A Procedure for Deriving Formulas to Convert Transition Rates to Probabilities for Multi-State Markov Models

For health-economic analyses that use multi-state Markov models, it is often necessary to convert from transition rates to transition probabilities, and for probabilistic sensitivity analysis and other purposes it is useful to have explicit algebraic formulas for these conversions, to avoid having to resort to numerical methods. However, if there are four or more states then the formulas can be extremely complicated. These calculations can be made using packages such as R, but many analysts and other stakeholders still prefer to use spreadsheets for these decision models. We describe a procedure for deriving formulas that use intermediate variables so that each individual formula is reasonably simple. Once the formulas have been derived, the calculations can be performed in Excel or similar software. The procedure is illustrated by several examples and we discuss how to use a computer algebra system to assist with it. The procedure works in a wide variety of scenarios but cannot be employed when there are several backward transitions and the characteristic equation has no algebraic solution, or when the eigenvalues of the transition rate matrix are very close to each other.inancial support for this study was provided in part by grants from the UK Medical Research Council (G0800270), British Heart Foundation (SP/09/002), UK National Institute for Health Research Cambridge Biomedical Research Centre, European Research Council (268834), and European Commission Framework Programme 7 (HEALTH-F2-2012-279233). This work was financially supported by the EPIC-CVD project. EPIC-CVD is a European Commission funded project under the Health theme of the Seventh Framework Programme, building on EPIC-Heart, which was funded by the Medical Research Council, the British Heart Foundation, and a European Research Council Advanced Investigator Award

A cost utility analysis alongside a cluster-randomised trial evaluating a minor ailment service compared to usual care in community pharmacy.

BACKGROUND: Minor ailments are "self-limiting conditions which may be diagnosed and managed without a medical intervention". A cluster randomised controlled trial (cRCT) was designed to evaluate the clinical, humanistic and economic outcomes of a Minor Ailment Service (MAS) in community pharmacy (CP) compared with usual care (UC). METHODS: The cRCT was conducted for 6 months from December 2017. The pharmacist-patient intervention consisted of a standardised face-to-face consultation on a web-based program using co-developed protocols, pharmacists' training, practice change facilitators and patients' educational material. Patients requesting a non-prescription medication (direct product request) or presenting minor ailments received MAS or UC and were followed-up by telephone 10-days after the consultation. The primary economic outcomes were incremental cost-utility ratio (ICUR) of the service and health related quality of life (HRQoL). Total costs included health system, CPs and patient direct costs: health professionals' consultation time, medication costs, pharmacists' training costs, investment of the pharmacy and consultation costs within the 10 days following the initial consultation. The HRQoL was obtained using the EuroQoL 5D-5L at the time of the consultation and at 10-days follow up. A sensitivity analysis was carried out using bootstrapping. There were two sub-group analyses undertaken, for symptom presentation and direct product requests, to evaluate possible differences. RESULTS: A total of 808 patients (323 MAS and 485 UC) were recruited in 27 CPs with 42 pharmacists (20 MAS and 22 UC). 64.7% (n = 523) of patients responded to follow-up after their consultation in CP. MAS patients gained an additional 0.0003 QALYs (p = 0.053). When considering only MAS patients presenting with symptoms, the ICUR was 24,733€/QALY with a 47.4% probability of cost-effectiveness (willingness to pay of 25,000€/QALY). Although when considering patients presenting for a direct product request, MAS was the dominant strategy with a 93.69% probability of cost-effectiveness. CONCLUSIONS: Expanding community pharmacists' scope through MAS may benefit health systems. To be fully cost effective, MAS should not only include consultations arising from symptom presentation but also include an oversight of self-selected products by patients. MAS increase patient safety through the appropriate use of non-prescription medication and through the direct referral of patients to GP. TRIAL REGISTRATION: ISRCTN, ISRCTN17235323 . Registered 07/05/2021 - Retrospectively registered

Arsenic in the cooper´s minerals: An option from the pirometalurgy

En: 1st Spanish National Conference on Advances in Materials Recycling and Eco – Energy Madrid, 12-13 November 2009.-- Editors: F. A. López, F. Puertas, F. J. Alguacil and A. Guerrero.-- 3 pages, 3 figures.The purpose of this paper presented at RECIMAT-09 is to address, briefly and as clearly as possible, expectations which may have arisen from the basic and applied research regarding the increasing problem of pollution caused by arsenic derived from copper metallurgy. In addition to the metallurgical problem which has not been resolved on an industrial scale, there are difficulties with the environment, with energy variables (both exothermic and endothermic reactions) and materials or by-products related to nanoscience and nanotechnology. This type of product may originate from the emergence of new solid phases due to condensation vapour. Finally, since large amounts of high quality AS2O3 metal are being produced naturally through this process, this would be a good time to look at the situation as a real opportunity rather than a problem that must be avoided. We need think only about what it would mean to lower costs and thus prices in the electrical industry - electronic: semiconductor and photovoltaic solar energy, mass and the economic feasibility of the chalcogens (chemical combinations between elements of the III and VI columns in the Periodic Chart) [1].The authors of this work wish to thank the Ministry of Education and Science in Spain (MEC): MAT2003-00502, the Ministry of Foreign Affairs and Cooperation (MAEC): MAEC-AECID-B/1629/04; B/2884/05; B/5814/06, B/7648/07.Peer reviewe

