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Like most of the world, low- and middle-income countries have faced a growing demand for new health technologies and higher budget constraints. It is necessary to have technical instruments to make decisions based on real-world evidence that allows maximization of the population’s health with a limited budget. We estimated the supply-based cost-effectiveness elasticity, which was then used to determine the cost-effectiveness threshold for the healthcare system of Colombia, a middle-income country where multiple insurers, paid under capitation rules, manage the compulsory contributions of the citizens and government subsidies. Using administrative data, we explored the variation of health expenditures and outcomes at the insurer, geographical region, diagnosis group and year levels. To deal with endogeneity in a two-way fixed-effects model, we instrumented health expenditures using characteristics of the health system such as drug-price regulation. We estimated the threshold to be US$4487.5 per years of life lost avoided [14.7 million Colombian pesos (COP) at 2019 prices] and US$5180.8 per quality-adjusted life-years gained (17 million COP at 2019 prices), around one times the gross domestic product GDP per capita. To the best of our knowledge, this is the first estimation of the cost-effectiveness threshold elasticity supply-based in a middle-income country with a managed healthcare system.

Computational Logic is a wide interdisciplinary field having its theoretical and practical roots in mathematics, computer science, logic, and artificial intelligence. Computational Logic try to produce efficient and powerful algorithms for deciding the satisfiability of formulas in logical theories. This work is about propositional and first order logic, and its implementation in the functional language Ocaml. In particular, the aim of this work is to explain the quantifier elimination algorithm. As an example, we develop the quantifier elimination algorithm for the Theory of dense linear orders. Quantifier elimination is an algorithm supported by some logical theories. By eliminating quantifiers from a formula, it makes it possible to test its satisfiability in the sense of propositional logic. Universidad de Sevilla. Grado en Matemáticas

Introduction: The use of an implantable cardioverter-defibrillator reduces the probability of sudden cardiac death in patients with heart failure. Objective: To determine the cost-utility relationship of an implantable cardioverterdefibrillator compared to optimal pharmacological therapy for patients with ischemic or nonischemic New York Heart Association class II or III (NYHA II-III) heart failure in Colombia. Materials and methods: We developed a Markov model including costs, effectiveness, and quality of life from the perspective of the Colombian health system. For the baseline case, we adopted a time horizon of 10 years and discount rates of 3% for costs and 3.5% for benefits. The transition probabilities were obtained from a systematic review of the literature. The outcome used was the quality-adjusted life years. We calculated the costs by consulting with the manufacturers of the device offered in the Colombian market and using national-level pricing manuals. We conducted probabilistic and deterministic sensitivity analyses. Results: In the base case, the incremental cost-effectiveness ratio for the implantable cardioverter-defibrillator was USD$ 13,187 per quality-adjusted life year gained. For a willingness-to-pay equivalent to three times the gross domestic product per capita as a reference (USD$ 19,139 in 2017), the device would be a cost-effective strategy for the Colombian health system. However, the result may change according to the time horizon, the probability of death, and the price of the device. Conclusions: The use of an implantable cardioverter-defibrillator for preventing sudden cardiac death in patients with heart failure would be a cost-effective strategy for Colombia. The results should be examined considering the uncertainty Resumen Introducción. El uso del desfibrilador cardioversor implantable reduce la probabilidad de muerte súbita en pacientes con insuficiencia cardíaca. Objetivo. Determinar la relación de costo-utilidad de un desfibrilador cardioversor implantable comparado con la terapia farmacológica óptima para pacientes con insuficiencia cardíaca isquémica o no isquémica de clase II o III según la New York Heart Association (NYHA II-III) en Colombia. Materiales y métodos. Se desarrolló un modelo de Markov que incluyó los costos, la efectividad y la calidad de vida desde la perspectiva del sistema de salud colombiano. Para el caso de base, se adoptó un horizonte temporal de 10 años y una tasa de descuento de 3 % para los costos y de una 3,5 % para los beneficios. Las probabilidades de transición se obtuvieron de una revisión sistemática de la literatura. Los años de vida ajustados por calidad se usaron como resultado de salud. Para estimar los costos unitarios se usaron manuales tarifarios nacionales y, para los costos del dispositivo, se consultó a los fabricantes que lo comercializan en el mercado colombiano. Se hicieron análisis de sensibilidad probabilísticos y determinísticos. Resultados. En el caso base el costo adicional por año de vida ajustado por calidad ganado con el desfibrilador cardioversor implantable fue de USD$ 13,187. Usando un umbral de tres veces el producto interno bruto per cápita como referencia (USD$ 19.139 en 2017), el dispositivo sería costo-efectivo para el sistema de salud colombiano. Sin embargo, este resultado depende del horizonte temporal, de la probabilidad de muerte y del precio del dispositivo. Conclusiones. El uso de un desfibrilador cardioversor implantable sería una estrategia costo-efectiva para Colombia, aunque los resultados deben examinarse teniendo en cuenta la incertidumbre.

