ABSTRACT
We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection-diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our asymptotic theory relies on a domain perturbation approach for small roughness amplitudes of the channel and holds for general surface shapes expandable as a Fourier series. We determine an anisotropic dispersion tensor, which depends on the characteristic wavelengths and amplitude of the surface structure. For surfaces whose corrugations are tilted with respect to the applied flow direction, we find that dispersion along the principal direction (i.e. the principal eigenvector of the dispersion tensor) is at an angle to the main flow direction and becomes enhanced relative to classical Taylor dispersion. In contrast, dispersion perpendicular to it can decrease compared to the short-time diffusivity of the particles. Furthermore, for an arbitrary surface shape represented in terms of a Fourier decomposition, we find that each Fourier mode contributes at leading order a linearly-independent correction to the classical Taylor dispersion diffusion tensor.
ABSTRACT
A Breast Cancer Outcomes model was developed at the ONCOTYROL research center to evaluate personalized test-treatment strategies in Austria. The goal was to evaluate the cost-effectiveness of a new 21-gene assay (ODX) when used in conjunction with the Adjuvant! Online (AO) decision aid to support personalized decisions about use of adjuvant chemotherapy in early-stage breast cancer patients in Austria. We applied a validated discrete-event-simulation model to a hypothetical cohort of 50 years old women over a lifetime horizon. The test-treatment strategies of interest were defined using three-letter acronyms. The first (second, third) letter indicates whether patients with a low (intermediate, high) risk according to AO were tested using ODX (Y yes, N no). The main outcomes were life-years gained, quality-adjusted life-years (QALYs), costs and cost effectiveness. Robustness of the results was tested in sensitivity analyses. Results were compared to a Canadian analysis conducted by the Toronto Health Economics and Technology Assessment Collaborative (THETA). Five of eight strategies were dominated (i.e., more costly and less effective: NNY, NYN, YNN, YNY, YYN). The base-case analysis shows that YYY (ODX provided to all patients) is the most effective strategy and is cost effective with an incremental cost-effectiveness ratio of 15,700 EUR per QALY gained. These results are sensitive to changes in the probabilities of distant recurrence, age and costs of chemotherapy. The results of the base-case analysis were comparable to the THETA results. Based on our analyses, using ODX in addition to AO is effective and cost effective in all women in Austria. The development of future genetic tests may require alternative or additional test-treatment strategies to be evaluated.
ABSTRACT
PURPOSE: The purpose of this study was to provide a clinician-friendly overview of decision-analytic models evaluating different treatment strategies for multiple myeloma (MM). METHODS: We performed a systematic literature search to identify studies evaluating MM treatment strategies using mathematical decision-analytic models. We included studies that were published as full-text articles in English, and assessed relevant clinical endpoints, and summarized methodological characteristics (e.g., modeling approaches, simulation techniques, health outcomes, perspectives). RESULTS: Eleven decision-analytic modeling studies met our inclusion criteria. Five different modeling approaches were adopted: decision-tree modeling, Markov state-transition modeling, discrete event simulation, partitioned-survival analysis and area-under-the-curve modeling. Health outcomes included survival, number-needed-to-treat, life expectancy, and quality-adjusted life years. Evaluated treatment strategies included novel agent-based combination therapies, stem cell transplantation and supportive measures. CONCLUSION: Overall, our review provides a comprehensive summary of modeling studies assessing treatment of MM and highlights decision-analytic modeling as an important tool for health policy decision making.