Supplementary material for "A procedure for deriving formulas to convert transition rates to probabilities for multi-state Markov models"

These four Excel files show how to use our procedure for converting transition rates to probabilities. Each file corresponds to one model. For further information and instructions see READ_ME.pdf.This is the supplementary material for the following publication: Jones E, Epstein D, García-Mochón L (2017), A procedure for deriving formulas to convert transition rates to probabilities for multi-state Markov models, Medical Decision Making 37 (7), 779–789.UK Medical Research Council [G0800270], British Heart Foundation [SP/09/002], UK National Institute for Health Research Cambridge Biomedical Research Centre European Research Council [268834], European Commission Framework Programme 7 [HEALTH-F2-2012-279233]. This work was financially supported by the EPIC-CVD project. EPIC-CVD is a European Commission funded project under the Health theme of the Seventh Framework Programme, building on EPIC-Heart, which was funded by the Medical Research Council, the British Heart Foundation, and a European Research Council Advanced Investigator Award

A New Advisor System to Detect the >Tap Hole Whistling and Splashing> in a Blast Furnace

The objective is to determine the moment from which a Blast Furnace tap hole must be closed and consequently the exit of materials (hot metal and slag), by studying the conventional video images obtained at the exit of the tap hole of the BF in order to optimize the process performance. This point is characterized by a remarkable increase in the width of the flow which corresponds to the maximum exit of the slag surrounding the melted metal (and a significant decrease in the pig iron). This video based system is compared to the information provided by the EMF signals (electromotive forces).Peer Reviewe

Solid-fluid characteristics at the blast furnace hearth according to the nodal wear model (NWM)

[ES]La porosidad del coque aparece como unas de las variables que más pueden afectar a la producción de arrabio y a la correspondiente corrosión de los revestimientos. Hasta el momento, en la bibliografía existente sobre la corrosión de los revestimientos, siempre se asocia un mayor desgaste con el correspondiente incremento del flujo del fluido (arrabio) en el crisol. No obstante, no se tiene referencia de ningún modelo determinístico que pudiera relacionar, desde el punto de vista teórico, las siguientes variables: corrosión de los revestimientos, porosidad del coque inactivo y flujo del arrabio en el crisol. El Modelo de Desgaste Nodal (MDN), además de justificar los perfiles de corrosión de los revestimientos a lo largo de la campaña, puede ser un instrumento eficaz para interpretar la porosidad del coque y los gradientes de velocidad del arrabio que se generan dentro del crisol.[EN]The coke porosity is one of the most important variables that can affect the pig iron production and the lining corrosion. Up to now, the existing bibliography about lining corrosion always connects a deeper wear to an increase in the fluid flow (pig iron) at the blast furnace hearth. However, there is no evidence of any deterministic model that could link, from the theoretical point of view, the following variables: lining corrosion, porosity of dead coke and flow of pig iron at the hearth. Besides justifying the lining corrosion profiles, the Nodal Wear Model (NWM) can be an effective instrument to interpret the coke porosity and the pig iron speed rates that are generated inside the hearth.Los autores del trabajo quieren agradecer al Ministerio de Educación y Ciencia-España (MEC): MAT2003- 00502, al Ministerio de Asuntos Exteriores y Cooperación (MAEC): MAEC-AECI-B/1629/04; B/2884/05; B/5814/06, B/7648/07 y al CSIC-Madrid por facilitar la cooperación científica y tecnológica entre el CENIM y la Universidad de Oviedo.Peer reviewe

A new >User-friendly> blast furnace advisory control system using a neural network temperature profile classifier

The adaptation of blast furnaces to the new technologies has increased the operation information so that the sensor information can be known at every moment. However this often results in the supply of excessive data volume to the plant operators. This paper describes an industrial application for self-organized maps (SOM) in order to help them make decisions regarding blast furnace control by means of pattern recognition and the matching of temperature profiles supplied by the thermocouples placed on the above burden. The classification of patterns via easy color coding indicates to the operator what the blast furnace operational situation is, thus making the necessary corrections easier. © 2010 ISIJ.Peer Reviewe

Determinación de los coeficientes de capa límite mediante el Modelo de Desgaste Nodal (MDN) para el estudio de la corrosión del crisol de alto horno

Corrosion of crucibles happens during the blast furnace operation, and it is important to make it as controlled as possible. The wear of the walls and the bottom of the crucible can be qualitatively estimated using temperature data and heat flux, but it is necessary to reach a better knowledge of the multiple mechanisms involved in its degradation. The Nodal Wear Model (NWM) can give us, through thermal boundary layer values, the way to develop the best corrosion model for the crucible.<br><br>Durante la operación de un alto horno, tiene lugar la corrosión del crisol que, se ha de procurar llevar a cabo de una manera controlada. Si bien el progreso del desgaste en paredes y fondo del crisol se puede intuir a través de medidas de temperatura y flujos de calor, se necesita alcanzar un conocimiento más preciso de los mecanismos que influyen en su degradación. El Modelo de Desgaste Nodal (MDN), puede proporcionar a través de los valores de la capa límite térmica, la posibilidad de desarrollar el concepto del patrón de corrosión más indicado para la instalación