RESUMEN: Objetivo: determinar, desde la perspectiva del sistema de salud colombiano, la relación de costo-efectividad del prasugrel comparado con clopidogrel, para el tratamiento de pacientes adultos con síndrome coronario agudo. Material y métodos: se construyó un modelo de Markov con ciclos anuales en el cual los pacientes pueden permanecer sin experimentar nuevos eventos cardiovasculares, sufrir un nuevo evento o morir. En el caso base se adoptó un horizonte temporal de 10 años y una tasa de descuento del 3%. Las probabilidades de transición se extrajeron del ensayo clínico TRITON-TIMI 38, de las estadísticas vitales del Departamento Nacional de Estadística y de la información de los pacientes colombianos del registro ACCESS. Para identificar y medir el uso de recursos se diseño un caso típico a partir de la revisión de guías y protocolos; para la valoración se emplearon manuales tarifarios colombianos. Se realizaron análisis de sensibilidad determinísticos y probabilísticos. Resultados: en el caso base, el costo por año de vida ajustado por calidad ganado con prasugrel es de $79987695 pesos colombianos Los resultados son sensibles a cambios en el horizonte temporal y al costo del clopidogrel. Bajo un umbral de disposición a pagar de 3 veces el PIB per cápita colombiano, la probabilidad de que el prasugrel sea costo efectivo es del 7%. Conclusiones: la decisión respecto a la inclusión del prasugrel en el tratamiento de pacientes con síndrome cororanario agudo, sometidos a intervención coronaria percutánea depende fundamentalmente del costo del clopidogrel que el decisor considere relevante para realizar la comparación. ABSTRACT: Objective: to determine the cost-effectiveness relation of prasugrel compared with clopidogrel for the treatment of adult patients with acute coronary syndrome from the perspective of Colombian health system. Material and methods: a Markov model with annual cycles in which patients can remain without experiencing new cardiovascular events, have a new event or die, was built. In the base case a time horizon of 10 years and a discount rate of 3% was adopted. Transition probabilities were taken from the clinical trial TRITON-TIMI 38, of vital statistics from the National Department of Statistics and from the information of Colombian patients in ACCESS registry. To identify and measure the use of resources, a typical case was designed from the review of guidelines and protocols; Colombian tariff manuals were used for assessment. Deterministic and probabilistic sensitivity analyzes were performed. Results: in the base case, the cost per year of quality-adjusted life gained with prasugrel is $ 79,987,695 Colombian pesos. The results are sensitive to changes in the timeframe and cost of clopidogrel. Under a threshold willingness to pay three times the per capita GDP of Colombia, the probability that prasugrel may be cost-effective, is 7%. Conclusions: the decision on the inclusion of prasugrel in the treatment of patients with acute coronary syndrome undergoing percutaneous coronary intervention depends mainly on the cost of clopidogrel that the decision maker considers relevant to perform the comparison. COL0135865 COL0015599

