25 research outputs found
Total domination in inflated graphs
AbstractThe inflation GI of a graph G is obtained from G by replacing every vertex x of degree d(x) by a clique X=Kd(x) and each edge xy by an edge between two vertices of the corresponding cliques X and Y of GI in such a way that the edges of GI which come from the edges of G form a matching of GI. A set S of vertices in a graph G is a total dominating set, abbreviated TDS, of G if every vertex of G is adjacent to a vertex in S. The minimum cardinality of a TDS of G is the total domination number Îłt(G) of G. In this paper, we investigate total domination in inflated graphs. We provide an upper bound on the total domination number of an inflated graph in terms of its order and matching number. We show that if G is a connected graph of order nâ„2, then Îłt(GI)â„2n/3, and we characterize the graphs achieving equality in this bound. Further, if we restrict the minimum degree of G to be at least 2, then we show that Îłt(GI)â„n, with equality if and only if G has a perfect matching. If we increase the minimum degree requirement of G to be at least 3, then we show Îłt(GI)â„n, with equality if and only if every minimum TDS of GI is a perfect total dominating set of GI, where a perfect total dominating set is a TDS with the property that every vertex is adjacent to precisely one vertex of the set
Systematic review on the recurrence of postoperative nausea and vomiting after a first episode in the recovery room â implications for the treatment of PONV and related clinical trials
BACKGROUND: Despite the presence of a plethora of publications on the prevention of postoperative nausea and vomiting (PONV) only little is known how to treat established symptoms. Besides the high effort of performing these efficacy trials (much more patients must give their consent than are actually included in a study) and ethical concerns, little is known about the rate of re-occurring PONV/vomiting after placebo. As a consequence investigators will have difficulties defining a clinically relevant effect for the new treatment which is crucial for any planning. A quantitative systematic review was performed in order to provide more reliable estimates of the incidence of re-occurring PONV/vomiting after placebo and to help investigators defining a clinically relevant treatment effect. METHODS: A systematic search of the literature was performed using an extended search strategy of a previous review. Data on the recurrence of PONV (any nausea or emetic symptom) and vomiting (retching or vomiting) was extracted from published reports treating PONV with placebo and unpublished results from two observational trials where no treatment was given. A nonlinear random effects model was used to calculate estimates of the recurrence of symptoms and their 95%-confidence intervals (95%-CI). RESULTS: A total of 29 trials (including the unpublished data) were eligible for the calculations. Depending on the length of observation after administering placebo or no treatment the recurrence rate of PONV was between 65% (95%-CI: 53%...75%) and 84% (95%-CI: 73%...91%) and that of vomiting was between 65% (95%-CI: 44%...81%) and 78% (95%-CI: 59%...90%). CONCLUSION: Almost all trials showed a considerable and consistently high rate of recurrence of emetic symptoms after placebo highlighting the need for a consequent antiemetic treatment. Future (placebo) controlled efficacy trials may use the presented empirical estimates for defining clinically relevant effects and for statistical power considerations
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Effect of Hydrocortisone on Mortality and Organ Support in Patients With Severe COVID-19: The REMAP-CAP COVID-19 Corticosteroid Domain Randomized Clinical Trial.
