Almost sure asymptotics for the maximum local time in Brownian environment

We study the asymptotic behaviour of the maximum local time L*(t) of the Brox's process, the diffusion in Brownian environment. Shi proved that the maximum speed of L*(t) is surprisingly, at least t log(log(log t)) whereas in the discrete case it is t. We show here that t log(log(log t)) is the proper rate and we prove that for the minimum speed the rate is the same as in the discrete case namely t/log(log(log t))

Rough paths and 1d sde with a time dependent distributional drift. Application to polymers

Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional stochastic differential equations, the drift of which is a distribution, by means of rough paths theory. Existence and uniqueness are established in the weak sense when the drift reads as the derivative of a H{\"o}lder continuous function. Regularity of the drift part is investigated carefully and a related stochastic calculus is also proposed, which makes the structure of the solutions more explicit than within the earlier framework of Dirichlet processes

Limit law of the local time for Brox's diffusion

We consider Brox's model: a one-dimensional diffusion in a Brownian potential W. We show that the normalized local time process (L(t;m_(log t) + x)=t; x \in R), where m_(log t) is the bottom of the deepest valley reached by the process before time t, behaves asymptotically like a process which only depends on W. As a consequence, we get the weak convergence of the local time to a functional of two independent three-dimensional Bessel processes and thus the limit law of the supremum of the normalized local time. These results are discussed and compared to the discrete time and space case which same questions have been solved recently by N. Gantert, Y. Peres and Z. Shi

The number of potential winners in Bradley-Terry model in random environment

We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number of potential winners.First we prove that under mild assumptions, mainly on their moments, if the strengths are unbounded, the asymptotic probability that the best player wins is 1. We also exhibit a sufficient convexity condition to obtain the same result when the strengths are bounded. When this last condition fails, the number of potential winners grows at a rate depending on the tail of the distribution of strengths. We also study the minimal strength required for an additional player to win in this last case

Learning the distribution of latent variables in paired comparison models with round-robin scheduling

Paired comparison data considered in this paper originate from the comparison of a large number N of individuals in couples. The dataset is a collection of results of contests between two individuals when each of them has faced n opponents, where n is much larger than N. Individual are represented by independent and identically distributed random parameters characterizing their abilities.The paper studies the maximum likelihood estimator of the parameters distribution. The analysis relies on the construction of a graphical model encoding conditional dependencies of the observations which are the outcomes of the first n contests each individual is involved in. This graphical model allows to prove geometric loss of memory properties and deduce the asymptotic behavior of the likelihood function. This paper sets the focus on graphical models obtained from round-robin scheduling of these contests.Following a classical construction in learning theory, the asymptotic likelihood is used to measure performance of the maximum likelihood estimator. Risk bounds for this estimator are finally obtained by sub-Gaussian deviation results for Markov chains applied to the graphical model

Cost effectiveness of treating multi-drug resistant tuberculosis by adding Deltyba™ to background regimens in Germany

SummaryObjectiveTo assess the cost-effectiveness of adding delamanid (Deltyba™) to a background regimen (BR) for treating multidrug-resistant tuberculosis (MDR-TB) in Germany.MethodsThe incremental cost-effectiveness of treating a cohort of MDR-TB patients, 38-years old on average, with Deltyba™ plus BR versus a five drug- BR regimen alone was compared in a Markov model over a period of 10 years. Cost per quality-adjusted life year (QALY) and disability-adjusted life years (DALY) were determined from a societal perspective. Recent data from a German cost calculation on MDR-TB were applied to the 24-month outcome results of patients participating in the placebo-controlled, phase II Otsuka's Trial 204. Costs and effectiveness were discounted at a rate of 3% and subjected to deterministic as well as probabilistic sensitivity analysis in a Monte Carlo simulation.ResultsBased on the current market prices the total discounted cost per patient on BR plus Deltyba™ was €142,732 compared to €150,909 for BR alone. The total discounted QALYs per patient were 8.47 for Deltyba™ versus 6.13 for BR alone. Accordingly, the addition of Deltyba™ proved to be dominant over the BR alone-strategy by simultaneously saving €8177 and gaining 2.34 QALYs. Deltyba™ was cost saving in 73% of probabilistic sensitivity analyses compared to BR alone and 100% cost effective at a willingness-to-pay (WTP) threshold of €10,000.ConclusionsUnder conditions prevalent in Germany, Deltyba™ added to a five drug BR regimen is likely to be cost-saving compared to BR alone under a wide range of assumptions. Adding delamanid remained cost-effective when costs due to loss of productivity were excluded as the QALYs gained by lower lethality and a higher proportion of successfully treated patients outweighed the delamanid drug costs. These results strongly support the application of Deltyba™ in treating MDR-TB patients