Introduction: Acute coronary syndrome is one of the most frequent medical emergencies in developing countries. Objective: To determine, from the perspective of the Colombian health system, the cost-effectiveness of ticagrelor compared to clopidogrel for the treatment of patients with acute coronary syndrome. Materials and methods: We conducted a cost-effectiveness analysis from the perspective of the Colombian health system comparing ticagrelor and clopidogrel for the treatment of patients with acute coronary syndrome. To estimate the expected costs and outcomes, a Markov model was constructed in which patients could remain stable without experiencing new cardiovascular events, suffer from a new event, or die. For the baseline case, a 10-year time horizon and a discount ratio of 3% for costs and benefits were adopted. The transition probabilities were extracted from the PLATO (Platelet Inhibition and Patient Outcomes) clinical trial. Vital statistics were drawn from the Departmento Administrativo Nacional de Estadística (DANE) and additional information from Colombian patients included in the Access registry. To identify and measure resource use, a standard case was built by consulting guidelines and protocols. Unit costs were obtained from Colombian rate lists. A probabilistic sensitivity analysis was conducted in which costs were represented by a triangular distribution, and the effectiveness through a beta distribution. Results: In the base case, the additional cost per quality-adjusted life-year gained with ticagrelor was COP$ 28,411,503. The results were sensitive to changes in the time horizon and the unit cost of clopidogrel. For a willingness-to-pay equivalent to three times the Colombian per capita gross domestic product, the probability of ticagrelor being cost-effective was 75%. Conclusions: Ticagrelor is a cost-effective strategy for the treatment of patients with acute coronary syndrome in Colombia. Introducción. El síndrome coronario agudo es una de las emergencias médicas más frecuentes en los países en desarrollo. Objetivo. Determinar, desde la perspectiva del sistema de salud colombiano, la relación de costo-efectividad del ticagrelor comparado con el clopidogrel para el tratamiento de pacientes con síndrome coronario agudo. Materiales y métodos. Se hizo un análisis de costo-efectividad desde la perspectiva del sistema de salud colombiano, comparando el ticagrelor y el clopidogrel para el tratamiento de pacientes con síndrome coronario agudo. Para estimar los costos y resultados esperados de las dos alternativas, se construyó un modelo de Markov en el cual los pacientes podían permanecer estables sin experimentar nuevos eventos cardiovasculares, sufrir de un nuevo evento coronario o morir. Para el caso de base, se adoptó un horizonte temporal de 10 años y una tasa de descuento de 3 % para los costos y beneficios. Las probabilidades de transición se extrajeron del estudio Platelet Inhibition and Patient Outcomes , PLATO. Las estadísticas vitales se consultaron en informes del Departamento Administrativo Nacional de Estadística (DANE) y los parámetros adicionales del modelo se basaron en la información de los pacientes colombianos incluidos en el registro en Access. Para identificar y medir el uso de recursos, se construyó un caso estándar a partir de guías y protocolos. Los costos unitarios se obtuvieron de manuales tarifarios colombianos. Se hizo un análisis de sensibilidad probabilístico en el que los costos se representaron por una distribución triangular y, las probabilidades de transición, mediante una distribución beta. Resultados. En el caso de base, el costo adicional por años de vida ajustados por calidad ganados con el ticagrelor fue de COP$ 28´411.503. Los resultados fueron sensibles a los cambios en el horizonte temporal y al costo unitario del clopidogrel. Para un umbral de costo-efectividad equivalente a tres veces el producto interno bruto per cápita de Colombia, la probabilidad de que el ticagrelor fuera costo-efectivo fue de 75 %. Conclusiones. El ticagrelor es una estrategia costo-efectiva para el tratamiento de los pacientes con síndrome coronario agudo en Colombia.

Introduction Ondansetron reduces hospitalization rates for diarrhea and vomiting in children, but is not yet routinely used. Objective To estimate from a social perspective the relative cost-effectiveness of ondansetron for the treatment of vomiting in children with gastroenteritis and at risk of dehydration in Colombia. Methods Cost-effectiveness analysis from a social perspective, including direct medical costs and costs for caregivers. With a decision tree we compared costs and health outcomes of usual treatment without antiemetic to usual treatment plus ondansetron in children under 5 years with gastroenteritis and vomiting. Effectiveness of intervention was measured as reduction in hospitalization rates, and the time horizon of the model was the episode. Probabilities were obtained from clinical trials and systematic reviews, measurement of resources use was based on protocols and expert opinions, while unit costs were obtained from Colombian tariff manuals. We performed a survey to estimate indirect costs for caregivers (n=81) that included questions about wage loss, transportation, meals expenditures and other out-of-pocket payments. Deterministic and probabilistic sensitivity analyses were performed. Results Usual treatment plus ondansetron is a dominant strategy compared to usual treatment without antiemetic yielding fewer hospitalizations and saving $44.562 Colombian pesos (23,98USD) per episode. Ondansetron was dominant in 98,91% of simulations of the probabilistic analysis. Conclusions Ondansetron is a dominant intervention that reduces hospitalization rates and costs for health system and caregivers. We recommend assessing the inclusion of this drug in the Colombian Health Benefit Plan for the treatment of gastroenteritis in children under 5 years.

