The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in Asia and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701).
IntroductionDue to the high prevalence of actinic keratosis (AK) and potential for lesions to become cancerous, clinical guidelines recommend that all are treated. The objective of this study was to evaluate the efficacy and safety of 5-fluorouracil (5-FU) 0.5%/salicylic acid 10% as field-directed treatment of AK lesions.MethodsThis multicenter, double-blind, vehicle-controlled study (NCT02289768) randomized adults, with a 25 cm2 area of skin on their face, bald scalp, or forehead covering 4–10 clinically confirmed AK lesions (grade I/II), 2:1 to treatment or vehicle applied topically once daily for 12 weeks. The primary endpoint was the proportion of patients with complete clinical clearance (CCC) of lesions in the treatment field 8 weeks after the end of treatment. Secondary endpoints included partial clearance (PC; ≥75% reduction) of lesions. Safety outcomes were assessed.ResultsOf 166 patients randomized, 111 received 5-FU 0.5%/salicylic acid 10% and 55 received vehicle. At 8 weeks after the end of treatment, CCC was significantly higher with 5-FU 0.5%/salicylic acid 10% than with vehicle [49.5% vs. 18.2%, respectively; odds ratio (OR) 3.9 (95% CI) 1.7, 8.7; P = 0.0006]. Significantly more patients achieved PC of lesions with treatment than with vehicle [69.5% vs. 34.6%, respectively; OR 4.9 (95% CI 2.3, 10.5); P < 0.0001]. Treatment-emergent adverse events, predominantly related to application- and administration-site reactions, were more common with 5-FU 0.5%/salicylic acid 10% than with vehicle (99.1% vs. 83.6%).ConclusionsCompared with vehicle, field-directed treatment of AK lesions with 5-FU 0.5%/salicylic acid 10% was effective in terms of CCC. Safety outcomes were consistent with the known and predictable safety profile.Trial registration NCT02289768.Funding Almirall S.A.Electronic supplementary materialThe online version of this article (doi:10.1007/s13555-016-0161-2) contains supplementary material, which is available to authorized users.
The concept of local accumulation time (LAT) was introduced by Berezhkovskii and co-workers to give a finite measure of the time required for the transient solution of a reaction-diffusion equation to approach the steady-state solution [A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Biophys. J. 99, L59 (2010); A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Phys. Rev. E 83, 051906 (2011)]. Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb [A. McNabb and G. C. Wake, IMA J. Appl. Math. 47, 193 (1991)]. Although McNabb's initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one-dimensional linear advection-diffusion-reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform-to-uniform transitions; these results provide a practical interpretation for MAT by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.
Berezhkovskii and co-workers introduced the concept of local accumulation time as a finite measure of the time required for the transient solution of a reaction-diffusion equation to effectively reach steady state [Biophys J. 99, L59 (2010); Phys. Rev. E 83, 051906 (2011)]. Berezhkovskii's approach is a particular application of the concept of mean action time (MAT) that was introduced previously by McNabb [IMA J. Appl. Math. 47, 193 (1991)]. Here, we generalize these previous results by presenting a framework to calculate the MAT, as well as the higher moments, which we call the moments of action. The second moment is the variance of action time, the third moment is related to the skew of action time, and so on. We consider a general transition from some initial condition to an associated steady state for a one-dimensional linear advection-diffusion-reaction partial differential equation (PDE). Our results indicate that it is possible to solve for the moments of action exactly without requiring the transient solution of the PDE. We present specific examples that highlight potential weaknesses of previous studies that have considered the MAT alone without considering higher moments. Finally, we also provide a meaningful interpretation of the moments of action by presenting simulation results from a discrete random-walk model together with some analysis of the particle lifetime distribution. This work shows that the moments of action are identical to the moments of the particle lifetime distribution for certain transitions.
Transport through crowded environments is often classified as anomalous, rather than classical, Fickian diffusion. Several studies have sought to describe such transport processes using either a continuous time random walk or fractional order differential equation. For both these models the transport is characterized by a parameter α, where α = 1 is associated with Fickian diffusion and α < 1 is associated with anomalous subdiffusion. Here, we simulate a single agent migrating through a crowded environment populated by impenetrable, immobile obstacles and estimate α from mean squared displacement data. We also simulate the transport of a population of such agents through a similar crowded environment and match averaged agent density profiles to the solution of a related fractional order differential equation to obtain an alternative estimate of α. We examine the relationship between our estimate of α and the properties of the obstacle field for both a single agent and a population of agents; we show that in both cases, α decreases as the obstacle density increases, and that the rate of decrease is greater for smaller obstacles. Our work suggests that it may be inappropriate to model transport through a crowded environment using widely reported approaches including power laws to describe the mean squared displacement and fractional order differential equations to represent the averaged agent density profiles.
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