The covering radius problem for sets of perfect matchings

Consider the family of all perfect matchings of the complete graph $K_{2n}$ with $2n$ vertices. Given any collection $\mathcal M$ of perfect matchings of size $s$, there exists a maximum number $f(n,x)$ such that if $s\leq f(n,x)$, then there exists a perfect matching that agrees with each perfect matching in $\mathcal M$ in at most $x-1$ edges. We use probabilistic arguments to give several lower bounds for $f(n,x)$. We also apply the Lov\'asz local lemma to find a function $g(n,x)$ such that if each edge appears at most $g(n, x)$ times then there exists a perfect matching that agrees with each perfect matching in $\mathcal M$ in at most $x-1$ edges. This is an analogue of an extremal result vis-\'a-vis the covering radius of sets of permutations, which was studied by Cameron and Wanless (cf. \cite{cameron}), and Keevash and Ku (cf. \cite{ku}). We also conclude with a conjecture of a more general problem in hypergraph matchings.Comment: 10 page

Disease acceptance and adherence to imatinib in Taiwanese chronic myeloid leukaemia outpatients

Background The launch of imatinib has turned chronic myeloid leukaemia (CML) into a chronic illness due to the dramatic improvement in survival. Several recent studies have demonstrated that poor adherence to imatinib may hamper the therapeutic outcomes and result in increased medical expenditures, whilst research on exploring the reasons for non-adherence to imatinib is still limited. Objective This study aimed to explore the experience of patients as they journey through their CML treatments and associated imatinib utilisation in order to understand the perceptions, attitudes and concerns that may influence adherence to imatinib treatment. Setting This study was conducted at oncology outpatient clinics in a medical centre in southern Taiwan. Methods CML patients who regularly attended the oncology outpatient clinics to receive imatinib treatment from October 2011 to March 2012 were invited to participate in the study. Semi-structured face-to-face interviews were used to explore patients’ experiences and views of their treatment, their current CML status and CML-related health conditions, their concerns about imatinib treatment and imatinib-taking behaviours. Patient interviews were recorded, transcribed verbatim and thematically analysed using the constant comparison approach. Main outcome measure Themes related to patients’ views of the disease and health conditions, worries and concerns influencing imatinib utilisation behaviours are reported. Results Forty-two CML patients participated in the interviews. The emerging themes included: acceptance of current disease and health status, misconceptions about disease progression, factors associated with adherence to imatinib, concerns and management of adverse drug effects. Participants regarded CML as a chronic disease but had misconceptions about disease progression, therapeutic monitoring, resistance to imatinib and symptoms of side effects. Participants were generally adherent to imatinib and favoured long-term prescriptions to avoid regular outpatient visits for medication refills. Experiencing adverse effect was the main reason influencing adherence and led to polypharmacy. Most participants altered medicine-taking behaviours to maintain long-term use of imatinib. Conclusion Taiwanese CML patients are adherent to imatinib but report changing their medication-taking behaviour due to adverse drug effects and associated polypharmacy. Patients’ misconceptions of the disease and medication suggests that it is necessary to improve communication between patients and healthcare professionals. Routinely providing updated information as part of the patient counselling process should be considered as a means of improving this communication

Association between adherence to calcium-channel blocker and statin medications and likelihood of cardiovascular events among US managed care enrollees