Objectives To determine the cost-effectiveness ratio of different courses of action for the diagnosis of Duchenne or Becker muscular dystrophy in Colombia. Methods The cost-effectiveness analysis was performed from the Colombian health system perspective. Decision trees were constructed, and different courses of action were compared considering the following tests: immunohistochemistry (IHC), Western blot (WB), multiplex polymerase chain reaction, multiplex ligation-dependent probe amplification (MLPA), and the complete sequencing of the dystrophin gene. The time horizon matched the duration of sample extraction and analysis. Transition probabilities were obtained from a systematic review. Costs were constructed with a type-case methodology using the consensus of experts and the valuation of resources from consulting laboratories and the 2001 Social Security Institute cost manual. Deterministic sensitivity and scenario analyses were performed with one or more unavailable alternatives. Costs were converted from Colombian pesos to US dollars using the 2014 exchange rate. Results In the base case, WB was the dominant strategy, with a cost of US $419.07 and a sensitivity of 100%. This approach remains the dominant strategy down to a 98.2% sensitivity and while costs do not exceed US $837.38. If WB was not available, IHC had the best cost-effectiveness ratio, followed by MLPA and sequencing. Conclusions WB is a cost-effective alternative for the diagnosis of patients suspected of having Duchenne or Becker muscular dystrophy in the Colombian health system. The IHC test is rated as the second-best detection method. If these tests are not available, MLPA followed by sequencing would be the most cost-effective alternative.

Natural deduction is a sound and complete proof procedure for propositional logic, that is, it only proves valid formulas and it proves every valid formula. In this work we establish the theory of propositional logic, and we prove the soundness and completeness theorems for natural deduction in propositional logic, following the Melving Fitting’s book First-Order Logic and Automated Theorem Proving. We also present a formalization of this theory in Isabelle/HOL. The formalization covers the sintax and semantic of propositional logic, the model existence theorem, and a natural deduction proof calculus together with a proof of soundness and completeness. For this purpose, we introduce Isabelle/HOL system in this work and the main concepts that we use in the above formalization. Universidad de Sevilla. Máster Universitario en Matemáticas

Background The use of a prophylactic antibiotic in an amputation surgery is a key element for the successful recovery of the patient. We aim to determine, from the perspective of the Colombian health system, the cost-effectiveness of administering a prophylactic antibiotic among patients undergoing lower limb amputation due to diabetes or vascular illness in Colombia. Methods A decision tree was constructed to compare the use and nonuse of a prophylactic antibiotic. The probabilities of transition were obtained from studies identified from a systematic review of the clinical literature. The chosen health outcome was reduction in mortality due to prevention of infection. The costs were measured by expert consensus using the standard case methodology, and the resource valuation was carried out using national-level pricing manuals. Deterministic sensitivity, scenarios, and probabilistic analyses were conducted. Results In the base case, the use of a prophylactic antibiotic compared with nonuse was a dominant strategy. This result was consistent when considering different types of medications and when modifying most of the variables in the model. The use of a prophylactic antibiotic ceases to be dominant when the probability of infection is greater than 48%. Conclusions The administration of a prophylactic antibiotic was a dominant strategy, which is a conclusion that holds in most cases examined; therefore, it is unlikely that the uncertainty around the estimation of costs and benefits change the results. We recommend creating policies oriented toward promoting the use of a prophylactic antibiotic during amputation surgery in Colombia. © 2016 Elsevier Inc.

