Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure

Acid-base changes and acetate metabolism during routine and high-efficiency hemodialysis in children

Acid-base changes and acetate metabolism during routine and high-efficiency hemodialysis in children. Changes in acid-base status and plasma acetate concentrations were studied in eight children during 11 hemodialysis sessions. During dialysis, the blood bicarbonate concentration fell (20.5 ± 0.7 to 19.6 ± 0.8 mEq/liter), the PCO2 fell (33.4 ± 0.8 to 27.5 ± 1.4 mm Hg), and the pH rose (7.42 ± 0.01 to 7.48 ± 0.02). During the hour after dialysis, the bicarbonate concentration rose to normal (23.4 ± 0.7 mEq/liter), the PCO2 rose (32.8 ± 0.8 mm Hg), and the pH remained unchanged. The half-life of plasma acetate, measured after dialysis, was 8.7 min. During five “high-efficiency” dialysis sessions (urea clearance, > 3.0 ml/min/kg), blood bicarbonate concentration fell 3.2 mEq/liter, PCO2 fell 8.7 mm Hg, and plasma acetate rose to 7.51 mmoles/liter, whereas during six “routine efficiency” dialysis sessions (urea clearance, 1.5 to 3.0 ml/min/kg), blood bicarbonate rose 1.0 mEq/liter, PCO2 fell 36 mm Hg, and plasma acetate rose to 3.52 mmoles/liter. At 1 hour after the end of dialysis, blood bicarbonate, PCO2, and plasma acetate concentrations were similar in the two groups. Clinical problems occurred more frequently in the high-efficiency group during dialysis although the difference was not significant. The data indicate that (1) dialysis with acetate buffer effectively corrects pre-dialysis metabolic acidosis, (2) although children have a high rate of acetate metabolism, during high-efficiency dialysis this rate is exceeded by the influx of acetate, and acid-base abnormalities occur. These abnormalities are transient but may cause clinical problems.Modifications acido-basiques et métabolisme de l'acétate au cours de l'hémodialyse de routine ou à efficacité élevée chez l'enfant. Les modifications de l'état acido-basique et des concentrations plasmatiques d'acétate ont été étudiées chez huit enfants au cours de 11 séances d'hémodialyse. Au cours de la dialyse les bicarbonates diminuent (20,5 ± 0,7 à 19,6 ± 0,8 mEq/ litre), la PCO2 diminue (33,4 ± 0,8 à 27,5 ± 1,4 mm Hg), et le pH augmente (7,42 ± 0,01 à 7,48 ± 0,02). Au cours de l'heure qui suit la dialyse les bicarbonates s'élèvent à une valeur normale, 23,4 ± 0,07 mEq/litre, la PCO2 s'élève à 32,8 ± 0,8 mm Hg, et le pH est inchangé. La demi vie de l'acétate plasmatique, mesurée après la dialyse, était de 8,7 min. Au cours de cinq séances de dialyse à haute efficacité (clearance de l'urée, > 3,0 ml/min/kg) les bicarbonates baissent de 3,2 mEq/litre, la PCO2 de 8,7 mm Hg, et l'acétate plasmatique s'est élevé à 7,51 mmoles/litre alors qu'au cours de six séances de dialyse d'efficacité moyenne (clearance de l'urée, 1,5 à 3,0 ml/min/kg) les bicarbonates ont augmenté de 1,0 mEq/litre, la PCO2 a diminué de 3,6 mm Hg, et l'acétate plasmatique s'est élevé à 3,52 mmoles/litre. Une heure après la fin de la dialyse les bicarbonates, la PCO2 et l'acétate plasmatique étaient semblables dans les deux groupes. Des problèmes cliniques sont survenus plus souvent au cours de la dialyse dans le groups à haute efficacité bien que la différence ne soit pas significative. Ces résultats indiquent que (1) la dialyse avec le tampon acétate corrige efficacement l'acidose métabolique pré-dialytique, (2) bien que l'enfant ait une capacité élevée de métaboliser l'acétate, cette capacité est débordée, au cours de la dialyse à haute efficacité, par l'entrée d'acétate et des anomalies acidobasiques surviennent. Ces anomalies sont transitoires et peuvent déterminer des problèmes cliniques

Increasing the information provided by probabilistic sensitivity analysis:The relative density plot

Background Results of probabilistic sensitivity analyses (PSA) are frequently visualized as a scatterplot, which is limited through overdrawing and a lack of insight in relative density. To overcome these limitations, we have developed the Relative Density plot (PSA-ReD). Methods The PSA-ReD combines a density plot and a contour plot to visualize and quantify PSA results. Relative density, depicted using a color gradient, is transformed to a cumulative probability. Contours are then plotted over regions with a specific cumulative probability. We use two real-world case studies to demonstrate the value of the PSA-ReD plot. Results The PSA-ReD method demonstrates proof-of-concept and feasibility. In the real-world case-studies, PSA-ReD provided additional visual information that could not be understood from the traditional scatterplot. High density areas were identified by color-coding and the contour plot allowed for quantification of PSA iterations within areas of the cost-effectiveness plane, diminishing overdrawing and putting infrequent iterations in perspective. Critically, the PSA-ReD plot informs modellers about non-linearities within their model. Conclusions The PSA-ReD plot is easy to implement, presents more of the information enclosed in PSA data, and prevents inappropriate interpretation of PSA results. It gives modelers additional insight in model functioning and the distribution of uncertainty around the cost-effectiveness estimate

A novel method for predicting the budget impact of innovative medicines:validation study for oncolytics