<p>Abstract</p> <p>Background</p> <p>Prior studies have found that patients taking single-pill amlodipine/atorvastatin (SPAA) have greater likelihood of adherence at 6 months than those taking 2-pill calcium-channel blocker and statin combinations (CCB/statin). This study examines whether this adherence benefit results in fewer cardiovascular (CV) events.</p> <p>Methods</p> <p>A retrospective cohort study was conducted using administrative claims data from the IMS LifeLink: US Health Plan Claims database, identifying adults already taking CCB or statin (but not both) who had an index event of either initiating treatment with SPAA or adding CCB to statin (or vice versa) between April 1, 2004 to August 31, 2005. Inclusion criteria included age 18+ years, continuously enrolled for minimum of 6 months prior and 18 months following treatment initiation, >1 diagnosis of hypertension, and no prescription claims for SPAA or added CCB or statin for 6 months prior. Exclusion criteria included >1 claim with missing or invalid days supplied, age 65+ years and not enrolled in Medicare Advantage, or history of prior CV events, cancer diagnosis, or chronic renal failure. The primary outcome measure was the rate of CV events (myocardial infarction, heart failure, angina, other ischemic heart disease, stroke, peripheral vascular disease, or revascularization procedure) from 6 to 18 months following index date, analyzed at three levels: 1) all adherent vs. non-adherent patients, 2) SPAA vs. dual-pill patients (regardless of adherence level), and 3) adherent SPAA, adherent dual-pill, and non-adherent SPAA patients vs. non-adherent dual-pill patients.</p> <p>Results</p> <p>Of 1,537 SPAA patients, 56.5% were adherent at 6 months, compared with 21.4% of the 17,910 CCB/statin patients (p < 0.001). Logistic regression found SPAA patients more likely to be adherent (OR = 4.7, p < 0.001) than CCB/statin patients. In Cox proportional hazards models, being adherent to either regimen was associated with significantly lower risk of CV event (HR = 0.77, p = 0.003). A similar effect was seen for SPAA vs. CCB/statin patients (HR = 0.68, p = 0.02). In a combined model, the risk of CV events was significantly lower for adherent CCB/statin patients (HR = 0.79, p = 0.01) and adherent SPAA patients (HR = 0.61, p = 0.03) compared to non-adherent CCB/statin patients.</p> <p>Conclusions</p> <p>Patients receiving SPAA rather than a 2-pill CCB/statin regimen are more likely to be adherent. In turn, adherence to CCB and statin medications is associated with lower risk of CV events in primary prevention patients.</p

The use of erlotinib in daily practice: a study on adherence and patients' experiences

<p>Abstract</p> <p>Background</p> <p>Adherence to pharmacological therapy is a complex and multi-factorial issue that can substantially alter the outcome of treatment. It has been shown that cancer patients, especially when using long-term medication, have similar adherence rates to those of patients with other diseases. The consequences of poor adherence are poor health outcomes and increased health care costs. Only few studies have focused on the use of oral anticancer agents in daily practice. Information about the reasons for non-adherence is essential for the development of interventions that may increase adherence. This paper presents the CAPER-erlotinib protocol, which is designed to study the relationship between adherence to erlotinib and both the plasma concentration and side-effects in patients with NSCLC. Further, the relationships between patient characteristics, disease characteristics, side-effects, quality of life, patient beliefs and attitude towards disease and medication, dose adjustments, reasons for discontinuation and plasma concentration of erlotinib will be explored.</p> <p>Methods/Design</p> <p>In this prospective observational cohort study 65 NSCLC patients of 18 years or older starting treatment with erlotinib will be followed for a period up to 16 weeks. The main study parameters are adherence, the plasma concentration of erlotinib and the number and grade of side-effects. At baseline and on erlotinib treatment in weeks 3-4, 8-9, 12 and 15-16, patients will be asked to fill out a questionnaire. In weeks 3-4, 8-9 and 15-16 blood samples are collected, which will be analysed for plasma concentration of erlotinib. Adherence will be measured using a medication event monitoring system.</p> <p>Discussion</p> <p>The present study aims to get more insight into patients' experiences with the use of erlotinib in daily practice and the various aspects that govern adherence. We hypothesize that side-effects play an important role in the way patients use erlotinib. We expect that the present study will provide valuable knowledge which will be useful for health care professionals to develop interventions to support patients. This approach will improve the adherence and persistence with the use of erlotinib in order to derive optimal benefit from the medication.</p> <p>Trial Registration</p> <p><a href="http://www.trialregister.nl/trialreg/admin/rctview.asp?TC=1830">NTR1830</a></p