Importance: Evidence regarding corticosteroid use for severe coronavirus disease 2019 (COVID-19) is limited. Objective: To determine whether hydrocortisone improves outcome for patients with severe COVID-19. Design, Setting, and Participants: An ongoing adaptive platform trial testing multiple interventions within multiple therapeutic domains, for example, antiviral agents, corticosteroids, or immunoglobulin. Between March 9 and June 17, 2020, 614 adult patients with suspected or confirmed COVID-19 were enrolled and randomized within at least 1 domain following admission to an intensive care unit (ICU) for respiratory or cardiovascular organ support at 121 sites in 8 countries. Of these, 403 were randomized to open-label interventions within the corticosteroid domain. The domain was halted after results from another trial were released. Follow-up ended August 12, 2020. Interventions: The corticosteroid domain randomized participants to a fixed 7-day course of intravenous hydrocortisone (50 mg or 100 mg every 6 hours) (nâ=â143), a shock-dependent course (50 mg every 6 hours when shock was clinically evident) (nâ=â152), or no hydrocortisone (nâ=â108). Main Outcomes and Measures: The primary end point was organ support-free days (days alive and free of ICU-based respiratory or cardiovascular support) within 21 days, where patients who died were assigned -1 day. The primary analysis was a bayesian cumulative logistic model that included all patients enrolled with severe COVID-19, adjusting for age, sex, site, region, time, assignment to interventions within other domains, and domain and intervention eligibility. Superiority was defined as the posterior probability of an odds ratio greater than 1 (threshold for trial conclusion of superiority >99%). Results: After excluding 19 participants who withdrew consent, there were 384 patients (mean age, 60 years; 29% female) randomized to the fixed-dose (nâ=â137), shock-dependent (nâ=â146), and no (nâ=â101) hydrocortisone groups; 379 (99%) completed the study and were included in the analysis. The mean age for the 3 groups ranged between 59.5 and 60.4 years; most patients were male (range, 70.6%-71.5%); mean body mass index ranged between 29.7 and 30.9; and patients receiving mechanical ventilation ranged between 50.0% and 63.5%. For the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively, the median organ support-free days were 0 (IQR, -1 to 15), 0 (IQR, -1 to 13), and 0 (-1 to 11) days (composed of 30%, 26%, and 33% mortality rates and 11.5, 9.5, and 6 median organ support-free days among survivors). The median adjusted odds ratio and bayesian probability of superiority were 1.43 (95% credible interval, 0.91-2.27) and 93% for fixed-dose hydrocortisone, respectively, and were 1.22 (95% credible interval, 0.76-1.94) and 80% for shock-dependent hydrocortisone compared with no hydrocortisone. Serious adverse events were reported in 4 (3%), 5 (3%), and 1 (1%) patients in the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively. Conclusions and Relevance: Among patients with severe COVID-19, treatment with a 7-day fixed-dose course of hydrocortisone or shock-dependent dosing of hydrocortisone, compared with no hydrocortisone, resulted in 93% and 80% probabilities of superiority with regard to the odds of improvement in organ support-free days within 21 days. However, the trial was stopped early and no treatment strategy met prespecified criteria for statistical superiority, precluding definitive conclusions. Trial Registration: ClinicalTrials.gov Identifier: NCT02735707
Omecamtiv mecarbil in chronic heart failure with reduced ejection fraction, GALACTICâHF: baseline characteristics and comparison with contemporary clinical trials
Aims:
The safety and efficacy of the novel selective cardiac myosin activator, omecamtiv mecarbil, in patients with heart failure with reduced ejection fraction (HFrEF) is tested in the Global Approach to Lowering Adverse Cardiac outcomes Through Improving Contractility in Heart Failure (GALACTICâHF) trial. Here we describe the baseline characteristics of participants in GALACTICâHF and how these compare with other contemporary trials.
Methods and Results:
Adults with established HFrEF, New York Heart Association functional class (NYHA)ââ„âII, EF â€35%, elevated natriuretic peptides and either current hospitalization for HF or history of hospitalization/ emergency department visit for HF within a year were randomized to either placebo or omecamtiv mecarbil (pharmacokineticâguided dosing: 25, 37.5 or 50âmg bid). 8256 patients [male (79%), nonâwhite (22%), mean age 65âyears] were enrolled with a mean EF 27%, ischemic etiology in 54%, NYHA II 53% and III/IV 47%, and median NTâproBNP 1971âpg/mL. HF therapies at baseline were among the most effectively employed in contemporary HF trials. GALACTICâHF randomized patients representative of recent HF registries and trials with substantial numbers of patients also having characteristics understudied in previous trials including more from North America (n = 1386), enrolled as inpatients (n = 2084), systolic blood pressureâ<â100âmmHg (n = 1127), estimated glomerular filtration rate <â30âmL/min/1.73 m2 (n = 528), and treated with sacubitrilâvalsartan at baseline (n = 1594).
Conclusions:
GALACTICâHF enrolled a wellâtreated, highârisk population from both inpatient and outpatient settings, which will provide a definitive evaluation of the efficacy and safety of this novel therapy, as well as informing its potential future implementation