Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations

Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$\partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N,$$ and assume that the solution $u$ behaves like the Gauss kernel as $t\to\infty$. In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\to\infty$. This paper is a generalization of our previous paper, and our arguments are applicable to the large class of nonlinear parabolic equations

Associations between adherence, depressive symptoms and health-related quality of life in young adults with cystic fibrosis

BACKGROUND: Cystic fibrosis (CF) is a life shortening disease, however prognosis has improved and the adult population is growing. Most adults with cystic fibrosis live independent lives and balance the demands of work and family life with a significant treatment burden. The aim of this study was to examine the relationships among treatment adherence, symptoms of depression and health-related quality of life (HRQoL) in a population of young adults with CF. METHODS: We administered three standardized questionnaires to 67 patients with CF aged 18–30 years; Morisky Medication Adherence Scale, Major Depression Inventory, and Cystic Fibrosis Questionnaire-Revised. RESULTS: There was a response rate of 77 % and a majority of the young adults (84 %) were employed or in an education program. Most participants (74 %) reported low adherence to medications. One third (32.8 %) of the participants reported symptoms of depression. HRQoL scores were especially low on Vitality and Treatment Burden, and symptoms of depression were associated with low HRQoL scores (p < 0.01) with medium to large deficits across on all HRQoL domains (Cohen’s d 0.60–1.72) except for the domain treatment burden. High depression symptom scores were associated with low adherence (r = −0.412, p < 0.001). CONCLUSIONS: Despite improved physical health, many patients with CF report poor adherence, as well as impaired mental wellbeing and HRQoL. Thus, more attention to mental health issues is needed

Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For the semilinear heat equation $u_t= \Delta u+ u^p$, various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure

Adherence with tobramycin inhaled solution and health care utilization

<p>Abstract</p> <p>Background</p> <p>Adherence with tobramycin inhalation solution (TIS) during routine cystic fibrosis (CF) care may differ from recommended guidelines and affect health care utilization.</p> <p>Methods</p> <p>We analyzed 2001-2006 healthcare claims data from 45 large employers. Study subjects had diagnoses of CF and at least 1 prescription for TIS. We measured adherence as the number of TIS therapy cycles completed during the year and categorized overall adherence as: low ≤ 2 cycles, medium >2 to <4 cycles, and high ≥ 4 cycles per year. Interquartile ranges (IQR) were created for health care utilization and logistic regression analysis of hospitalization risk was conducted by TIS adherence categories.</p> <p>Results</p> <p>Among 804 individuals identified with CF and a prescription for TIS, only 7% (n = 54) received ≥ 4 cycles of TIS per year. High adherence with TIS was associated with a decreased risk of hospitalization when compared to individuals receiving ≤ 2 cycles (adjusted odds ratio 0.40; 95% confidence interval 0.19-0.84). High adherence with TIS was also associated with lower outpatient service costs (IQR: $2,159-$8444 vs. $2,410-$14,423) and higher outpatient prescription drug costs (IQR: $35,125-$60,969 vs. $10,353-$46,768).</p> <p>Conclusions</p> <p>Use of TIS did not reflect recommended guidelines and may impact other health care utilization.</p

An 18-month study of the safety and efficacy of repeated courses of inhaled aztreonam lysine in cystic fibrosis

Chronic airway infection with Pseudomonas aeruginosa (PA) causes morbidity and mortality in patients with cystic fibrosis (CF). Additional anti-PA therapies are needed to improve health status and health-related quality of life. AIR-CF3 was an international 18-month, open-label study to evaluate the safety and efficacy of repeated courses of aztreonam for inhalation solution (AZLI, now marketed as Cayston®) in patients aged ≥6 years with CF and PA infection who previously participated in one of two Phase 3 studies: AIR-CF1 or AIR-CF2. Patients received up to nine courses (28 days on/28 days off) of 75 mg AZLI two (BID) or three times daily (TID) based on randomization in the previous trials. 274 patients, mean age 28.5 years (range: 8–74 years), participated. Mean treatment adherence was high (92.0% BID group, 88.0% TID group). Hospitalization rates were low and adverse events were consistent with CF With each course of AZLI, FEV1 and scores on the Cystic Fibrosis Questionnaire-Revised Respiratory Symptomscale improved and bacterial density in sputum was reduced. Benefits waned in the 28 days off therapy, but weight gain was sustained over the 18months. There were no sustained decreases in PA susceptibility. A dose response was observed; AZLI TID-treated patients demonstrated greater improvements in lung function and respiratory symptoms over 18 months. Repeated intermittent 28-day courses of AZLI treatment were well tolerated. Clinical benefits in pulmonary function, health-related quality of life, and weight were observed with each course of therapy. AZLI is a safe and effective new therapy in patients with CF and PA airway infection

