Gregorio Rubio

Modeling the recurrence-progression process in bladder carcinoma

Wei-Lin-Weissfeld (WLW) method is used to analyze different states of the superficial vesical carcinoma distinguishing between recurrences and the possibility of progression. Two approaches are considered in this analysis to represent different aspects of the disease from a clinical point of view: the first one attempts to focus on the effect of the clinico-pathological factors on recurrences by regarding a progression before the recurrence as a censoring event, meanwhile the second one analyzes these same effects on either recurrence or progression, whichever comes first. A predictive model of recurrence or progression based on clinico-pathological factors is presented.

Explicit solution of Black–Scholes option pricing mathematical models with an impulsive payoff function☆

This paper deals with the construction of explicit solutions of the Black-Scholes equation with a weak payoff function. By using the Mellin transform of a class of weak functions a candidate integral formula for the solution is first obtained and then it is proved that it is a rigorous solution of the problem. Well known solutions of option pricing value problems are obtained as particular cases of the solution proposed here.

Modeling bladder cancer using a Markov process with multiple absorbing states

The aim of this study is to analyze survival until extirpation in bladder carcinoma. For this it is necessary to study the different stages of this chronic disease: multiple recurrences and progression. The sum of two random independent variables is considered, each of them being associated with a homogeneous time-continuous Markovian process of multiple absorbing states. The distribution function of the variable sum is modeled by means of a new associated Markov process. In order to maintain manageable problem dimension we have applied the Frechet derivate and the Kronecker matrix representation.

A flowgraph model for bladder carcinoma

BackgroundSuperficial bladder cancer has been the subject of numerous studies for many years, but the evolution of the disease still remains not well understood. After the tumor has been surgically removed, it may reappear at a similar level of malignancy or progress to a higher level. The process may be reasonably modeled by means of a Markov process. However, in order to more completely model the evolution of the disease, this approach is insufficient. The semi-Markov framework allows a more realistic approach, but calculations become frequently intractable. In this context, flowgraph models provide an efficient approach to successfully manage the evolution of superficial bladder carcinoma. Our aim is to test this methodology in this particular case.ResultsWe have built a successful model for a simple but representative case.ConclusionThe flowgraph approach is suitable for modeling of superficial bladder cancer.

Computing survival functions of the sum of two independent Markov processes: an application to bladder carcinoma treatment

The study of the sum of two independent phase-type (PH)-distributed variables, each of them being associated with a Markovian process with one absorbing state, is considered in this paper. The distribution function of the variable sum is computed, obtaining a new PH-distributed function of higher order. As the order increases in the new function, the exponential function of a block upper triangular matrix is calculated in terms of its respective blocks to reduce the dimension of the problem. The obtained results are applied to bladder carcinoma data.

Exact solution of variable coefficient mixed hyperbolic partial differential problems

This paper is concerned with the construction of exact series solution of mixed variable coefficient hyperbolic problems.

Bayesian prediction for flowgraph models with covariates. An application to bladder carcinoma

Statistical Flowgraph Models are an efficient tool to model multi-state stochastic processes. They support both frequentist and Bayesian approaches. Inclusion of covariates is also available. In this paper we propose an easy way to perform a Bayesian approach with covariates. Results are presented with an application to bladder carcinoma data.

A Markov model for analyzing the evolution of bladder carcinoma

A Markovian approach to analyze different states of the superficial vesical carcinoma is considered, taking into account up to two recurrences and the possibility of progression. So, three transient states are considered: free of disease, first, and second recurrence; and an absorbent state, the progression. A methodology based in phase-type distributions is also used, that allows the usual quantities of interest in survival studies to be expressed in a well-structured form. This type of distribution has shown its utility in queue theory, and has the advantage that mathematical expressions can be presented in a closed form that allows algebraic treatment.

Accurate numerical solution of coupled time dependent parabolic initial value problems

This paper deals with the construction of numerical solutions with a prefixed accuracy of initial value problem for coupled time dependent initial value problems using Fourier transform, numerical integration and numerical resolution of differential equations. An algorithm is included.

Computable explicit bounds for the discretization error of variable stepsize multistep methods

Abstract This paper deals with the achievement of explicit computable bounds for the global discretization error of variable stepsize multistep methods which are perturbation of strongly stable fixed stepsize methods. The approach is based on the study of the growth of solutions of certain variable coefficient difference equations satisfied by the global discretization error.