Objectivos: Estimar la razón costo efectividad de la medición de la actividad enzimática de la galactosamina 6 sulfato sulfatasa (GALNS) en leucocitos en comparación con no hacer la medición de la actividad enzimática para la confirmación diagnóstica de la MPS IVA desde la perspectiva del pagador en Colombia Metodologías: Estudio de análisis costo efectividad en el que se empleó como modelo un árbol de decisión. El desenlace fue los casos diagnosticados correctamente con MPS tipo IVA. Se incluyó los costos de la cuantificación enzimática de GALNS en leucocitos, consulta con genetista, consulta con especialidades médicas y costos de procedimientos diagnósticos. El horizonte temporal fue inferior a un año. Se realizó análisis de sensibilidad probabilístico (ASP). Resultados: El costo incremental fue de -($99.165.014) pesos colombianos con una efectividad incremental de 20 casos. El ASP confirma los resultados de los datos basales, en que la cuantificación de la actividad enzimática GALNS fue menos costosa y más efectiva que el comparador. Conclusiones: La cuantificación de la actividad enzimática GALNS es una tecnología dominante para la confirmación diagnóstica de MPS IVA comparado con no hacer la cuantificación de la actividad enzimática desde la perspectiva del pagador en Colombia Objectives: to develop a cost-effectiveness analysis of one-piece drainable pouch (OPDP) versus two-piece drainable pouch (TPDP) for colostomates under the perspective of patient’s out-of-pocket expenses in Rio de Janeiro, Brazil. Methods: data was collected from the prescriptions used for the colostomy pouch change and based on the best practices for the care and prevention of injuries in peristomal skin, according to the domiciliary visits from a stomotherapy service during the year 2014. Materials for the periestomal skin care and wound/dermatitis prevention were considered (US$ currency rate = R$3,20). Results: the drainable pouch represented 36.3%(US$285.0) of the costs per patient/month for the OPDP and 54.3% (US$212.5) for the TPDP. However, costs related to the inputs needed for each pouch change (eg. adhesive removers, skin protective) represent 63.7% for the OPDP and 45.7% for the TPDP. Total costs with the OPDP was US$784.42 and US$391.06 for the TPDP drainable pouch, showing a cost-saving profile if the TPDP was chosen as the standard care (incremental –US$393.37). Conclusions: based on the patient’s outcomes, the best practices regarding the periostomal skincare, the patient’s preferences and costs, the adoption of the two-piece drainable pouch for colostomates shows to be cost-effective when compared to the one-piece drainable pouch. Further studies regarding the colostomate’s quality of life are needed

Acute coronary syndrome is one of the most frequent medical emergencies in developing countries.To determine, from the perspective of the Colombian health system, the cost-effectiveness of ticagrelor compared to clopidogrel for the treatment of patients with acute coronary syndrome.We conducted a cost-effectiveness analysis from the perspective of the Colombian health system comparing ticagrelor and clopidogrel for the treatment of patients with acute coronary syndrome. To estimate the expected costs and outcomes, a Markov model was constructed in which patients could remain stable without experiencing new cardiovascular events, suffer from a new event, or die. For the baseline case, a 10-year time horizon and a discount ratio of 3% for costs and benefits were adopted. The transition probabilities were extracted from the PLATO (Platelet Inhibition and Patient Outcomes) clinical trial. Vital statistics were drawn from the Departmento Administrativo Nacional de Estadística (DANE) and additional information from Colombian patients included in the Access registry. To identify and measure resource use, a standard case was built by consulting guidelines and protocols. Unit costs were obtained from Colombian rate lists. A probabilistic sensitivity analysis was conducted in which costs were represented by a triangular distribution, and the effectiveness through a beta distribution.In the base case, the additional cost per quality-adjusted life-year gained with ticagrelor was COP$ 28,411,503. The results were sensitive to changes in the time horizon and the unit cost of clopidogrel. For a willingness-to-pay equivalent to three times the Colombian per capita gross domestic product, the probability of ticagrelor being cost-effective was 75%.Ticagrelor is a cost-effective strategy for the treatment of patients with acute coronary syndrome in Colombia.

Economic evaluation is a tool that can provide useful information to decision-makers in health. The methodological quality of Colombian studies has not been assessed in a systematic way.To assess the methodological quality of economic evaluations in health care in Colombia.Systematic review of economic studies that assessed both costs and effectiveness of at least two technologies related to a decision problem in Colombia. Search was performed in international and Colombian databases and was completed with manual searches and contact with authors. Data was synthesized in tables that included relevant information about the studies. Methodological quality was evaluated using a predefined instrument. Searches were performed between January and February.48 studies were included in the review. Perspective of the study, incremental analyzes and description of alternatives were usually well specified. However, more than half of the articles did not state clearly the time horizon or discount rate and most studies did not address equity and implementation issues. Management of uncertainty was also problematic.Economic evaluation in health care in Colombia has grown considerably in recent years. However, methods vary considerably between studies and therefore their usefulness for decisionmaking in health is limited. It is necessary to standardize methods in order to generate evidence of higher quality to support decisions within the Colombian health care system.