Using rival effects to identify synergies and improve merger typologies

"The strategic management literature has found it difficult to differentiate between collusive and efficiency-based synergies in horizontal merger activity. We propose a schematic to classify mergers that yields more information on merger types and merger effects, and that can, moreover, distinguish between mergers characterized largely by collusion-based synergies and mergers characterized largely by efficiency-based synergies. Crucial to the proposed measurement procedure is that it encompasses the impact of merger events not only on merging firms - as is custom - but also on non-merging competitor firms (the rivals). Employing the event-study methodology with stock-market data on samples of large horizontal mergers drawn from the US and UK (an Anglo-Saxon sub-sample) and from the European continent, we demonstrate how the proposed schematic can better clarify the nature of merger activity." (author's abstract)"Die Literatur über strategisches Management hatte bisher Schwierigkeiten, zwischen wettbewerbsschädlichen und Effizienz steigenden Synergien bei horizontalen Zusammenschlüssen zu differenzieren. Wir schlagen einen konzeptionellen Rahmen vor, um Fusionen zu klassifizieren, welcher mehr Informationen sowohl über die Fusionstypologie als auch über die Wirkung von Zusammenschlüssen entschlüsselt und welcher eine klare Abgrenzung zwischen wettbewerbsschädlichen und wettbewerbsfreundlichen Fusionen erlaubt. Fundamental für diesen konzeptionellen Rahmen ist, dass er nicht nur die Wirkung der Fusion auf die fusionierenden Unternehmen (was typisch in der Literatur ist) umfasst, sondern auch ihre Wirkung auf die Rentabilität der Wettbewerber. Wir wenden eine Ereignisstudienmethode mit Aktiendaten an, um unsere Kategorisierung empirisch umzusetzen. Im Vergleich einer Stichprobe von Fusionen in der angelsächsischen Welt (US und Großbritannien) mit Fusionen zwischen kontinentaleuropäischen Firmen zeigen wir, wie unsere Methodologie hilfreich sein kann, die Art der Fusionsaktivitäten zu identifizieren." (Autorenreferat

Efficacy and safety of azithromycin maintenance therapy in primary ciliary dyskinesia (BESTCILIA): a multicentre, double-blind, randomised, placebo-controlled phase 3 trial.

BACKGROUND Use of maintenance antibiotic therapy with the macrolide azithromycin is increasing in a number of chronic respiratory disorders including primary ciliary dyskinesia (PCD). However, evidence for its efficacy in PCD is lacking. We aimed to determine the efficacy and safety of azithromycin maintenance therapy for 6 months in patients with PCD. METHODS The Better Experimental Screening and Treatment for Primary Ciliary Dyskinesia (BESTCILIA) trial was a multicentre, double-blind, parallel group, randomised, placebo-controlled phase 3 trial done at 6 European PCD clinics (tertiary paediatric care centres and university hospitals in Denmark, Germany, Netherlands, Switzerland, and UK). Patients with a confirmed diagnosis of PCD, aged 7-50 years old, and predicted FEV1 greater than 40% were recruited. Participants were randomly assigned (1:1), stratified by age and study site, via a web-based randomisation system to azithromycin 250 mg or 500 mg as tablets according to bodyweight (</≥ 40 kg) or identical placebo, three times a week for 6 months. The random allocation sequence was a permuted block randomisation, with a block size of four, generated by an external consultancy. Participants, investigators, and care providers were masked to treatment allocation. The primary endpoint was the number of respiratory exacerbations over 6 months. Analysis was by intention to treat. This study is registered in the EU Clinical Trials Register, EudraCT number 2013-004664-58. FINDINGS Between June 24, 2014, and Aug 23, 2016, 102 patients were screened, of whom 90 were randomly assigned to either azithromycin (n=49) or placebo (n=41). The study was ended without having included the planned number of participants due to recruitment difficulties. The mean number of respiratory exacerbations over 6 months was 0·75 (SD 1·12) in the azithromycin group compared with 1·62 (1·64) in the placebo group, and participants receiving azithromycin had significantly lower rate of exacerbations during the individual treatment periods (rate ratio 0·45 [95% CI 0·26-0·78]; p=0·004). Four serious adverse events were reported, occurring in one (2%) of 47 participants in the azithromycin group and in three (7%) of 41 participants in the placebo group. Loose stools or diarrhoea were more common in the azithromycin group than in the placebo group (11 [23%] vs two [5%]). INTERPRETATION This first multinational randomised controlled trial on pharmacotherapy in PCD showed that azithromycin maintenance therapy for 6 months was well tolerated and halved the rate of respiratory exacerbations. Azithromycin maintenance therapy is an option for patients with PCD with frequent exacerbations potentially leading to reduced need for additional antibiotic treatments and preventing irreversible lung damage. FUNDING European Commission Seventh Framework Programme and Children's Lung Foundation (Denmark)

Development of the CFQ-R-8D: estimating utilities from the cystic fibrosis questionnaire-revised

Objective Cystic fibrosis (CF) limits survival and negatively affects health-related quality of life (HRQOL). Cost-effectiveness analysis (CEA) may be used to make reimbursement decisions for new CF treatments; however, generic utility measures used in CEA, such as EQ-5D, are insensitive to meaningful changes in lung function and HRQOL in CF. Here we develop a new, CF disease–specific, preference-based utility measure based on the adolescent/adult version of the Cystic Fibrosis Questionnaire-Revised (CFQ-R), a widely used, CF-specific, patient-reported measure of HRQOL. Methods Blinded CFQ-R data from 4 clinical trials (NCT02347657, NCT02392234, NCT01807923, and NCT01807949) were used to identify discriminating items for a classification system using psychometric (eg, factor and Rasch) analyses. Thirty-two health states were selected for a time-trade-off (TTO) exercise with a representative sample of the UK general population. TTO utilities were used to estimate a preference-based scoring algorithm by regression analysis (Tobit models with robust standard errors clustered on participants with censoring at −1). Results A classification system with 8 dimensions (CFQ-R-8D; Physical Functioning, Vitality, Emotion, Role Functioning, Breathing Difficulty, Cough, Abdominal Pain, and Body Image) was generated. TTO was completed by 400 participants (mean age, 47.3 years; 49.8% female). Among the regression models evaluated, the Tobit heteroscedastic–ordered model was preferred, with a predicted utility range from 0.236 to 1, no logical inconsistencies, and a mean absolute error of 0.032. Conclusion The CFQ-R-8D is the first disease-specific, preference-based scoring algorithm for CF, enabling estimation of disease-specific utilities for CEA based on the well-validated and widely used CFQ-R