Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis
Epilepsy is one of the most ancient diseases. Despite the efforts of scientists and doctors to improve the quality of live of epileptic patients, the disease is still a mystery in many senses. Anti-epileptic drugs are fundamental to reduce epileptic seizures but it have some adverse effects, which i...
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MDPI AG
2020-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/7/1120 |
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| author | Isabel Barrachina-Martínez Ana Navarro-Quiles Marta Ramos José-Vicente Romero María-Dolores Roselló David Vivas-Consuelo |
| author_facet | Isabel Barrachina-Martínez Ana Navarro-Quiles Marta Ramos José-Vicente Romero María-Dolores Roselló David Vivas-Consuelo |
| author_sort | Isabel Barrachina-Martínez |
| collection | DOAJ |
| description | Epilepsy is one of the most ancient diseases. Despite the efforts of scientists and doctors to improve the quality of live of epileptic patients, the disease is still a mystery in many senses. Anti-epileptic drugs are fundamental to reduce epileptic seizures but it have some adverse effects, which influence the quality of life outcomes of the patients. In this paper, we study the effectiveness of anti-epileptic drugs taking into account the inherent uncertainty. We establish a model, which allows to represent the natural history of epilepsy, using Markov chains. After randomizing the mathematical model, we compute the first probability density function of the solution stochastic process applying the random variable transformation technique. We also take advantage of this method to determine the distribution of some key quantities in medical decision, such as the time until a certain proportion of the population remains in each state and the incremental cost-effectiveness ratio. The study is completed computing all these quantities using data available in the literature. In addition, regarding the incremental cost-effectiveness ratio, different third generation anti-epileptic treatments are compared with the Brivaracetam, a new third generation anti-epileptic drug. |
| first_indexed | 2024-03-10T18:35:32Z |
| format | Article |
| id | doaj.art-5be03f45ec1e4671849e8e8441ea60dc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:35:32Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5be03f45ec1e4671849e8e8441ea60dc2023-11-20T06:15:21ZengMDPI AGMathematics2227-73902020-07-0187112010.3390/math8071120Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness AnalysisIsabel Barrachina-Martínez0Ana Navarro-Quiles1Marta Ramos2José-Vicente Romero3María-Dolores Roselló4David Vivas-Consuelo5Research Centre for Health Economics and Management, INECO, Department of Economics and Social Sciences, Universitat Politècnica de València, Edificio 7J, Camino de Vera s/n, 46022 Valencia, SpainDepartment of Statistics and Operational Research, Universitat de València, Dr. Moliner 50, 46100 Burjassot, SpainResearch Centre for Health Economics and Management, INECO, Department of Economics and Social Sciences, Universitat Politècnica de València, Edificio 7J, Camino de Vera s/n, 46022 Valencia, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Edificio 8G, Camino de Vera s/n, 46022 Valencia, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Edificio 8G, Camino de Vera s/n, 46022 Valencia, SpainResearch Centre for Health Economics and Management, INECO, Department of Economics and Social Sciences, Universitat Politècnica de València, Edificio 7J, Camino de Vera s/n, 46022 Valencia, SpainEpilepsy is one of the most ancient diseases. Despite the efforts of scientists and doctors to improve the quality of live of epileptic patients, the disease is still a mystery in many senses. Anti-epileptic drugs are fundamental to reduce epileptic seizures but it have some adverse effects, which influence the quality of life outcomes of the patients. In this paper, we study the effectiveness of anti-epileptic drugs taking into account the inherent uncertainty. We establish a model, which allows to represent the natural history of epilepsy, using Markov chains. After randomizing the mathematical model, we compute the first probability density function of the solution stochastic process applying the random variable transformation technique. We also take advantage of this method to determine the distribution of some key quantities in medical decision, such as the time until a certain proportion of the population remains in each state and the incremental cost-effectiveness ratio. The study is completed computing all these quantities using data available in the literature. In addition, regarding the incremental cost-effectiveness ratio, different third generation anti-epileptic treatments are compared with the Brivaracetam, a new third generation anti-epileptic drug.https://www.mdpi.com/2227-7390/8/7/1120anti-epileptic drugsuncertainty quantificationfirst probability density functionrandom variable transformation techniqueMarkov model |
| spellingShingle | Isabel Barrachina-Martínez Ana Navarro-Quiles Marta Ramos José-Vicente Romero María-Dolores Roselló David Vivas-Consuelo Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis Mathematics anti-epileptic drugs uncertainty quantification first probability density function random variable transformation technique Markov model |
| title | Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis |
| title_full | Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis |
| title_fullStr | Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis |
| title_full_unstemmed | Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis |
| title_short | Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis |
| title_sort | probabilistic study of the effect of anti epileptic drugs under uncertainty cost effectiveness analysis |
| topic | anti-epileptic drugs uncertainty quantification first probability density function random variable transformation technique Markov model |
| url | https://www.mdpi.com/2227-7390/8/7/1120 |
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