495 patients who received convalescent plasma, 1997 died (23%), and of 7982 control patients, 1952 died (24%). The combined risk ratio for all-cause mortality was 0.97 (95% confidence interval: 0.92; 1.02) with between-study heterogeneity not beyond chance (I2 = 0%). The RECOVERY trial had 69.8% and the unpublished evidence 25.3% of the weight in the meta-analysis. CONCLUSIONS: Convalescent plasma treatment of patients with COVID-19 did not reduce all-cause mortality. These results provide strong evidence that convalescent plasma treatment for patients with COVID-19 should not be used outside of randomized trials. Evidence synthesis from collaborations among trial investigators can inform both evidence generation and evidence application in patient care

Extending valuations to formal completions

International audienc

Key polynomials for simple extensions of valued fields

In this paper we present a refined version of MacLane's theory of key polynomials [16]-[17], similar to those considered by M. Vaquié [24]-[27], and reminiscent of related objects studied by Abhyankar and Moh (approximate roots [1], [2]) and T.C. Kuo [14], [15].Let (K, ν_0) be a valued field. Given a simple transcendental extension of valued fields ι : K → K(x) we associate to ι a countable well ordered set of polynomials of K[x] called key polynomials. We define limit key polynomials and give an explicit description of them. We show that the order type of the set of key polynomials is bounded by ω × ω. If char k_ν_0 = 0 and rk ν_0 = 1, the order type is bounded by ω + 1

Additional file 2 of Association between convalescent plasma treatment and mortality in COVID-19: a collaborative systematic review and meta-analysis of randomized clinical trials

Additional file 2. Email invitation

Additional file 7 of Association between convalescent plasma treatment and mortality in COVID-19: a collaborative systematic review and meta-analysis of randomized clinical trials

Additional file 7. Sensitivity analyses: various meta-analytic approaches

Additional file 1 of Association between convalescent plasma treatment and mortality in COVID-19: a collaborative systematic review and meta-analysis of randomized clinical trials

Additional file 1. Search strategy

Additional file 5 of Association between convalescent plasma treatment and mortality in COVID-19: a collaborative systematic review and meta-analysis of randomized clinical trials

Additional file 5. Risk of bias

Association between convalescent plasma treatment and mortality in COVID-19: a collaborative systematic review and meta-analysis of randomized clinical trials

Abstract Background Convalescent plasma has been widely used to treat COVID-19 and is under investigation in numerous randomized clinical trials, but results are publicly available only for a small number of trials. The objective of this study was to assess the benefits of convalescent plasma treatment compared to placebo or no treatment and all-cause mortality in patients with COVID-19, using data from all available randomized clinical trials, including unpublished and ongoing trials (Open Science Framework, https://doi.org/10.17605/OSF.IO/GEHFX ). Methods In this collaborative systematic review and meta-analysis, clinical trial registries (ClinicalTrials.gov, WHO International Clinical Trials Registry Platform), the Cochrane COVID-19 register, the LOVE database, and PubMed were searched until April 8, 2021. Investigators of trials registered by March 1, 2021, without published results were contacted via email. Eligible were ongoing, discontinued and completed randomized clinical trials that compared convalescent plasma with placebo or no treatment in COVID-19 patients, regardless of setting or treatment schedule. Aggregated mortality data were extracted from publications or provided by investigators of unpublished trials and combined using the Hartung–Knapp–Sidik–Jonkman random effects model. We investigated the contribution of unpublished trials to the overall evidence. Results A total of 16,477 patients were included in 33 trials (20 unpublished with 3190 patients, 13 published with 13,287 patients). 32 trials enrolled only hospitalized patients (including 3 with only intensive care unit patients). Risk of bias was low for 29/33 trials. Of 8495 patients who received convalescent plasma, 1997 died (23%), and of 7982 control patients, 1952 died (24%). The combined risk ratio for all-cause mortality was 0.97 (95% confidence interval: 0.92; 1.02) with between-study heterogeneity not beyond chance (I2 = 0%). The RECOVERY trial had 69.8% and the unpublished evidence 25.3% of the weight in the meta-analysis. Conclusions Convalescent plasma treatment of patients with COVID-19 did not reduce all-cause mortality. These results provide strong evidence that convalescent plasma treatment for patients with COVID-19 should not be used outside of randomized trials. Evidence synthesis from collaborations among trial investigators can inform both evidence generation and evidence application in patient care