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

García-Mora, Belén; Santamaría, C.; Rubio, Gregorio; Pontones, J.L.

doi:10.1016/j.cam.2015.03.045

Cited by 4 publications

(2 citation statements)

References 13 publications

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“…Distributions of waiting times in each transition are modelled by means of a PHD made of a mixture of Erlang distributions [13]. The procedure is described in [14] and [15]. Then we make up the convolution of PHDs corresponding to the transitions 0 → 1 and 1 → 2, using Theorem 1.…”

Section: The First Approachmentioning

confidence: 99%

Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

García-Mora

Santamaría

Rubio

2018

Journal of Computational and Applied Mathematics

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The most common assumptions in reliability studies are that failures occur independently and with the same distribution. However, these two assumptions are unrealistic in practice since inter-failure times are usually correlated and not identically distributed. In this sense the Markov Arrival Process (MAP) is an active research field for managing these features. We study two versions of the MAP approach. The first one is a model which we developed in previous works. The second one is based on a non-stationary MAP of second order. We compare the results of both models with simulated data.

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Section: The First Approachmentioning

confidence: 99%

Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

García-Mora

Santamaría

Rubio

2018

Journal of Computational and Applied Mathematics

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“…Chen-Charpentier et al [7], one performs a dynamical analysis to a model of bone remodeling based of a system of differential equations involving delay that describes bone tissue regeneration taking into account key aspects such as periodicity and retard to the process. This block of papers devoted to the application of mathematics to modeling medicine's problems ends with the paper by B. García-Mora et al [8]. This contribution gives a Bayesian-based approach for including covariates within the framework of flowgraph models.…”

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confidence: 97%

Mathematical modeling and computational methods

Torregrosa

Jódar

López

et al. 2016

Journal of Computational and Applied Mathematics

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Markovian modeling for dependent interrecurrence times in bladder cancer

García-Mora

Santamaría

Rubio

2020

Math Methods in App Sciences

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A methodology to model a process in which repeated events occur is presented. The context is the evolution of non‐muscle‐invasive bladder carcinoma (NMIBC), characterized by recurrent relapses. It is based on the statistical flowgraph approach, a technique specifically suited for semi‐Markov processes. A very useful feature of the flowgraph framework is that it naturally incorporates the management of censored data. However, this approach presents two difficulties with the process to be modeled. On one hand, the management of covariates is not straightforward. However, it is of great interest to know how the characteristics of a certain patient influence the evolution of the disease. On the other hand, repeated events on the same subject are generally not independent, in which case the semi‐Markov framework is not sufficient because the semi‐Markov assumption implies independence among waiting time distributions. We solve this issue by extending the flowgraph methodology using the Markovian arrival process (MAP), which does successfully model the dependence between events. Along the way, we provide a procedure to consider covariates and censored times in MAPs, a pending task needed in this field. In short, we have managed to extend the flowgraph methodology beyond the semi‐Markovian framework, simplifying the incorporation of covariates and keeping the management of censored times. All of which has allowed us to build a multistate model of the evolution of NMIBC. The developed model allows us to compute the Survival function for any evolution of a patient with specific clinic‐pathological characteristics in this primary tumor.

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

Cited by 4 publications

References 13 publications

Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

Mathematical modeling and computational methods

Markovian modeling for dependent interrecurrence times in bladder cancer

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