Background High budget impact (BI) estimates of new drugs have led to decision-making challenges potentially resulting in restrictions in patient access. However, current BI predictions are rather inaccurate and short term. We therefore developed a new approach for BI prediction. Here, we describe the validation of our BI prediction approach using oncology drugs as a case study. Methods We used Dutch population-level data to estimate BI where BI is defined as list price multiplied by volume. We included drugs in the antineoplastic agents ATC category which the European Medicines Agency (EMA) considered a New Active Substance and received EMA marketing authorization (MA) between 2000 and 2017. A mixed-effects model was used for prediction and included tumor site, orphan, first in class or conditional approval designation as covariates. Data from 2000 to 2012 were the training set. BI was predicted monthly from 0 to 45 months after MA. Cross-validation was performed using a rolling forecasting origin with e|Ln(observed BI/predicted BI)| as outcome. Results The training set and validation set included 25 and 44 products, respectively. Mean error, composed of all validation outcomes, was 2.94 (median 1.57). Errors are higher with less available data and at more future predictions. Highest errors occur without any prior data. From 10 months onward, error remains constant. Conclusions The validation shows that the method can relatively accurately predict BI. For payers or policymakers, this approach can yield a valuable addition to current BI predictions due to its ease of use, independence of indications and ability to update predictions to the most recent data

Phase I/II Clinical Trial-Based Early Economic Evaluation of Acalabrutinib for Relapsed Chronic Lymphocytic Leukaemia

Objectives: The objective of this study was to construct an early economic evaluation for acalabrutinib for relapsed chronic lymphocytic leukaemia (CLL) to assist early reimbursement decision making. Scenarios were assessed to find the relative impact of critical parameters on incremental costs and quality-adjusted life-years (QALYs). Methods: A partitioned survival model was constructed comparing acalabrutinib and ibrutinib from a UK national health service perspective. This model included states for progression-free survival (PFS), post-progression survival (PPS) and death. PFS and overall survival (OS) were parametrically extrapolated from ibrutinib publications and a preliminary hazard ratio based on phase I/II data was applied for acalabrutinib. Deterministic and probabilistic sensitivity analyses were performed, and 1296 scenarios were assessed. Results: The base-case inc

The Application and Implications of Novel Deterministic Sensitivity Analysis Methods

Deterministic sensitivity analyses (DSA) remain important to interpret the effect of uncertainties in individual parameters on results of cost-effectiveness analyses. Classic DSA methodologies may lead to wrong conclusions due to a lack of or misleading information regarding marginal effects, non-linearity, likelihood and correlations. In addition, tornado diagrams are misleading in some situations. Recent advances in DSA methods have the potential to provide decision makers with more reliable information regarding the effects of uncertainties in individual parameters. This practical application discusses advances to classic DSA methods and their implications. Three methods are discussed: stepwise DSA, distributional DSA and probabilistic DSA. For each method, the technical specifications, options for presenting results, and its implications for decision making are discussed. Options for visualizing DSA results in incremental cost-effectiveness ratios and in incremental net benefits are presented. The use of stepwise DSA increases interpretability of marginal effects and non-linearities in the model, which is especially relevant when arbitrary ranges are implemented. Using the probability distribution of each parameter in distributional DSA provides insight on the likelihood of model outcomes while probabilistic DSA also includes the effects of correlations between parameters. Probabilistic DSA, preferably expressed in incremental net benefit, is the most appropriate method for providing insight on the effect of uncertainty in individual parameters on the estimate of cost effectiveness. However, the opportunities provided by probabilistic DSA may not always be needed for decision making. Other DSA methods, in particular distributional DSA, can sometimes be sufficient depending on model features. Decision makers must determine to which extent they will accept and implement these new and improved DSA methodologies and adjust guidelines accordingly

Cost-effectiveness of clopidogrel vs. ticagrelor in patients of 70 years or older with non-ST-elevation acute coronary syndrome

OBJECTIVE: The POPular AGE trial showed that clopidogrel significantly reduced bleeding risk compared with ticagrelor without any signs of an increase in thrombotic events. The aim of this analysis was to estimate the long-term cost-effectiveness of clopidogrel compared with ticagrelor in these patients aged 70 years or older with non-ST-elevation acute coronary syndrome (NSTE-ACS). METHODS AND RESULTS: A 1-year decision tree based on the POPular AGE trial in combination with a lifelong Markov model was developed to compare clopidogrel with ticagrelor in terms of clinical outcomes, costs, and quality-adjusted life years (QALYs) in elderly patients (above 70 year) with NSTE-ACS. Cost-effectiveness was assessed from a Dutch healthcare system perspective. Events rates and utility data observed in the POPular AGE trial were combined with lifetime projections to evaluate costs and effects for a fictional cohort of 1000 patients. Treatment with clopidogrel instead of ticagrelor led to a cost saving of €1484 575 (€1485 per patient) and a decrease of 10.96 QALYs (0.011 QALY per patient) in the fictional cohort. In an alternative base case with equal distribution over health states in the first year, treatment with clopidogrel led to an increase in QALYs. In all scenario analyses, treatment with clopidogrel was cost-saving. CONCLUSION: Clopidogrel is a cost-saving alternative to ticagrelor in elderly patients after NSTE-ACS, though regarding overall cost-effectiveness clopidogrel was not superior to ticagrelor, as it resulted in a small negative effect on QALYs. However, based on the results of the alternative base case and clinical outcomes of the POPular AGE trial, clopidogrel could be a reasonable alternative to ticagrelor for elderly NSTE-ACS patients with a higher bleeding risk