CD-independent subsets in meet-distributive lattices

A subset $X$ of a finite lattice $L$ is CD-independent if the meet of any two incomparable elements of $X$ equals 0. In 2009, Cz\'edli, Hartmann and Schmidt proved that any two maximal CD-independent subsets of a finite distributive lattice have the same number of elements. In this paper, we prove that if $L$ is a finite meet-distributive lattice, then the size of every CD-independent subset of $L$ is at most the number of atoms of $L$ plus the length of $L$. If, in addition, there is no three-element antichain of meet-irreducible elements, then we give a recursive description of maximal CD-independent subsets. Finally, to give an application of CD-independent subsets, we give a new approach to count islands on a rectangular board.Comment: 14 pages, 4 figure

Improving the physician-patient cardiovascular risk dialogue to improve statin adherence

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to evaluate the effectiveness of a patient education program developed to facilitate statin adherence.</p> <p>Methods</p> <p>A controlled trial was designed to test the effectiveness of a multifaceted patient education program to facilitate statin adherence. The program included a brief, in-office physician counseling kit followed by patient mailings. The primary end point was adherence to filling statin prescriptions during a 120-day period. Patients new to statins enrolled and completed a survey. Data from a national pharmacy claims database were used to track adherence.</p> <p>Results</p> <p>Patients new to statin therapy exposed to a patient counseling and education program achieved a 12.4 higher average number of statin prescription fill days and were 10% more likely to fill prescriptions for at least 120 days (<it>p </it>= .01).</p> <p>Conclusion</p> <p>Brief in-office counseling on cardiovascular risk followed by patient education mailings can be effective in increasing adherence. Physicians found a one-minute counseling tool and pocket guidelines useful in counseling patients.</p

Adherence with statins in a real-life setting is better when associated cardiovascular risk factors increase: a cohort study

<p>Abstract</p> <p>Background</p> <p>While the factors for poor adherence for treatment with statins have been highlighted, the impact of their combination on adherence is not clear.</p> <p>Aims</p> <p>To estimate adherence for statins and whether it differs according to the number of cardiovascular risk factors.</p> <p>Methods</p> <p>A cohort study was conducted using data from the main French national health insurance system reimbursement database. Newly treated patients with statins between September 1 and December 31, 2004 were included. Patients were followed up 15 months. The cohort was split into three groups according to their number of additional cardiovascular risk factors that included age and gender, diabetes mellitus and cardiovascular disease (using co-medications as a <it>proxy</it>). Adherence was assessed for each group by using four parameters: <it>(i) </it>proportion of days covered by statins, <it>(ii) </it>regularity of the treatment over time, <it>(iii) </it>persistence, and <it>(iv) </it>the refill delay.</p> <p>Results</p> <p>16,397 newly treated patients were identified. Of these statin users, 21.7% did not have additional cardiovascular risk factors. Thirty-one percent had two cardiovascular risk factors and 47% had at least three risk factors. All the parameters showed a sub-optimal adherence whatever the group: days covered ranged from 56% to 72%, regularity ranged from 23% to 33% and persistence ranged from 44% to 59%, but adherence was better for those with a higher number of cardiovascular risk factors.</p> <p>Conclusions</p> <p>The results confirm that long-term drug treatments are a difficult challenge, particularly in patients at lower risk and invite to the development of therapeutic education.</p

Incidence density of serious infection, opportunistic infection, and tuberculosis associated with biologic treatment in patients with rheumatoid arthritis &amp;ndash; a systematic evaluation of the literature

Trung N Tran,1 Herve Caspard,1 Fabio Magrini21Clinical Development, MedImmune, Gaithersburg, MD, USA; 2Eli Lilly, San Diego, CA, USAAbstract: Summary data on the incidence density (ie, incidence per person-year [PY]) of serious infection, opportunistic infection, and tuberculosis associated with each of the nine biologic therapies currently indicated in rheumatoid arthritis patients are not available. To summarize these data, a systematic review was conducted with searches on PubMed and Embase of literature ranging from January 1998 to November 2011. Incidence density was extracted and reported using the definitions from the respective publications. If the incidence density was not reported, estimation was made using available information. A total of 72 published studies met the inclusion criteria and were reviewed, including 44 clinical trials, open-label extension studies, or meta-analyses, and 28 observational studies. Additional calculation of the incidence density was performed in 12 studies for serious infection and in 13 studies for opportunistic infection or tuberculosis. The incidence of serious infection was consistent across studies and biologic therapies, ranging from 0 to 11/100 PY but mainly clustered from 2 to 6/100 PY. Fewer incidence data were available for opportunistic infection and tuberculosis. The incidence of opportunistic infection and tuberculosis ranged widely, from 0.01 to 3.0/100 PY and 0.01 to 2.6/100 PY, respectively. The data on serious infection may be used to evaluate the public health risk and benefit of biologic treatment. They may also serve as a point of reference for future studies. The limited data on opportunistic infection and the lack of a consistent definition of opportunistic infection invite caution for a benchmark rate for opportunistic infection as a composite category.Keywords: DMARD, biologic, review, safety, infection, adverse even

Abstract Concept Lattices

International audienceWe present a view of abstraction based on a structure preserving reduction of the Galois connection between a language of terms and the powerset of a set of instances O. Such a relation is materialized as an extension-intension lattice, namely a concept lattice when L is the powerset of a set P of attributes. We define and characterize an abstraction A as some part of either the language or the powerset of O, defined in such a way that the extension-intension latticial structure is preserved. Such a structure is denoted for short as an abstract lattice. We discuss the extensional abstract lattices obtained by so reducing the powerset of O, together together with the corresponding abstract implications, and discuss alpha lattices as particular abstract lattices. Finally we give formal framework allowing to define a generalized abstract lattice whose language is made of terms mixing abstract and non abstract conjunctions of properties