A forgotten little chapter on isoperimetric inequalities. On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

[EN]Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle

Assessment of candidemia-attributable mortality in critically ill patients using propensity score matching analysis

[EN] Introduction: Candidemia in critically ill patients is usually a severe and life-threatening condition with a high crude mortality. Very few studies have focused on the impact of candidemia on ICU patient outcome and attributable mortality still remains controversial. This study was carried out to determine the attributable mortality of ICU-acquired candidemia in critically ill patients using propensity score matching analysis. Methods: A prospective observational study was conducted of all consecutive non-neutropenic adult patients admitted for at least seven days to 36 ICUs in Spain, France, and Argentina between April 2006 and June 2007. The probability of developing candidemia was estimated using a multivariate logistic regression model. Each patient with ICU-acquired candidemia was matched with two control patients with the nearest available Mahalanobis metric matching within the calipers defined by the propensity score. Standardized differences tests (SDT) for each variable before and after matching were calculated. Attributable mortality was determined by a modified Poisson regression model adjusted by those variables that still presented certain misalignments defined as a SDT > 10%. Results: Thirty-eight candidemias were diagnosed in 1,107 patients (34.3 episodes/1,000 ICU patients). Patients with and without candidemia had an ICU crude mortality of 52.6% versus 20.6% (P < 0.001) and a crude hospital mortality of 55.3% versus 29.6% (P = 0.01), respectively. In the propensity matched analysis, the corresponding figures were 51.4% versus 37.1% (P = 0.222) and 54.3% versus 50% (P = 0.680). After controlling residual confusion by the Poisson regression model, the relative risk (RR) of ICU- and hospital-attributable mortality from candidemia was RR 1.298 (95% confidence interval (CI) 0.88 to 1.98) and RR 1.096 (95% CI 0.68 to 1.69), respectively. Conclusions: ICU-acquired candidemia in critically ill patients is not associated with an increase in either ICU or hospital mortality.