Analysis of a recurrence related to critical non-homogeneous Branching processes

Some classes of controlled branching processes (with nonhomogeneous migration or with nonhomogeneous state-dependent immigration) lead in the critical case to a recurrence for the extinction probabilities. Under some additional conditions it is known that this recurrence depends on some parameter β and converges for 0 < β < 1. Now we show that the recurrence does converge for all positive values of the parameter β, which leads to an extension of some limit theorems for the corresponding branching processes. We also give a generalization of the recurrence and an asymptotic analysis of its behavior.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Supplementary Material for: Ergocalciferol versus Cholecalciferol for Nutritional Vitamin D Replacement in CKD

<b><i>Background/Aims:</i></b> Is cholecalciferol (D₃) superior to ergocalciferol (D₂) in treating nutritional vitamin D deficiency in chronic kidney disease (CKD)? The answer to this question has not been fully explored. <b><i>Methods:</i></b> A retrospective analysis of 57 patients with non-dialysis-requiring CKD was conducted to assess the relative effectiveness of D₂ versus D₃ replacement on circulating 25(OH)D levels. Levels of 25(OH) D were assessed at baseline, after attempted repletion with D₂, and then after attempted repletion with D₃. The relative paired differences of the drug treatment effects were tested using t-tests. Multiple regression modeling was used to determine the factors significantly associated with differential responsiveness to the drugs. <b><i>Results:</i></b> The mean (SEM) age was 66.4 ± 1.4 and mean eGFR was 40.5 ± 2.2 ml/min/1.73 m². The baseline 25(OH)D level was 15.3 ± 0.8 ng/ml. After standardizing to 100,000 units of drug, increases after cholecalciferol (2.7 ± 0.3 ng/ml) were more than twice as great as those from ergocalciferol (1.1 ± 0.3 ng/ml) (p < 0.0001). A sensitivity analysis, which pooled the results of an additional 109 individuals treated with ergocalciferol alone, revealed similar findings (standardized change 2.7 ± 0.3 vs. 1.6 ± 0.3 ng/ml, p = 0.0025). Factors associated with a superior response to cholecalciferol were lower baseline 25(OH) D level at the start of therapy (p = 0.015) and the interaction of sex and age (p = 0.0048), with younger females tending to benefit relatively more from cholecalciferol than older males did. <b><i>Conclusion:</i></b> Cholecalciferol may be superior to ergocalciferol in treating nutritional vitamin D deficiency in non-dialysis CKD

Antiinflammatory therapy with canakinumab for atherosclerotic disease

BACKGROUND: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. METHODS: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P=0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P=0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P=0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P=0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P=0.31). CONCLUSIONS: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. Copyright © 2017 Massachusetts Medical Society