Abstract
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.
Highlights
We have evaluated the use of anti-epileptic drugs in the treatment of refractory epilepsy, that is, we forecast the number of epileptic patients depending on its response to a given treatment
Our approach resorts in the application of the random variable transformation method to compute the first probability density function of the solution stochastic process of the corresponding randomized Markov chain
The randomization has been done in the entries of the deterministic Markov model, considering each probability in the transition matrix an absolutely continuous random variable
Summary
From 2000 B.C., multiple reports of epileptic seizures can be found [1]. epilepsy can be considered one of the most ancient diseases that we have knowledge. We study from a probabilistic point of view the effectiveness of AEDs in epileptic patients This analysis will be done in general for any treatment. The randomized binary Markov chain has been studied recently in [17], where authors analyse classical binary Markov chains by considering the components of the transition matrix and the initial conditions as randomized quantities This theoretical idea has been applied to analyse statistically the stroke disease [12]. Where | J |, which is assumed to be different from zero, denotes the absolute value of the Jacobian defined by the determinant In this contribution, RVT technique is applied to determine the distribution of two important quantities in medicine: the time until a fixed proportion of the population remains in each one of the four stages and the cost-effectiveness ratio.
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