Prevalence of latent tuberculosis infection among health care workers in a hospital for pulmonary diseases

<p>Abstract</p> <p>Background</p> <p>Little is known about the prevalence of latent tuberculosis infections (LTBI) in health care workers (HCW) in low-incidence countries especially in hospitals for pulmonary diseases. With Interferon-gamma release assays (IGRA), a new method for diagnosis of LTBI is available which is more specific than the tuberculin skin test (TST).</p> <p>Objectives</p> <p>The study was designed to estimate prevalence of LTBI among 270 HCW in a Hospital of Pulmonary Diseases routinely screened for TB.</p> <p>Methods</p> <p>LTBI was assessed by the QuantiFERON-Gold In Tube (QFT-IT). Information on gender, age, workplace, job title, BCG vaccination and history of both TB and TST were collected using a standardised questionnaire. Adjusted odds ratios for potential risk factors for LTBI were calculated.</p> <p>Results</p> <p>The prevalence of LTBI was 7.2%. In HCW younger than 30 years LTBI prevalence was 3.5% and in those older than 50 years 22%. Physicians and nurses showed a higher prevalence rate than other professions (10.8% to 4.5%). The putative risk factors for LTBI were age (>50 year OR 9.3, 95%CI 2.5–33.7), working as physicians/nurses (OR 3. 95%CI 1.2–10.4) and no previous TST in medical history (OR 4.4, 95%CI 1.01–18.9) when compared to those with a negative TST.</p> <p>Conclusion</p> <p>Prevalence of LTBI assessed by QFT-IT is low, this indicates a low infection risk even in hospitals for pulmonary diseases. No statement can be made regarding the occupational risk as compared to the general population because there are no LTBI prevalence data from Germany available. The higher LTBI prevalence rate in older HCWs might be due to the cohort effect or the longer time at risk.</p

Systematic review of cost and cost-effectiveness of different TB-screening strategies

<p>Abstract</p> <p>Background</p> <p>Interferon-γ release assays (IGRAs) for TB have the potential to replace the tuberculin skin test (TST) in screening for latent tuberculosis infection (LTBI). The higher per-test cost of IGRAs may be compensated for by lower post-screening costs (medical attention, chest x-rays and chemoprevention), given the higher specificity of the new tests as compared to that of the conventional TST. We conducted a systematic review of all publications that have addressed the cost or cost-effectiveness of IGRAs. The objective of this report was to undertake a structured review and critical appraisal of the methods used for the model-based cost-effectiveness analysis of TB screening programmes.</p> <p>Methods</p> <p>Using Medline and Embase, 75 publications that contained the terms "IGRA", "tuberculosis" and "cost" were identified. Of these, 13 were original studies on the costs or cost-effectiveness of IGRAs.</p> <p>Results</p> <p>The 13 relevant studies come from five low-to-medium TB-incidence countries. Five studies took only the costs of screening into consideration, while eight studies analysed the cost-effectiveness of different screening strategies. Screening was performed in high-risk groups: close contacts, immigrants from high-incidence countries and healthcare workers. Two studies used the T-SPOT.TB as an IGRA and the other studies used the QuantiFERON-TB Gold and/or Gold In-Tube test. All 13 studies observed a decrease in costs when the IGRAs were used. Six studies compared the use of an IGRA as a test to confirm a positive TST (TST/IGRA strategy) to the use of an IGRA-only strategy. In four of these studies, the two-step strategy and in two the IGRA-only strategy was more cost-effective. Assumptions about TST specificity and progression risk after a positive test had the greatest influence on determining which IGRA strategy was more cost-effective.</p> <p>Conclusion</p> <p>The available studies on cost-effectiveness provide strong evidence in support of the use of IGRAs in screening risk groups such as HCWs, immigrants from high-incidence countries and close contacts. So far, only two studies provide evidence that the IGRA-only screening strategy is more cost-effective.</p